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MULTIPHOTON ABSORPTION IN GRAPHENE

AND METAL-ORGANIC FRAMEWORKS

CHEN WEIQIANG

(B. Sc. Nankai University, CHINA )

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS

NATIONAL UNIVERSITY OF SINGAPORE

2015

THESIS DECLARATION

I hereby declare that this thesis is my original work and it has been

written by me in its entirety, under the supervision of Professor Ji Wei,

Department of Physics, National University of Singapore, between

Jan/2012 and Dec/2015.

I have duly acknowledged all the sources of information which have

been used in the thesis.

This thesis has also not been submitted for any degree in any university

previously.

The content of the thesis has been partly published in:

1). W. Q. Chen, Y. Wang, W. Ji, "Two-Photon Absorption in Graphene

Enhanced by the Excitonic Fano Resonance," J. Phys. Chem. C 119,

16954-16961 (2015).

2). H. S. Quah*, W. Q. Chen*, M. K. Schreyer, H. Yang, M. W. Wong,

W. Ji, J. J. Vittal, "Multiphoton Harvesting Metal-Organic

Frameworks," Nat. Commun. 6 (2015). (* denoting equal

contribution)

Chen Weiqiang

7 December 2015

Acknowledgements

i

ACKNOWLEDGEMENTS

It is my great pleasure to have this opportunity to express my heartfelt

gratitude to the following people and institutions who have offered me valuable

help during my PhD study. I would not have been able to complete the work

presented in this thesis without their assistance, encouragement and support.

My deepest gratitude goes first and foremost to Professor Ji Wei and Assistant

Professor Wang Haifeng, my supervisors, for their intellectual and indispensable

guidance, constructive criticism and long-term encouragement during my PhD

project. With his expertise and wide knowledge, professor Ji Wei helped me to

obtain a deep understanding of the research in nonlinear optics. Under Professor

Wang Haifeng's professional guidance, I learned a lot in the field of nonlinear

optical imaging. Without their invaluable help and support, the thesis could not

have reached its present form.

I would wish to give my sincere appreciations to our collaborator Dr. Wang Yu

from the Institute of Process Engineering, Chinese Academy of Sciences for

providing the precious CVD graphene samples. I also would like to express my

sincere gratitude to our collaborators, Mr. Quah Hong Sheng and Professor

Jagadese J, Vittal from Department of Chemistry for their help in sample

synthesis and fruitful discussions.

I am sincerely grateful to National University of Singapore president graduate

fellowship program for its significant role in supporting this dissertation. Without

Acknowledgements

ii

this important economic support, it would not have been possible for me to

complete my PhD study. My sincere appreciation goes to NUS's idea that "Let all

the talent students focus on their study without worrying about economic

problems".

Besides, I would wish to acknowledge all of my current and past group

members in Femtosecond Laser Spectroscopy lab: Dr. Venkatram Nalla, Dr. Yang

Hongzhi, Dr. Venkatesh Mamidala, Ms. Radhu Subha, Ms. Wang Qian, Mr. Xu

Zhe, Mr. Yu Miao, Mr. Zhou Feng for their cooperation, valuable discussion and

assistance. My sincere thanks go to Dr. Venkatram Nalla for his invaluable

instructions and fruitful discussions.

Furthermore, I would like to give my special appreciation to my friends in

NUS. To Dr. Gao Nengyue, Dr. Sudheer, Dr. Chen Jianqiang, Dr. Pan Yanlin, Dr.

Wang Xingzhu, Mr. Liu Shuanglong, Mr. Chu Leiqiang, Mr. Ma Haijiao, Mr.

Zhang Lingchao, Mr. Wang Dongyang, Mr. Liu Bing, Mr. Zhu Hai, Mr. Shen

Lijion, Mr. Feng Shixiao, Mr. Liu Wei and Mr. Hou Chenguang for their

accompany, support and help.

Finally, I should express my gratitude to my beloved parents who have always

been helping me, supporting me and encouraging me with their everlasting love

and patience throughout my graduate study. In particular, I should also thank my

girl friend Lin Long for her believing, understanding and everlasting support.

Table of Contents

iii

Table of Contents

Acknowledgements……………………………………………………………….i

Table of Contents...……………………………………………………………...iii

Summary……….……………………………………………………………….vii

List of Tables……….………………………………………………………..........x

List of Figures……….…………………………………………………………...xi

List of Publications……….…………………………………………………..xviii

Chapter 1 Introduction……….…………………………………………….........1

1.1 Introduction to nonlinear optics ………………………………………………1

1.2 Nonlinear optical absorption ………………………………….........................3

1.2.1 Multiphoton absorption (MPA)………………………………………....5

1.2.2 One-photon absorption (1PA) saturation………………………………10

1.3 Introduction to graphene……………………………………………………..14

1.4 Introduction to metal-organic frameworks (MOFs)…………………………22

1.5 Objectives and scopes of this dissertation…………………………………...28

1.6 Layout of this dissertation……………………………………………………30

References………………………………………………………………………..32

Chapter 2 Experimental techniques and theoretical analyses……………….46

2.1 Introduction…………………………………………………………………..46

2.2 The femtosecond laser systems………………………………………………47

2.2.1 Coherent Libra ultrafast amplifier system……………………………..49

2.2.2 Light-Conversion TOPAS optical parametric amplifier……………….51

2.2.3 TEM00 Gaussian laser beam……………………………………………53

2.3 Z-scan technique……………………………………………………………..55

2.3.1 Open-aperture Z-scan technique……………………………………….56

2.3.2 Data analyses for two-photon absorption (2PA)……………………….59

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iv

2.3.3 Data analyses for one-photon absorption (1PA) saturation……………62

2.3.4 Data analyses for materials exhibiting both 1PA saturation and 2PA….65

2.4 Transient absorption measurement (or pump-probe technique)……………..68

2.5 Multiphoton excited photoluminescence (MEPL) measurement……………71

2.5.1 MEPL measurement for solution sample………………………………72

2.5.1.1 Experimental setup and related details…………………………72

2.5.1.2 Theoretical data analyses……………………………………….74

2.5.2 MEPL measurement for solid powder sample…………………………75

2.5.2.1 Experimental setup and related details…………………………75

2.5.2.2 Theoretical data analyse...............................................................76

2.6 Transient photoluminescence (PL) characterization technique……………...79

2.6.1 PL lifetime measurement with fast photodiode coupled with

oscilloscope…………………………………………………………...79

2.6.2 Time-correlated single photon counting (TCSPC) technique…………80

References……………………………………………………………………….81

Chapter 3 One-photon absorption of CVD-grown graphene films………….86

3.1 Introduction to CVD-grown graphene films…………………………………86

3.2 Characterization of the CVD-grown graphene films………………………...90

3.2.1 Introduction……………………………………………………………90

3.2.2 Optical microscopic characterization for homogeneity………………..91

3.2.3 Micro-Raman spectroscopic characterization for crystallinity, density of

defect states, layer number and interlayer coupling…………………..92

3.2.4 Optical reflection contrast spectra for characterization of layer

number...................................................................................................97

3.3 1PA of graphene in the UV-VIS-NIR spectral range…………………….......99

3.3.1 Introduction……………………………………………………………99

3.3.2 1PA of graphene enhanced by the excitonic Fano resonance in the

UV-VIS spectral range……………………………………………….100

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v

3.4 Conclusion………………………………………………………………….104

References………………………………………………………………………106

Chapter 4 Two-photon absorption and one-photon absorption saturation of

graphene in the visible spectral range………………………………………..113

4.1 Introduction…………………………………………………………………113

4.2 Open-aperture Z-scan measurements on CVD graphene and the related

theoretical data analyses……………………………………………………118

4.3 2PA spectrum of graphene in the visible range enhanced by the excitonic Fano

resonance…………………………………………………………………...129

4.4 1PA saturation in graphene in the NIR and visible spectral range…………135

4.5 Conclusion…………………………………………………………………142

References……………………………………………………………………...143

Chapter 5 Structural and linear optical properties of metal-organic

frameworks (MOFs) and ligands……………………………………………..148

5.1 Introduction…………………………………………………………………148

5.2 Characterization for the ligands and MOFs………………………………...152

5.3 Linear optical properties of ligands and MOFs…………………………….158

5.4 Conclusion………………………………………………………………….168

References………………………………………………………………………170

Chapter 6 Efficient frequency-upconverted photoluminescence of

metal-organic frameworks (MOFs) excited by simultaneous multiphoton

absorption……………………………………………………………………...174

6.1 Introduction…………………………………………………………………174

6.2 Two-, three-, and four-photon excited PL measurements on MOFs and data

analyses……………………………………………………………………..178

6.2.1 Multiphoton excited frequency-upconverted PL measurements on MOFs

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vi

and ligands in the solid-state form…………………………………...179

6.2.2 Data analyses to determine the multiphoton action cross-sections of the

investigated samples…………………………………………………184

6.3 Results and discussion……………………………………………………...186

6.4 Experimental and theoretical studies on the 2PA properties of the ligand

An2Py in the molecule level………………………………………………..192

6.4.1 Experimental studies on the 2PA properties of the ligand An2Py in the

molecule level………………………………………………………..193

6.4.2 Theoretical investigations on the 2PA properties of the ligand An2Py in

the molecule level……………………………………………………198

(i) Theoretical calculations of the 2PA properties of An2Py molecule in

DMSO utilizing the response theory method………………………200

6.5 Conclusion………………………………………………………………….206

References………………………………………………………………………207

Chapter 7 Conclusions………………………………………………………...214

7.1 Summary of results…………………………………………………………214

7.2 Suggestions for the future research work…………………………………..218

Summary

vii

Summary

Materials possessing large multiphoton absorption are of direct relevance

to both photonics applications and materials physics. In this dissertation, we

present our investigations into two novel materials: namely, (1) graphene and

(2) metal-organic frameworks (MOFs). The dissertation divides into two parts.

The first part of the dissertation reports our systematical Z-scan

measurements onto two-photon absorption (2PA) in graphene in the spectral

range of 435-1100 nm with femtosecond laser pulses. We report that the

measured 2PA coefficients of graphene in the near-infrared (NIR) range of

800-1100 nm can be explained by a theoretical model based on the optical

transitions near the Dirac point (K point). We also determine the 2PA

coefficients of graphene in the visible spectrum (435-700 nm) and observe an

enhancement induced by the excitonic Fano resonance at the saddle point (M

point). By applying the second-order, time-dependent perturbation theory on

interband transitions among three states near the saddle point, we develop a

semi-empirical model to take excitons in graphene into consideration. And the

model is in agreement with the photon-energy dependence of the observed

2PA spectrum with a scaling factor of B = (1~5) × 102 cm/MW/eV

5. Our

results verify, for the first time, that the excitonic Fano resonance plays an

important role for the 2PA of graphene in the visible spectrum. Besides, we

also detail our measurements on the spectral dependence of one-photon

Summary

viii

absorption (1PA) saturation in graphene over the visible-NIR range. A

quadratic photon energy dependence of the measured saturation

intensity/fluence is observed over the investigated spectral range. The

underlying photo-dynamics is discussed.

In the second part of the dissertation, we investigate multiphoton excited

photoluminescence (MEPL) from three solid-state crystals of metal-organic

frameworks (MOFs): (1) [Zn2(trans,trans-4,4 stilbenedicarboxylic acid

(SDC))2(trans, trans-9, 10-bis (4-pyridylethenyl) anthracene (An2Py))] (MOF

1a); (2) [Zn2(trans,trans-4,4 stilbenedicarboxylic acid (SDC))2(trans, trans-9,

10-bis (4-pyridylethenyl) anthracene (An2Py))]∙perylene (MOF 2) and (3)

[Zn2(trans,trans-4,4 stilbenedicarboxylic acid (SDC))2(trans, trans-9, 10-bis

(4-pyridylethenyl) anthracene (An2Py))]∙anthracene (MOF 3). We select the

nonlinear optically active ligand (An2Py) based on well-established guiding

principles in the architecting of chromophores with relatively large nonlinear

optical properties to synthesize MOF 1a. Subsequently, two high quantum

yielding chromophores are encapsulated into the pore spaces of MOF 1a to

obtain MOFs 2 and 3. MEPL measurements show the crucial role of two-,

three- and four-photon absorption in the excited PL from both the ligand and

the MOFs in the solid-state form. Our experimental results reveal that MOF

1a exhibits largely enhanced MEPL compared to that of its ligand. This is

induced by the rigidifying of the chromophore in the MOF framework which

minimizes the aggregation-caused quenching. Further enhancement on the

Summary

ix

MEPL is achieved in MOFs 2 and 3. The Förster resonance energy transfer

(FRET) between the host MOF and the guest molecules leads to such an

enhancement. Our experimental finding provides possible solutions to

aggregation-caused quenching in the MEPL of organic molecules in the

solid-state form and discloses a fresh route for producing photonic materials

and devices in the solid-state form.

List of Tables

x

List of Tables

Table 3.1 Advantages and disadvantages of various graphene synthesis methods.

Table 4.1 Fitting parameters used in the modeling of Z-scans on the 10-layer

graphene sample at selected wavelengths in the range from 1100 to 435 nm as in

Figure 4.3 and their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.4.

Table 4.2 Fitting parameters used in the modeling of Z-scans at 800 nm on 5-,

and superimposed 10-, 15- and 20-layer graphene samples as in Figure 4.5(a) and

their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.6(a).


and superimposed 10-, 15- and 20-layer graphene samples as in Figure 4.5(b) and

their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.6(b).

Table 5.1 Crystal cells data of MOFs 1-3.

Table 5.2 Absolute PL quantum yield measurements.

Table 6.1 Molar concentration calculations of the samples and standard enclosed

in the cuvette used for MEPL measurements.

Table 6.2 2PA coefficients and cross sections at selected wavelengths in the

wavelength range of 560 – 680 nm.

Table 6.3 The excitation energies and oscillator strengths of the first five excited

states of the An2Py molecule in DMSO.

Table 6.4 Calculated 2PA cross-sections of the first five excited states of An2Py

molecule in DMSO.

List of Figures

xi

List of Figures

Figure 1.1 Schematic diagrams of (a) degenerate 2PA and (b) non-degenerate

2PA

Figure 1.2 Schematic diagram of the resonant interaction in the two-level system.

Figure 1.3 Electronic band structure of graphene including both bands and

bands [1.60].

Figure 1.4 Electronic dispersion in the first Brillouin zone of graphene under the

-band approximation and nearest-neighbor approximation. The K point and M

point are pointed out by the arrows.

Figure 2.1 Photograph and schematic layout of the Coherent Libra laser system.

Figure 2.2 Photograph of the Light-Conversion TOPAS optical parametric

amplifier.

Figure 2.3 Sketch of the basic layout of the Coherent Libra ultrafast amplifier

system.

Figure 2.4 (a) Sketch of the basic three stages in the Light-Conversion TOPAS

optical parametric amplifier, SF - superfluorescence; (b) Photos of the layout of

the optical components in our Light-Conversion TOPAS optical parametric

amplifier; (c) Photos of the two external mixers and one wavelength separator

arranged outside the TOPAS box.

Figure 2.5 (a) Schematic illustration of the beam width w(z) of a TEM00 mode

Gaussian laser beam along the propagation direction z. (b) The two-dimensional

intensity profile of a Gaussian beam that is propagating out of the page.

Figure 2.6 Schematic illustration of the open-aperture Z-scan set-up for

measuring nonlinear optical absorption properties.

Figure 2.7 A photograph of our Z-scan setup.

Figure 2.8 Typical open-aperture Z-scan signals for both 1PA saturation (dashed

curve) and 2PA (solid line), respectively.

Figure 2.9 The open-aperture Z-scan signal for 0.5-mm-thick hexagonal CdS

single crystal and the related theoretical fitting.

List of Figures

xii

Figure 2.10 Dependence of the normalized transmittance T (z = 0) on the peak

laser intensity at the focal point I00 for the pure 1PA saturation (blue triangle),

pure 2PA (black square), and concurrence of both 1PA saturation and 2PA (red

circle) [2.29].

Figure 2.11 Schematic diagram of the pump-probe experimental set-up.

Figure 2.12 Photograph of our pump-probe experimental set-up.

Figure 2.13 Frequency-degenerate pump-probe experiment signal of the standard

sample 0.5-mm-thick hexagonal CdS crystal at 800 nm excitation.

Figure 2.14 Schematic illustration of the experimental setup for the MEPL

measurement for solution sample. OPA, WS, and SP are short for optical

parametric amplifier, wavelength separator, and short-pass optical filter,

respectively.


measurement for solid powder sample. OPA, WS, and SP are short for optical


respectively.

Figure 2.16 Schematic illustration of the experimental setup for TCSPC

measurement. OPA, WS, PD and SPAD are short for optical parametric amplifier,

wavelength separator, photodiode and single photon counting avalanched

photodiode, respectively.

Figure 3.1 Larger-scale optical images of mono-, 5-, and superimposed 10-, 15-,

20-layer graphene films on quartz substrate. (a) Monolayer graphene on quartz; (b)

5-layer graphene on quartz; (c) superimposed 10-layer graphene on quartz; (d)

superimposed 15- and 20-layer graphene on quartz.

Figure 3.2 (a), (b) and (c) show the optical microscopic images of the single-, 5-

and 10-layer graphene films on quartz, respectively.

Figure 3.3 Schematic illustration of a typical energy diagram of the Raman

scattering process.

Figure 3.4 Schematic illustration of the experimental setup in a typical Raman

spectrometer

Figure 3.5 (a) shows the micro-Raman spectra of the monolayer (black) and

5-layer (red) graphene films on quartz; and (b) displays the micro-Raman spectra

List of Figures

xiii

of the 5-layer (black), 10-layer (red), 15-layer (blue), and 20-layer (dark cyan)

graphene films on quartz.

Figure 3.6 Optical reflection contrast spectra of the 5- and 10-layer graphene

films on quartz.

Figure 3.7 (a) Comparison between the measured 1PA spectra of CVD-grown

monolayer graphene on quartz substrate and that of micromechanically exfoliated

monolayer graphene on SiO2 substrate in Ref. [3.56]; (b) and (c) theoretical

modeling of Fano resonance based on the ab initio GW calculation and JDOS

method to fit the measured 1PA spectra of the monolayer graphene; and (d) the

1PA spectra of 5- and 10-layer graphene on quartz substrate and the

corresponding theoretical modeling with JDOS method.

Figure 4.1 (a) Schematic open-aperture Z-scan set-up; (b) open-aperture Z-scans

on the 10-layer sample measured at a maximum on-axis irradiance (I00 at z = 0) of

4.0 ± 0.5 GW/cm2. The symbols are the experimental data and the solid curves are

the numerical simulations based on Eq. (4.1). The z position is normalized to z0

which is the Rayleigh range.

Figure 4.2 (a,b) Open-aperture Z-scans on the monolayer graphene sample at 800

and 535 nm, respectively. The symbols are the experimental data at various

values of I00. The green lines are Z-scans on quartz substrate at I00 = 20 GW/cm2.

Figure 4.3 Z-scans on the 10-layer graphene sample at selected wavelengths

in the range (a) from 1100 to 640 nm and (b) from 575 to 435 nm. The

symbols are the experimental data at various values of I00. The solid curves are

the theoretical fits based on Eq. (4.1). The green lines are Z-scans on quartz

substrate at I00 = 20 GW/cm2.

Figure 4.4 Plots of ΔT/T0 vs. I00 at z = 0. The symbols are the experimental data

at various values of I00. The solid and dashed curves are the modeling with 𝛽 ≠ 0

and = 0, respectively.

Figure 4.5 Open-aperture Z-scan measurements on the 5- and superimposed

10-, 15- and 20-layer CVD-grown graphene films on the quartz substrate at

800 and 535 nm. The symbols are the experimental Z-scan data at various values

of I00. The solid curves are the theoretical fits based on Eq. (4.1). The green lines

are Z-scans on quartz substrate at I00 = 20 GW/cm2.

Figure 4.6 Plots of ΔT/T0 (at z = 0) vs. I00 corresponding to the Z-scan

measurements in Figure 4.5. The symbols are the experimental data at various

values of I00. The solid and dashed curves are the modeling with and without the

term of two-photon absorption, respectively.

List of Figures

xiv

Figure 4.7 (a) βmono spectrum of graphene. The symbols ( ) are the

experimental data. The solid curves are theoretical modeling: (i) the blue curve

( ) is expressed by Eq. (4) in Ref. [4.16]; and (ii) the cyan curve ( ) and

red curve ( ) are given by Eq. (4.4) and Eq. (4.6), respectively. (b) Modeling

by using Eq. (4.6) with = 0, 0.5 and 5 eV.

Figure 4.8 βmono values measured at 800 nm and 535 nm as a function of layer

number. The black symbols are the obtained βmono values at 800 nm and 535 nm,

and the solid red lines are guidelines.

Figure 4.9 Quadratic photon energy dependence of the obtained 1PA saturation

intensities in the spectral range from 1.1 to 2.9 eV. The black symbols are

experimental data and the solid curve is quadratic fit.

Figure 4.10 (a) Measured saturation fluence (symbols) as a function of photon

energy and (b) comparison with theoretical modeling. The solid line ( ) is a fit

with a slope of 2. The symbols ( ) are our measurements in this study, and

other symbols are the data from previous reports by various groups [4.3, 4.5,

4.12-4.17].

Figure 4.11 Degenerate pump-and-probe measurements on the 10-layer

graphene film at 800 nm. The symbols are the experimental data and the solid

curves are the biexponential fits.

Figure 4.12 Degenerate pump-and-probe measurements on CdS at 800 nm.

The symbols are the experimental data and the solid curves are the biexponential

fits.

Figure 4.13 Is values measured at 800 nm and 535 nm as a function of layer

number. (a) and (b) display the layer number dependence of the obtained 1PA

saturation intensities Is at 800 nm and 535 nm (black symbols), the solid curves

are the theoretical modeling based on the analysis method given in Ref. [4.15].

Figure 5.1 (a) Optimized molecular structure of the organic ligand An2Py in the

ground state and (b) Optimized molecular structure of the organic ligand H2SDC

in the ground state.

Figure 5.2 The theoretically calculated Frontier Molecular Orbitals of An2Py

molecule.

Figure 5.3 Crystal structure packing. (a-c) A view of a portion of MOFs 1, 2

and 3. (d-f) Pcu packing of MOFs 1, 2 and 3. (g-i) Packing of MOFs 1, 2 and

3.(j-l) Simplified toplogical net of MOFs 1-3 showing 4-fold interpenetrating pcu

nets.

List of Figures

xv

Figure 5.4 X-ray powder patterns of MOF 1 and MOF 1a, and structure

solution by total pattern and analysis solution. (TOP) Structure solution of the

desolvated compound MOF 1a by rietveld refinements. Despite efforts to fully

remove the solvent molecule, the reabsorption of moisture from the atmosphere

led to the sample retaining 7.77% of the uncompressed phase. (Bottom) The

pictorial representation of the framework compression of MOF 1 to MOF 1a due

to desolvation.

Figure 5.5 Simulated and bulk PXRD patterns of MOF 2.


Figure 5.7 (a), (b) and (c) Photos of compact well powdered single crystals of

MOFs 1a, 2 and 3 packed in a 1-mm-thick quartz cuvette, respectively.

Figure 5.8 Solution UV-VIS absorption spectra of organic compounds used.

Figure 5.9 Solution linear photoluminescence spectra of organic compounds

used.

Figure 5.10 Comparison of the linear PL spectra of MOF 1a with those of two

ligands An2Py and H2SDC in solutions, revealing that the PL of MOF 1a mainly

originates from one of its ligands, An2Py. The linear PL spectra of An2Py in

solid-state was found to be slightly blue-shifted (~ 10 nm) from that of An2Py in

solution, which is believed to be caused by the packing effect (‘crystal property’)

in the solid-state An2Py.

Figure 5.11 Comparison of the UV-VIS absorption spectra of the main ligand

An2Py in chloroform and the linear PL spectra of the co-ligand H2SDC in

chloroform, showing the partial spectral overlap.

Figure 5.12 Comparison of the linear PL spectra of the three MOFs 1a-3, which

are similar to each other. And it indicates that the emission of the guest molecules

perylene and anthracene in MOFs 2 and 3 seem to be quenched upon excitation.

Figure 5.13 Comparison of the one-photon excitation spectra of the MOFs 1a-3

and An2Py in solid-sate, which are collected at their peak PL emission

wavelength. It reveals that the one-photon excitation spectra of the MOFs 1a-3

are similar to each other, and are similar to that of the main ligand An2Py in

solid-state.

Figure 5.14 Comparison between the UV-VIS one-photon absorption spectra of

the ligand An2Py in chloroform solution and the one-photon excitation spectra of

An2Py in solid-state acquired at its peak PL emission wavelength.

List of Figures

xvi

Figure 5.15 Emission spectra of the guests and MOFs 2, 3 together with the

excitation spectra of parent MOF 1a showing the occurrence of FRET. (a)

The emission spectrum of the perylene dye coincides with the excitation region of

the parent MOF 1a leading to an emission at 570 nm. The emission of perylene is

not observed in MOF 2. (b) The emission spectrum of the anthracene dye

coincides with the excitation region of the parent MOF 1a leading to an emission

at 560 nm. The emission of anthracene is not observed in MOF 3.

Figure 6.1 Spectra of the excitation laser source at various wavelengths (a)

Incident laser spectra at wavelengths of 800, 850, 900, 950, 1000, 1070, and 1100

nm, and (b) third-harmonic generation (THG) spectral profiles of the excitation

laser beams (with higher intensities) passing through a 1-mm-thick quartz plate at

wavelengths of 1150, 1200, 1250, 1300, 1350, 1400, 1450, and 1500 nm.

Figure 6.2 Multi-photon excited photoluminescence images of the MOFs 1a-3

and ligands in the solid-state form (well ground powder) at 800, 1200, and 1500

nm femtosecond pulsed laser excitation.

Figure 6.3 Photoluminescence spectra of the three MOFs in the solid-state

form (well ground powder) with femtosecond pulsed laser excitation. The

inset shows the dependence on laser intensity. (a) Two-photon excited emission

at 800 nm of MOFs 1a-3. (b) Three-photon excited emission at 1200 nm of

MOFs 1a-3. (c) Four-photon excited emission at 1500 nm of MOFs 1a-3.

Definition of peak excitation laser intensity on the sample surface I0(d) is as Eq.

(2.47) in the Chapter 2.

Figure 6.4 Excitation intensity dependence of MEPL peak intensity for the MOFs

and ligands An2Py, H2SDC at excitation wavelengths of 800, 1200 and 1500 nm.

As a calibration, excitation intensity dependence of perylene was measured at 800

nm. Definition of peak excitation laser intensity on the sample surface I0(d) is as

Eq. (2.47) in the Chapter 2.

Figure 6.5 Comparison of one-photon-excited and multiphoton-excite PL spectra

of MOFs 1a, 2 and 3.

Figure 6.6 Slopes n plotted as a function of laser excitation wavelength, where n

is defined by the excitation intensity dependence of the MEPL signals of MOFs

1a, 2 and 3 and ligand An2Py that is proportional to (excitation intensity)n.

Figure 6.7 Two-photon action cross-sections of An2Py, MOFs 1a, 2, 3.

Figure 6.8 Three-photon action cross-sections of An2Py, MOFs 1a, 2, 3.

Figure 6.9 Four-photon action cross-sections of An2Py, MOFs 1a, 2, 3.

List of Figures

xvii

Figure 6.10 (a) and (b) Schematic illustrations of the FRET processes in MOFs 2

and 3, respectively.

Figure 6.11 Time resolved PL measurements. PL decay curves of the MOF 3

(green line) and its guest anthracene (black line), the red curves are the fitting

with mono-exponential decays of 1.67 ns and 3.96 ns, respectively. This result

indicates the FRET efficiency in MOF 3 is E = 1- compound 3/Anthracene = 1-

1.67/3.96 ≈ 58%.

Figure 6.12 (a) Schematic illustration of the open-aperture Z-scan set-up, photos

of the An2Py solution and pure DMSO solvent contained in a 1-mm-thick cuvette

are also shown, the left is the An2Py solution, and the right is the pure DMSO

solvent; (b) open-aperture Z-scans on the An2Py solution measured at a

maximum on-axis irradiance (I00 at z = 0) of 250 ± 30 GW/cm2. The symbols are

the experimental data and the solid curves are the theoretical fit based on Eq.

(2.16).

Figure 6.13 (a) Two-photon excited PL signals of the An2Py and the Rhodamine

6G solutions excited at 800 nm with peak laser irradiance of 200 ± 25 GW/cm2;

Inset: photograph of the 2PA excited PL measurement on An2Py solution

contained in a 1-cm-thick cuvette; (b) Intensity dependence of acquired 2PA

excited PL signals of An2Py solution at 800nm in log-log scale.

Figure 6.14 The measured 2 spectrum of the An2Py solution.

Figure 6.15 The comparison between the experimental and theoretical 1PA

spectra of An2Py in DMSO. The 1PA of An2Py in DMSO is almost the same as

that in chloroform. Gaussian broadening with half-width of 0.4 eV is considered

for the theoretical results.

Figure 6.16 The comparison between the experimentally measured 2 spectrum

of the An2Py solution and the theoretical calculated one utilizing the response

theory.

List of Publications

xviii

List of Publications

International Journals:

1). W. Q. Chen, Y. Wang, W. Ji, "Two-Photon Absorption in Graphene Enhanced

by the Excitonic Fano Resonance," J. Phys. Chem. C 119, 16954-16961

(2015).

2). H. S. Quah*, W. Q. Chen*, M. K. Schreyer, H. Yang, M. W. Wong, W. Ji, J. J.

Vittal, "Multiphoton Harvesting Metal-Organic Frameworks," Nat. Commun.

6 (2015). (* denoting equal contribution)

Conference Presentations:

1). W. Q. Chen, Y. Wang, V. Nalla, Z. Xu, W. Ji, "One-Photon Absorption

Saturation Vs Two-Photon Absorption," 7th International Conference on

Materials for Advanced Technologies (ICMAT), ICMAT13-A-3047 (L-PO2-5)

SUNTEC, Singapore, (2013).

2). W. Q. Chen, Y. Wang, W. Ji, "Absorption Saturation and Two-Photon

Absorption in Graphene," MRS Proceedings, 1698, mrss14-1698-jj02-04,

MRS Spring Meeting (2014).

3). W. Q. Chen, F. Zhou, W. Ji, "Multiphoton Absorption Spectroscopy of

Two-Dimensional Materials," Proceedings of the 11th Australian Conference

on Vibrational Spectroscopy (ACOVS11) and the 5th Asian Spectroscopy

Conference (ASC5), pp. 81, (2015).

Chapter 1 Introduction

1


1.1 Introduction to nonlinear optics

Even though Pockels and Kerr electrooptic effects [1.1] and light-induced

resonant absorption saturation [1.2, 1.3] were known about one hundred years ago,

the systematic investigations of nonlinear optics began after the invention of laser

by Maiman in 1960. Laser beam with sufficient intensity makes the experimental

demonstration of plenty of nonlinear optical phenomena possible. The

experimental discovery of second-harmonic generation (SHG) from a quartz

crystal by Franken et al utilizing ruby-laser radiation in 1961[1.4] is considered as

the start of nonlinear optics in laser era. Following this pioneering work, a vast

catalog of nonlinear optical effects including sum- and differential-frequency

generation, four-wave mixing, stimulated Raman scattering, self-focusing,

nonlinear optical absorption and so on have been experimentally achieved [1.1,

1.5-1.7].

Contrary to conventional (or linear) optics where the optical properties of

materials are independent of the intensity of light, in the nonlinear optics regime

with intense laser beam applied, the optical properties of materials can be

modified and become functions of the light intensity [1.1, 1.5, 1.6]. As a result,

the response of materials to the applied optical field behaves in a nonlinear

manner. The typical example is the SHG where the intensity of generated light


2

with double frequency scales as the square of the intensity of the excitation laser

beam [1.1].

Both linear optics and nonlinear optics are based on the Maxwell’s equations

which govern the propagation of light through optical media [1.5, 1.6].

(1.1)

(1.2)

(1.3)

0 (1.4)

BE

t

DH J

t

D

B

Through assuming that there are no extraneous free charges and no free currents,

we have: 𝜌 = 0 and 𝐽 = 0. Also consider the material as nonmagnetic, then

�⃗⃗� = 𝜇0�⃗⃗⃗�. In Maxwell’s equations, the displacement filed �⃗⃗⃗� and electric field �⃗⃗�

are related by the polarization vector �⃗⃗�(𝑡) as follows:

0( ) ( ) ( ) (1.5)D t E t P t

From Eqs. (1.1-1.5), the wave equation can be derived as follows [1.5, 1.6]:

2 2

2 2 2 2

0

1 1(1.6)

PE E

c t c t

The fundamental parameter of the light-matter interaction theory is the electronic

polarization of the material �⃗⃗�(𝑡), which is induced by the applied light. In linear

optics, the induced polarization is linearly dependent on the electric field of the

applied light [1.1, 1.5, 1.6]:

(1)

0( ) ( ) (1.7)P t E t


3

where (1) is the linear susceptibility and is a second-rank tensor. On the other

hand, in the regime of nonlinear optics at presence of intense laser light, Eq. (1.7)

should be generalized and the induced polarization is expressed as follows [1.1,

1.5, 1.6]:

(1) (2) (3)

0( ) ( ) ( ) ( ) ( ) ( ) ( ) (1.8)P t E t E t E t E t E t E t

where (2) is the second-order nonlinear optical susceptibility and is a third-rank

tensor; (3) is the third-order nonlinear optical susceptibility and is a fourth-rank

tensor; and so on. Especially, in the centrosymmetric media, all the even-order

nonlinear optical susceptibilities vanish, i.e. (2) = (4) = (6) = ∙∙∙ = 0 [1.1]. In this

dissertation, we explore two-, three-, and four-photon absorption in novel

materials. In particular, we study the magnitude of multiphoton absorption which

is defined by a quantity called the multiphoton absorption coefficient. These

multiphoton absorption coefficients are related to the imaginary part of (3) , (5)

and (7), respectively, as[1.6]:

(3)Im ( ; , , ) (1.9)

(5)Im ( ; , , , , ) (1.10)

(7)

4 Im ( ; , , , , , , ) (1.11)

1.2 Nonlinear optical absorption

The response of a material to light may be divided into three categories,

namely, (1) absorption; (2) refraction; and (3) emission. Here, we focus on

material’s absorption. Nonlinear optical absorption refers to the change of


4

materials’ transmittance as a function of light intensity, and is related to the

imaginary part of the nonlinear optical susceptibility defined in Eqs. (1.9-1.11)

[1.6]. Nonlinear optical absorption belongs to the nonparametric nonlinear optical

processes, which involve the electron population transfer from one real energy

state to another. Other nonparametric nonlinear optical processes include

stimulated Raman scattering and Raman amplification. In contrast, the initial and

final electronic states of the system are the same in the parametric nonlinear

optical processes. The typical parametric nonlinear optical processes include:

optical parametric amplification, harmonic generation, and four-wave mixing.

Nonlinear optical absorption include multiphoton absorption (MPA),

one-photon absorption (1PA) saturation, excited state absorption, and free-carrier

absorption [1.6]. In 1931, two-photon absorption (2PA) was theoretically

predicted by Goeppert-Mayer by utilizing the second-order quantum perturbation

theory [1.8]. One year after the laser was invented (1961), 2PA induced

upconversion photoluminescence was firstly demonstrated by Kaiser and Garrett

[1.9]. Since then, accompanying the rapid development of lasers with high

intensity, not only 2PA has been experimentally demonstrated in a wide variety of

materials, MPA (n >2) has also been observed in many material systems.

Moreover, other nonlinear optical absorption processes like 1PA saturation,

excited state absorption, free-carrier absorption have been widely investigated

[1.6]. In the following, we will focus our demonstration and discussion on the


5

MPA and 1PA saturation as they will be involved in the research presented in this

dissertation.

1.2.1 Multiphoton absorption (MPA)

In the MPA process, n (n 2) photons of identical or different energies are

simultaneously absorbed by the material system to excite an electron transition

from the ground state to a higher-lying excited state. 2PA is a typical MPA

process, which corresponds to the imaginary part of third-order nonlinear optical

susceptibility. Here, we take 2PA as an example to illustrate the MPA process.

If n photons from the same optical filed oscillating at the same frequency

are absorbed by the material, such MPA process is referred as degenerate MPA

[1.6]. Figure 1.1(a) illustrates the schematic diagram of degenerate 2PA.

Otherwise, the MPA process is referred as nondegenerate MPA. Figure 1.1 (b)

shows schematic diagram of nondegenerate 2PA. In both Figures, two photons are

simultaneously absorbed by the material via the intermediate (or virtual) states.

Figure 1.1 Schematic diagrams of (a) degenerate 2PA and (b) non-degenerate

2PA

ħ2

ħ1

Excited State

Ground State

Virtual State

(b) (a)

ħ

ħ

Excited State

Ground State

Virtual State


6

According to the quantum mechanical theory [1.6, 1.10], photon has odd

intrinsic parity and brings one unit of angular momentum with angular

momentum of +1 or -1. As a result, the selection rule for 2PA is different from

1PA. And such difference mainly results from the requirement of the conservation

of angular momentum: 1PA requires the angular momentum of the electron to be

changed by +1 or -1, while the angular momentum of the electron is needed to be

changed by +2, 0, or -2 for 2PA.

In MPA, the absorption coefficient is defined as = nIn-1, where n is

n-photon absorption coefficient and I is the light intensity. Usually, such an

absorption coefficient is several orders of magnitude smaller than the linear

absorption coefficient 0. MPA coefficient n can be directly related to the

imaginary part of nonlinear optical susceptibility (2n-1). n is a macroscopic

parameter to characterize the MPA properties of the material. On the other hand,

there is also a microscopic parameter to describe the individual molecule’s MPA

properties, which is called the MPA cross-section n. For degenerate MPA, the

relation between n and n can be expressed as:

1

(1.12)

n

n

nN

where ħ is the photon energy and N is the number density of molecules in the

system. As for degenerate 2PA, we have:

2 (1.13)N


7

In principles, n of materials can be theoretically calculated through utilizing

nth-order time-dependent quantum perturbation theory [1.8, 1.11-1.13], which is a

microscopic approach and was firstly proposed and developed by

Goeppert-Mayer [1.8]. Applying this theoretical framework, the probability of a

direct electronic transition from initial ground state |i > to final excited state |f >

excited by degenerate simultaneous n-photon absorption can be expressed as

[1.11]:

32

3

2( ) ( ) (1.14)

(2 )n if f i

d kW M E k E k n

where:

1.15[ ( 1) ] ( 2 ) ( )

f m m l u v v i

if

m l u v m l u v v i

H H H HM

E E n E E E E

（）

|i > and |f > are the electronic wavefunctions of the initial ground state and the

final excited state, respectively, whose eigen-energies are Ei and Ef ; and |m >,

|l >, ∙∙∙,|u >, |v >, correspond to the all-possible intermediate states with

eigen-energies of Em, El, ∙∙∙ Eu, Ev; the summations extend over all possible

intermediate states and the delta function corresponds to energy-conversion

requirements; H is the interaction Hamiltonian and can be written as: 𝐻 =

(𝑒/𝑚𝑐)𝐴 ∙ �⃗⃗� ; 𝐴 is the vector potential of the excitation light, �⃗⃗� is the

momentum operator of the electron. The electron-photon interaction term in Eq.

(1.15) is :

, (1.16)m l m l m l

eV H A P

mc


8

The obtained multiphoton transition probability Wn can be related to the MPA

coefficient by the following equation:

2 / 1.17n

n nW n I （）

For example, two-photon transition probability and its relation to the 2PA

coefficient is demonstrated as follows:

23

2 3

2( ) ( ) 2 (1.18)

( ) (2 )

f m m i

f i

m m i

H H d kW E k E k

E E

2

24 / (1.19)W I

These equations are the most fundamental expressions of MPA coefficients

and could be applied to any material system. However, it is a big challenge to

obtain the exact solution, since it is difficult to perform the summations over all

possible intermediate states. Consequently, various attempts have been carried out

to simplify the expressions of MPA coefficients or to convert the states’

summation to other types of calculations which do not require the information

about all the other excited states (intermediate states).

For example, by taking a two-band model consisting of a conduction band and

a valence band of opposite curvature and considering both bands as parabolic and

doubly degenerate, a simplified semi-empirical expression was obtained for the

degenerate 2PA coefficients of direct-bandgap semiconductors [1.14]:

3/2

52 3

0

2 / 1( ) (1.20)

2 /

p g

g g

E EK

n E E


9

where Eg is the direct bandgap of the semiconductor; n0 is linear refractive index;

and 𝐸𝑝 = 2|𝑝𝑣𝑐⃗⃗ ⃗⃗ ⃗⃗ |2/𝑚0, Ep ≈ 21eV for most direct gap semiconductors; K is a

material independent constant and 𝐾 = 29𝑒4/(5√𝑚0𝑐2), K = 1940 in units such

that is in cm/GW and Eg and Ep are in eV. Note that constant K is an

experimentally determined scaling parameter, for example the best fit of Eq. (1.20)

to the data in [1.15] yielded K = 3100 in the same units as above. This is because

the simplified expression cannot provide very accurate values for all the

semiconductors as it only considers the transitions between the two bands.

Another example is that for organic molecules in solution, few-states models

considering only transitions between these selected few states are used to

approximately calculate their degenerate 2PA and 3PA cross-sections [1.16, 1.17].

Moreover, response theory method has also been applied to accurately determine

the degenerate MPA coefficients of organic molecules [1.18, 1.19], since it takes

all the states into account. The advantage of this method is it effectively converts

the summation calculations to solving a system of equations, which does not need

the information about all the excited states.

Several experimental techniques can be applied to characterize MPA

coefficients of materials, which include open-aperture Z-scan, nonlinear

transmission, and multiphoton excited photoluminescence. Since MPA is a third-

or higher-order nonlinear optical process which can only be observed under high

intensity excitation, short pulsed lasers are usually utilized. The intensity of the


10

excitation beam as a function of the propagation depth z in the MPA material is

governed by the below differential equation [1.6]:

( ) 1.21n

dII I

dz （）

MPA is an intriguing property of material and can be applied to a variety of

practical applications such as: optical limiting, three-dimensional optical data

storage, three-dimensional microfabrication, photodynamic therapy and

high-contrast biological imaging [1.1, 1.6, 1.20-1.23].

1.2.2 One-photon absorption (1PA) saturation

1PA saturation is another type of nonlinear optical absorption and is different

from MPA, where the absorption of materials decreases with increasing light

intensity. Qualitatively, as electrons in the ground-sate of a material are intensely

excited into the upper energy state at a large rate, most of the excited electrons do

not have enough time to decay back, resulting in ground-state depletion and

excited-state filling. Consequently, the material can only absorb a smaller fraction

of the excitation light under higher-intensity excitation, leading to the 1PA

saturation. Materials exhibiting such a phenomenon are usually referred to as

saturable absorbers.

Quantitatively, in a homogeneously broadened two-level system, 1PA

saturation can be described by applying a dynamic two-level model based on

density matrix equations of motion for the dominant resonant transition [1.1, 1.5,

1.6]. Figure 1.2 illustrates the energy diagram for the near-resonant excitation in a


11

two-level system. By assuming the optical filed is applied adiabatically onto the

material and neglecting the relaxation and dephasing terms, the macroscopic

polarization induced in the ensemble of two-level systems by an excitation filed

of frequency under the rotating-wave approximation can be written as [1.5]:

𝑃(𝑡) = −sgn(𝜔)sgn(∆)𝑁𝑒2|r⃗𝑎𝑏 ∙ e⃗⃗|

ℏ√∆2 + Ω2𝐸(𝑡) (1.22)

where

Ω = 𝑒r⃗𝑎𝑏 ∙ e⃗⃗𝐸(𝑡)/ℏ (1.23)

is the on-resonance Rabi flopping frequency; sgn() and sgn() denote the sign

of and ; = ab - is the off-resonance detuning; 𝑒r⃗𝑎𝑏 ∙ e⃗⃗ is the two-level

transition moment; N is the number density of two-level atoms; E(t) is the applied

electric field.

Figure 1.2 Schematic diagram of the resonant interaction in the two-level system.

By comparing Eq. (1.22) to the other expression of polarization 𝑃𝜔(𝑡) =

𝜀0�̅�(𝜔; 𝐸𝜔)𝐸𝜔(𝑡) and substituting the expression in Eq. (1.23), we can obtain

the expression of ‘corrected’ susceptibility including the field effect as [1.5]:

�̅�(𝜔; 𝐸) = −sgn(𝜔)sgn(∆)𝑁𝑒2|r⃗𝑎𝑏 ∙ e⃗⃗|2

𝜀0√(ℏ∆)2 + [𝑒|r⃗𝑎𝑏 ∙ e⃗⃗|𝐸(𝑡)]2 (1.24)

ħba ħ

Ground State Ea

Excited State Eb ħ


12

Eq. (1.24) can only be applied to approximately interpretate the optical

nonlinearity of the two-level system, and it cannot provide quantitative

explanations for many experimental measurements since both dephasing and

relaxation processes are ignored. Consequently, a modified expression was

developed to take both the dephasing and relaxation times into account [1.5]:

�̅�(𝜔; 𝐸) = −𝑁𝑒2|r⃗𝑎𝑏 ∙ e⃗⃗|2𝑤0𝑇2(∆𝑇2 + 𝑖)

𝜀0ℏ[1 + (∆𝑇2)2 + [𝑒|r⃗𝑎𝑏 ∙ e⃗⃗|𝐸(𝑡)]2𝑇1𝑇2] (1.25)

where w0 denotes the population inversion under thermal equilibrium conditions;

T1 is the longitudinal relaxation time and T2 is the dephasing time for the resonant

transition. Eq. (1.25) provides a simple and revealing interpretation of the optical

nonlinearity exhibited by the two-level system under steady-state conditions.

Moreover, the absorption coefficient can be represented by α(𝐼) = 𝛼0/(1 +

𝐼/𝐼𝑠), in which 𝐼𝑠 is the saturation intensity and can be written as [1.5]:

𝐼𝑠(∆) = {2𝑒2𝑇1𝑇2

𝜀0𝑛0(𝜔)𝑐ℏ2[1 + (∆𝑇2)2]|r⃗𝑎𝑏 ∙ e⃗⃗|2}

−1

(1.26)

𝑛0(𝜔) is the linear refractive index. Since the intensity dependent absorption

coefficient α(𝐼) can be experimentally characterized, the 1PA saturation of the

homogeneous-broadened two-level system can be quantified by this α(𝐼) with

the characteristic parameter 𝐼𝑠.

All the above descriptions and derivations are for 1PA saturation in a

homogeneously broadened two-level system. On the other hand, the 1PA

saturation behavior in an inhomogeneously broadened two-level system is


13

different, since each of the absorbers (atoms or molecules) in the inhomogeneous

system has a unique resonant frequency caused by some internal properties of the

system [1.5, 1.6]. Specifically, the saturation of 1PA in an

inhomogeneously-broadened system has a characteristic of (1 + 𝐼/𝐼𝑠)−1/2 which

is less sensitive to the excitation intensity I than that in a homogeneous system

[1.5, 1.6]. Moreover, the saturation intensity is independent of the detuning and

is equivalent to 𝐼𝑠(0) in such system [1.5, 1.6].

1PA saturation of a material can be characterized by the open-aperture Z-scan

or the nonlinear transmission measurement. Usually pulsed lasers are applied in

the measurements for the reason that 1PA saturation will only occur at

high-intensity excitation. The attenuation of the intensity of the excitation light in

the homogeneously-broadened material systems can be written as [1.6]:

𝑑𝐼

𝑑𝑧= −𝛼(𝐼) = −

𝛼0

1 + 𝐼/𝐼𝑠

𝐼 (1.27)

While for the inhomogeneously-broadened material systems, the differential

equation becomes [1.6]:

𝑑𝐼

𝑑𝑧= −𝛼(𝐼) = −

𝛼0

(1 + 𝐼/𝐼𝑠)1/2𝐼 (1.28)

Generally, there are no analytical solutions for these two equations. But the

numerical solutions for both the transmitted light intensity and the energy

transmittance can be acquired utilizing appropriate numerical calculation

methods.


14

Materials possessing such 1PA saturation are in great demand in real

applications. A typical example is that they can be utilized as saturable absorbers

in the passive mode-locking technology to generate ultrashort laser pulses [1.24].

It should be pointed out that not only 1PA saturation can occur in satuarble

absorbers, but some other nonlinear optical processes can take place

simultaneously, which makes an impact onto mode-locking performance. The

presence of 2PA in the semiconductor saturable absorber mirrors (SESAMs) [1.25]

was demonstrated to increase the region for stable continuous wave mode-locking

(CWML).

1.3 Introduction to graphene

Graphene is a two-dimensional atomic crystal with hexagonal lattice of

sp2-bonded carbon atoms. Since it is discovered in 2004 by Andre Geim and

Konstantin Novoselov from the University of Manchester [1.26], graphene has

attracted enormous research interest over a wide range of fields including

fundamental physics, electronics, photonics, optoelectronics, biology and so on

[1.27-1.29]. It exhibits many superior properties, such as ultrahigh

room-temperature carrier mobility up to 2.5105 cm2V-1 s-1 [1.30]; very large

thermal conductivity which can be above 3,000W mK-1 [1.31]; universal optical

absorption of ≈ 2.3% across the near-infrared (NIR) and short-wavelength

infrared (SWIR) spectral regions [1.32,1.33]; ultrafast optically-excited carrier

dynamics [1.28,1.34-1.39]; and giant nonlinear optical properties [1.40-1.44].


15

Provided with these supreme properties, various kinds of graphene-based

potential applications have been proposed and developed [1.27-1.29], including

flexible transparent conductors, high-frequency transistors, photodetectors, optical

modulators, saturable absorber for mode-locked laser generator, and numerous

bio-applications. In 2004, Andre Geim and Konstantin Novoselov demonstrated a

simple method, i.e. micromechanical exfoliation, to produce graphene films with

high quality [1.26]. However, their sizes are limited to few tens of micrometers.

From then on, many other synthesis techniques have been developed to obtain

high quality and scalable graphene films suitable for real applications. Some of

these synthesis techniques are: liquid-phase exfoliation of graphite powder using

ultrasonication [1.45-1.47]; carbon segregation from silicon carbide (SiC)

[1.48-1.51]; chemical vapor deposition (CVD) of graphene on metal substrate

[1.52-1.56]. Among these methods, chemical vapor deposition of graphene on

metal substrate is a promising method for real applications since it can produce

relatively high-quality graphene films with large sizes, high throughput and low

cost [1.52-1.56].

The intriguing applications of graphene in electronics, photonics,

optoelectronics and nonlinear optics are based on its attractive optical and

electronic properties, which are determined by the distinctive electronic structure.

A tight-binding Hamiltonian can be applied to describe the electronic structure of

graphene [1.57, 1.58]. The computational result for electronic structure of


16

graphene by Boukhvalov, Katsnelson & Lichtenstein [1.59] indicates the sp2

hybridized states ( states) form occupied and empty bands separated by a huge

gap (>10 eV at Γ point), whereas the states form a single band with a conical

self-crossing point (K or K’), as demonstrated in Figure 1.3. Therefore, the

bands can be neglected and only the two remaining -bands are relevant and

needed to be considered [1.57]. The conical point of the -bands is a

characteristic of the peculiar electronic structure of graphene [1.60]. Within this

-band approximation and considering that electrons can only hop to

nearest-neighbor atoms, the dispersion relation can be derived as [1.58]:

3 (1.29)E k t f k

where t ≈ 2.7 eV is the nearest-neighbor hopping energy. And the plus and minus

signs corresponds to the upper (*) and the lower () band, respectively.

𝑓(�⃗⃗�) can be expressed as [1.58]:

3 3

2cos 3 4cos cos (1.30)2 2

y y xf k k a k a k a

is the wave vectors and a ≈ 0.142 nm is the carbon-carbon distance.

Figure 1.4 illustrates the obtained electronic dispersion relation. The lower ()

band is fully occupied, while the upper (*) band is totally empty. These empty

and occupied bands touch at the K (or K’) points, and the Fermi surface is defined

by K and K’ [1.28]. Near the Dirac points (K or K’), the dispersion relation in Eq.

(1.29) yields linear - and *-bands for the Dirac fermions as:

,x yk k k


17

(1.31)FE k v q

is the momentum measured relative to the Dirac points. F is the Fermi

velocity and F = 3at/(2ħ) ≈ 1106 m/s.

Figure 1.3 Electronic band structure of graphene including both bands (red

lines) and bands (dotted blue lines) [1.60].

Figure 1.4 Electronic dispersion in the first Brillouin zone of graphene under the

-band approximation and nearest-neighbor approximation. The K, K’ points and

M point are pointed out by the arrows.

In this dissertation, we pay our attention to the enticing and unique linear and

nonlinear optical properties of graphene, which are essential to applications in

photonics and nonlinear optics. It has been demonstrated that graphene possesses

universal interband 1PA in the NIR and SWIR spectra ranges [1.33], which only

q k K

M K K’


18

depends on the fine structure constant. Furthermore, the 1PA of graphene in the

ultraviolet and visible spectral regimes has been manifested to be enhanced by the

excitonic Fano resonance around the saddle point (M-point) [1.61-1.63]. On the

other hand, intraband transitions in graphene have been reported to lead to a

Drude-model-like frequency dependence in the measured 1PA spectra of graphene

in the THz spectral regime [1.64]. Linear refractive index of graphene has also

been characterized over the NIR-VIS-UV spectral range. Wang et al [1.65] have

reported five times stronger dispersion of linear refractive in graphene than bulk

graphite in the range of 488 – 633 nm, with ng = 2.4 at 488nm and ng = 3.0 at 633

nm. Weber et al [1.66] have acquired the linear refractive index of graphene in

the spectral region of 210-1000nm and revealed a peak in the UV range similar to

the measured 1PA, with peak position at ~ 300 nm and peak refractive index ng ~

3.5.

In addition to these unique linear optical properties, graphene also presents

fascinating nonlinear optical properties. Hendry et al have reported remarkably

large and weakly wavelength dependent |(3)| in graphene in the NIR range [1.29],

through four-wave mixing experiments and theoretical calculations based on

nonlinear quantum response theory. Third-harmonic generation (THG) has also

been observed in the single- and few-layer graphene films with excitation

wavelength at 1720 nm [1.43]. Furthermore, recently excitonic Fano resonance

around the saddle point of graphene has been reported to result in strong


19

third-harmonic generation in monolayer graphene excited at 790 nm, which is in

three-photon resonance with the excitonic peak [1.44]. Interestingly, through

applying appropriate substrate or injecting electric current into graphene, the

inversion of symmetry property of graphene can be modified and SHG can be

observed in graphene [1.67-1.69].

Besides these, we are more concerned with the nonlinear optical absorption in

graphene. 1PA saturation in Graphene has been extensively investigated and

applied into the passive mode-locking technology to generate ultrafast laser

pulses [1.70, 1.71]. Under intense laser irradiation, photo-excited carriers in

graphene increase in density resulting in filling of the conduction band and

depleting of the valence band and lead to 1PA saturation. The occurrence of this

band filling is due to Pauli exclusion principle [1.28, 1.70]. 1PA saturation in

graphene is greatly related to its photo-excited carrier dynamics, which has been

substantially studied by the time-resolved transient transmission measurements

[1.34-1.39]. Two relaxation processes are revealed by these time-resolved

measurements, including a faster one with timescale of ~ 100 fs and a slower one

with time scale of ~ 1ps [1.28]. The fast relaxation process is related to the

intraband carrier-carrier scattering and optical phonon emission, while the slower

one is associated with the subsequent thermalization of the carriers with the lattice

through carrier-acoustic phonon scattering and electron interband relaxation.


20

Moreover, plenty of research work has been conducted to understand the

underlying mechanisms of 1PA saturation in graphene and to determine the

saturation intensity. Several theoretical studies based on different theoretical

models have been carried out for the fundamental understanding on the 1PA

process in graphene and to predict the saturation intensity [1.72-1.76]. Besides the

theoretical studies, various experimental techniques have been utilized to

determine the saturation intensity of graphene, including open-aperture Z-scan,

optical-power-dependent transmittance, and pump-probe measurements [1.41,

1.71, 1.72, 1.74, 1.76, 1.77-1.82]. However, these previous investigations, either

theoretical or experimental, focused on the light intensity dependence of 1PA

saturation in graphene at wavelengths around 800 nm and 1550 nm. Little is

known about the spectral dependence of 1PA saturation in graphene which is

desirable for both realistic applications and fundamental understanding. Vasko has

theoretically calculated the saturation intensities of graphene at photon energies of

ћω ≈ 0.12, 0.8 and 1.5 eV, but his theoretical results seem to underestimate the

thresholds. Because he completely neglected Coulomb-scattering in his

calculations, which has been recently demonstrated to be an important underlying

mechanism for interband 1PA saturation in graphene at high photo-carrier

densities [1.76]. In Ref. [1.82], 1PA saturation in epitaxial graphene has been

observed in the spectral range from 0.03 to 0.245 eV and its quadratic photon

energy dependence has been established in a phenomenological way. However,


21

until now, no research effort has been conducted to study the spectral dependence

of 1PA saturation in graphene in the spectral range from visible to NIR.

Apart from 1PA saturation, 2PA has also been identified in graphene. 2PA in

graphene is a nonlinear optical process where two photons with identical energy

are simultaneously absorbed to excite the electrons from the valence band to the

conduction band. Such nonlinear optical property of graphene is essential to

potential applications in photonics and optoelectronics. Especially, in Ref. [1.83],

Sun et al have utilized the quantum interference between 1PA and 2PA in epitaxial

graphene in infrared range for coherent control and noncontact generation of

ballistic photocurrents. Utilizing such noncontact method for generating electrical

currents can overcome the difficulty of making reliable contacts for future

graphene-based electronic devices. Moreover, Yang et al [1.41] have

quantitatively characterized the giant two-photon absorption in AB-stacking

bilayer graphene in the NIR spectral region, both theoretically and experimentally.

However, up to date, the effect of excitonic Fano resonance around the saddle

point (M point) of the first Brillouin zone of graphene on its 2PA has not been

revealed. Such an excitonic Fano resonance effect was previously demonstrated to

significantly enhance the 1PA and third-harmonic generation of graphene [1.44,

1.61-1.63]. Moreover, 2PA of graphene has not been systematically investigated

in the visible spectral region.


22

1.4 Introduction to metal-organic frameworks (MOFs)

Metal-organic frameworks (MOFs) consisting of metal ions (or clusters)

linked together by organic bridging ligands have recently emerged as an extensive

class of crystalline materials with relatively high porosity [1.84-1.86]. Different

from metal organic polymers, MOFs exhibit topologically diverse and

aesthetically pleasing crystalline structures and consequently have predictability

of structure-property relationship [1.84, 1.86, 1.87]. In addition, the crystalline

structures of MOFs are fine-tunable and can be designed according to targeted

properties based on the geometries of the organic linkers and coordination modes

of the metal ions/clusters [1.88-1.90]. Another key feature of the MOFs’ structure

is their high porosity and uniform pore structures [1.91-1.93]. The organic ligands

in the MOFs are usually referred to as “struts”, and are typically mono-, di-, tri-,

or tetravalent ligands [1.94]. Various metals have been utilized to synthesize

MOFs, such as transition metals (e.g. Cu, Zn), alkaline earth elements (e.g. Sr,

Ba), p-block elements (e.g. In, Ga) and so on [1.95-1.99]. Up to date, diverse

approaches have been proposed and developed to synthesize MOFs, including the

solvothermal technique, the slow evaporation method, and electrochemical

synthesis and others [1.87]. Most of these syntheses methods are liquid-phase

syntheses, in which solvent is added to a mixture of solid salt and ligand or

separate metal salt and ligand solutions are mixed together in a reaction vial.


23

The high porosity which can be up to 90% free volume, the resulting

incredibly large internal surfaces, tunable pore size and adjustable internal surface

properties have made MOFs intriguing for large numbers of functional

applications, such as gas storage and separation, chemical sensing, proton

conduction and drug delivery, and etc [1.100-1.104].

Apart from the porous feature, the fine-tunable crystalline structures of MOFs

have enabled the rational design of noncentrosymmetric MOFs for applications in

second-order nonlinear optics, especially, the SHG [1.105]. Taking advantage of

the highly directional metal-ligand coordination bonds and the well-defined

geometry of metal centers, noncentrosymmetric MOFs exhibiting large

second-order nonlinear optical properties can be rationally designed and

synthesized in a systematic way with the combination of synthetic chemistry and

crystal engineering [1.105,1.106]. In most SHG-active MOFs, d10 metal ions are

commonly utilized as the secondary building units (SBU) to avoid the unwanted

d-d transitions in the visible regime and to minimize optical losses. Zn2+ and Cd2+

are the most widely used connecting metal ions, since both of them can have

tetrahedral or pseudotetrahedral coordination extensions which are intrinsically

noncentrosymmetric [1.105]. Moreover, SHG-active MOFs have been categorized

into six groups based on their design geometry or principles without considering

the different metal ions applied [1.105], namely (1) 1-D chains; (2) 2-D


24

frameworks; (3) 3-D diamondoid frameworks; (4) other 3-D frameworks; (5)

octupolar MOFs; and (6) MOFs built from chiral ligands.

The combination of the properties of organic linkers and metal ions/clusters

and the possible synergistic interplay between them have made MOFs attractive

for many functional applications, such as magnetism [1.107], catalysis [1.108],

luminescence [1.109], ferroelectrics [1.110], and electrochemical sensors [1.111].

Through controllable integration of MOFs and a variety of functional

materials one can create new multifunctional composites/hybrids to incorporate

the advantages and reduce the weak points of both components [1.112]. MOF

composites/hybrids (also called as MOFs) can have properties superior than those

of the individual components. Lots of active species have been successfully

applied to synthesize MOF composites with supreme performance unattainable by

the individual constituents [1.113-1.115], including metal nanoparticles/nanorods,

quantum dots (QDs), organic polymers, carbon nanotubes, graphene,

biomolecules and other molecular species. With the remarkable new properties,

enhanced performance and multifunctional nature resulting from the synergistic

combination of MOF and other active components, MOF composites provide

promising applications in functional and protective coatings, heterogeneous

catalysis, storage and separation, sensing, and biology [1.113, 1.116-1.119].

Additionally, MOF composites can not only be utilized directly as innovative

advanced materials, but also be applied as precursors of novel inorganic solids.


25

In this dissertation, we focus our attention on the linear and nonlinear

photoluminescence (PL) generated from the MOFs. Taking advantage of

traditional organic and inorganic PL materials, MOFs can generate unique and

superior luminescent properties and have been rapidly developed as a new type of

multifunctional luminescent materials [1.109]. Both the organic linkers and the

metal ions/clusters in MOFs can provide the platforms to generate PL. The

metal-ligand charge transfer related luminescence within the MOFs provides an

additional dimensional of luminescent functionality [1.109]. Beside these, the

luminescent properties of MOFs can be further tuned by encapsulating guest

molecules or ions, which can directly emit luminescence or induce luminescence

through the interactions with host MOFs [1.109, 1.111, 1.120]. Up to date, many

potentially useful luminescent MOFs with superior properties have been

developed for various real applications such as: NIR luminescent devices,

white-light-emitting devices, optical display devices and chemical sensors [1.121].

Via combining the magnetism and biocompatibility into the luminescent MOFs,

they can also be utilized for biomedical applications [1.122].

Most of the above-said luminescent MOFs exhibit linear PL with the photon

energy of the emission light smaller than that of the excitation light. Multiphoton

excited photoluminescence (MEPL) with the emitted photon energy larger than

the excited photon energy is an intriguing property and can be utilized for diverse

applications in bio-photonics and nonlinear optics. Such as


26

frequency-upconverted lasing, optical limiting, optical data storage and high

contrast bio-imaging [1.6, 1.20-1.23]. Lanthanides-based MOFs can generate the

frequency-upconverted PL [1.120], however, it is excited by sequential stepwise

multiphoton absorption instead of simultaneous multiphoton absorption which

provides higher contrast in bio-imaging. In addition, the absorption and

consequential PL response did not originate from the ligand in the framework but

the lanthanide ion in such lanthanides-based MOFs [1.120], thus restricting

amenability only to the metal ion.

Recently frequency-upconverted PL in MOFs was demonstrated through

encapsulating suitable dyes into their solvent accessible void [1.123, 1.124],

where two-photon lasing [1.123] and imaging [1.124] were achieved. However,

the two-photon absorption and resultant PL response in these two cases originates

from the guest organic dyes instead of the ligand in the framework, which limits

the amenability as the ability of encapsulating guest molecules is restricted by the

pore size of MOFs. Until now, multiphoton excited frequency-upconverted PL

originating from the organic ligands of MOFs has not been investigated except for

one most recent report by Qian et al [1.125], which was published during the

period when our work was reviewed by reviewers. In their work, Qian et al

demonstrated two-photon excited PL of a MOF (ZJU-56-0.20) originating from

its zwitterionic ligand [1.125]. Such a photoactive ligand was incorporated into

the MOF via a multivariate strategy. In addition, only two-photon excited PL


27

have been reported in MOFs, higher-order nonlinear PL (like three- or

four-photon excited PL) in MOFs is still unavailable in literature. Moreover, the

impact of interactions between host MOFs and guest molecules on the nonlinear

PL in MOFs are still unknown.

In this dissertation, we demonstrate efficient two-, three- and four-photon

excited PL in a solid-state MOF (MOF 1a) originating from the organic ligand.

Such MEPL in the solid-state MOF was found to be largely enhanced compared

to that of its organic ligand in solid-state form, due to the aggregation-caused

quenching was minimized by the rigid framework sustained by the MOF.

Furthermore, by encapsulating two high quantum yielding organic dyes into pore

spaces of the MOF 1a, we achieved further enhancement on the MEPL in the

resultant new MOFs (MOFs 2 and 3) which stems from the Förster resonance

energy transfer (FRET) between the host MOF and the guests.

The nonlinear PL observed in the MOFs provides a possible solution to the

aggregation-caused quenching in the nonlinear PL of organic molecules in the

solid-state form due to their rigid framework and relatively high porosity.

Therefore, MOFs can serve as promising efficiently nonlinear luminescent

materials in the solid-sate form.


28

1.5 Objectives and scopes of this dissertation

The objectives of the research work presented in this dissertation are to

investigate the nonlinear optical properties of two novel materials,

two-dimensional graphene films and three-dimensional metal-organic frameworks

(MOFs). Specifically, they consist of three parts, as follows:

(1) First of all, 2PA in graphene has been demonstrated to have potential

applications in photonics and optoelectronics [1.41, 1.83]. The excitonic Fano

resonance around the saddle point (M point) of the first Brillouin zone of

graphene is speculated to play an important role on the 2PA of graphene in the

visible spectrum. But, up to date, 2PA of graphene has not been investigated in

this spectral range. Furthermore, understanding the spectral dependence of 1PA

saturation in graphene is essential to facilitate graphene-based mode-locking

technology in a broad spectral range. However, until now, little is known and no

study has been conducted on the spectral dependence of 1PA saturation in

graphene in the NIR and visible range. Therefore, in this dissertation, we are

going to unambiguously determine and systematically investigate both interband

2PA and 1PA saturation in high-quality, CVD-grown graphene films, by

performing open-aperture Z-scan measurements on these graphene films utilizing

femtosecond laser pulses (150 fs, 1kHz). Based on the second-order,

time-dependent perturbation theory, a semi-empirical model is to be developed to

take both interband transitions among three states near the saddle point of


29

graphene and interference between band-to-band transitions and excitons into

consideration, in order to provide a theoretical understanding of the impact of

excitonic Fano resonance around the M point of graphene on its 2PA in the visible

range. Moreover, degenerate pump-probe experiments at 800 nm will be carried

out on these CVD graphene films to confirm that the photo-excited carrier

relaxation time in these samples (~ 1 ps) is larger than the laser pulse duration

(150 fs). With laser pulse duration less than the carrier relaxation time, the

obtained saturation intensities of graphene in the NIR and visible range are to be

converted to saturation fluences and compared with the previous experimental

and theoretical results, in order to gain more insight into the spectral dependence

of 1PA saturation in graphene.

(2) Efficient frequency-upconverted luminescent materials in the solid-state

form are highly preferable in real applications due to their higher resistance to

photobleaching. However, frequency-upconverted PL excited by multiphoton

absorption in organic molecules is usually quenched in the solid-state form by

aggregation effects. Multiphoton excited frequency-upconverted PL in the MOFs

seems to provide a possible solution to this problem due to its rigid framework

and porous feature. Very recently, two-photon imaging and lasing were reported

by encapsulating nonlinear optically active chromophores into the pore spaces of

MOFs [1.123, 1.124]. However, the two-photon absorption and the resultant PL

were originated from the guest molecules, which may limit the amenability due to


30

the ability of encapsulating guest molecules is restricted by the pore sizes of

MOFs. Until now, no research work has been conducted to study the MEPL in

MOFs, where both the multiphoton absorption and PL are originated from the

ligands. In this dissertation, two, three, and four-photon excited PL in a MOF

(MOF 1a), which contains a nonlinear optically active ligand, is to be measured

and compared with that of the ligand in the solid-state form, in order to

demonstrate the enhancement.

(3) The effect of the interaction between the host MOF and the guest

molecules on the multiphoton excited frequency-upconverted PL of the MOF has

not been revealed so far. In this dissertation, the effect of such interaction is to be

investigated by encapsulating two high quantum yielding organic dyes into the

above mentioned MOF (MOF 1a). Multiphoton excited frequency-upconverted

PL from the resultant MOFs (MOFs 2 and 3) is to be acquired and compared to

that of the host MOF (MOF 1a), to indicate the further enhancement.

1.6 Layout of this dissertation

Chapter 2 of this dissertation introduces the experimental setups and basic

operational principles of the applied experimental techniques, including the

open-aperture Z-scan, pump-probe, MEPL measurements and time-resolved PL

measurements. Moreover, their related theoretical data analyses for determining

nonlinear optical properties of investigated materials are also reviewed in the

same chapter.


31

In Chapter 3, syntheses and characterization of our graphene films are detailed.

It also presents the experimentally measured 1PA spectra of these graphene films

in the UV-VIS-NIR spectral range (185 – 1500 nm), revealing an excitonic Fano

resonance feature which is similar to previous theoretical and experimental

reports [1.61-1.63]. Two theoretical modelings based on the ab initio GW

calculations [1.61, 1.63] and the joint density of states (JDOS) method [1.126] are

applied to fit the observed excitonic Fano resonance feature in the acquired 1PA

spectra.

Chapter 4 reports our measured spectral dependence of 2PA and 1PA

saturation in graphene in the NIR and visible spectral range (435-1100 nm) from

the open-aperture Z-scan data. A semi-empirical model based on the second-order,

time-dependent perturbation theory is developed to analyze the effect of excitonic

Fano resonance on the acquired 2PA spectrum in the visible range. The

photo-excited carrier dynamics in graphene are confirmed by the degenerate

pump-probe data at 800 nm. In the last, the obtained 1PA saturation fluences of

graphene in the NIR and visible range are compared with other theoretical and

experimental reports on 1PA saturation in graphene, revealing a quadratic photon

energy dependence of the 1PA saturation in graphene in a broad spectral range.

In Chapter 5, we describe the characterization and linear optical properties of

our MOFs, organic ligands and guest molecules. The measurements for the linear

optical properties of these samples reveal that: (1) the linear and nonlinear PL


32

emission properties of the MOF 1a originate mainly from its nonlinear optically

active ligand trans, trans-9, 10-bis (4-pyridylethenyl) anthracene (An2Py); (2) the

guest molecules have PL emissions in the excitation region of MOF 1a, and the

emission of the guest molecules does not show in the resultant MOFs 2 and 3,

demonstrating the occurrence of FRET between the host MOF 1a and the guest

molecules. Furthermore, we measure the absolute PL quantum yields of the

MOFs and the organic ligands, and compare them with each other.

Chapter 6 starts with our experimental measurements on the multiphoton

excited frequency-upconverted PL in MOFs and ligands in the solid-sate form.

Theoretical data analyses are applied to obtain the multiphoton action

cross-sections of the ligand An2Py and the MOFs in the solid-sate form, and the

comparison and discussion on the acquired results are detailed. It also presents

our experimental and theoretical studies on the two-photon absorption properties

of the main organic ligand An2Py in the molecule level (i.e. in solution),

demonstrating that the utilized organic ligand possessing relatively large nonlinear

optical properties.

The last chapter of this dissertation, the Chapter 7, summarizes the important

findings reported in this dissertation and provides suggestions for the future

research work.

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Chapter 2 Experimental techniques and theoretical analyses

46

Chapter 2

Experimental techniques and theoretical analyses

2.1 Introduction.

Various experimental techniques have been employed to carry out the

investigations in this dissertation. In order to characterize the quality and other

fundamental properties of the CVD-grown graphene films, we have performed

experimental measurements utilizing micro-Raman spectroscopy, optical

microscopy, reflection contrast spectroscopy, and steady-state UV-VIS-IR 1PA

spectroscopy. On the other hand, to study the nonlinear optical absorption

properties of these CVD graphene films, we have applied the open-aperture

Z-scan technique and time-resolved, frequency degenerated, pump-probe

technique (or transient absorption measurement). Moreover, we have measured

the steady-state UV-VIS-IR absorption spectra, PL spectra, and absolute PL

quantum yields of the organic ligands and guest molecules of MOFs in solution,

in order to investigate their linear optical properties. Solid-state PL spectra and

excitation spectra at peak PL wavelength, and absolute PL quantum yields have

been acquired to characterize the linear optical properties of the ligands and

MOFs in solid-state form. In addition, for the purpose of investigating the

nonlinear optical properties of the main organic ligand in solution, we have

performed the Z-scan measurements and two-photon excited PL measurements.

Finally, two-, three- and four-photon excited PL measurements have been


47

employed to study the nonlinear optical properties of MOFs and their ligands in

solid-state form. Besides these, time-resolved PL measurements have been

performed to study the Förster resonance energy transfer between the host MOF

and the guest molecules.

Among all these experimental techniques, the operation principles,

experimental set-up and theoretical data analyses of the open-aperture Z-scan

technique, time-resolved, frequency degenerated pump-probe technique,

multiphoton excited PL (MEPL) measurement, and time resolved PL

measurement will be described in detail in this chapter. Since these experimental

techniques are vital to the study of nonlinear optical properties of materials, and

they have been applied into our investigations on the nonlinear optical properties

of graphene, organic molecules and MOFs in the following chapters. The

operation principles and working details of the other experimental techniques are

well explained and documented in many textbooks. Therefore, they will not be

detailedly depicted here, and will be briefly described in following chapters. All

the utilized nonlinear optical techniques in this dissertation involve femtosecond

(fs) laser pulses. Hence we will start with detailing the laser systems applied.

2.2 The femtosecond laser systems

In this dissertation, all the nonlinear optical measurements and ultrafast

spectroscopy were carried out with laser pulses of 1kHz repetition rate, ~ 150 fs

pulse duration and at selected wavelengths in the range of 435-1500 nm. The laser

pulses were provided by the Coherent Libra ultrafast amplifier laser system,


48

together with the Light-Conversion TOPAS optical parametric amplifier.

The Coherent Libra ultrafast amplifier laser system includes five parts: (1) a fs

Ti:Sapphire oscillator at 800 nm served as the seed laser (Coherent, Vitesse TM

800-2), which has a repetition rate of 80 MHz, and a pulse duration of ~100 fs; (2)

a Q-switched Nd:YLF green pump laser at 527 nm (Coherent, Evolution), which

has a repetition rate of 1 kHz and a pulse duration of 300 ns; (3) a Ti:Sapphire

regenerative amplifier (Coherent, Libra); (4) the laser pulse stretcher; and (5) the

laser pulse compressor. The output from the Coherent Libra ultrafast amplifier

laser system is at 800 nm with a repetition rate of 1 kHz, and a pulse duration ~

150 fs. Such fs laser pulses are utilized to pump the optical parametric amplifier

to generate tunable wavelength laser pulses from 285 nm to 2600 nm.

Figure 2.1(a) shows a photograph of the Coherent Libra laser system, and

Figure 2.1(b) presents the schematic layout in the laser system. Figure 2.2 is the

photo of the Light-Conversion TOPAS optical parametric amplifier.

Figure 2.1 Photograph and schematic layout of the Coherent Libra laser system.

(a)

(b)


49

Figure 2.2 Photograph of the Light-Conversion TOPAS optical parametric

amplifier.

2.2.1 Coherent Libra ultrafast amplifier system

At present, chirped pulse amplification (CPA) technique [2.1] has been

applied to the Ti: Sapphire regenerative amplifier system to generate most of the

amplified fs laser pulses. In the CPA technique, the fs laser pulses are not directly

amplified in order to avoid damaging the gain materials or reaching the saturation

of the gain which would prevent further amplification. Instead, the fs laser pulses

from the Ti: Sapphire oscillator are first stretched by a large factor (~105), and

then the resulting long pulses are amplified safely. Subsequently, a pulse

compressor is employed to compress the amplified long pulses to the original

pulse duration. Moreover, the group velocity dispersion introduced by the stretch

process can be compensated by such compression.

In our Coherent Libra ultrafast amplifier system, the diode-pumped solid state

mode-locked fs Ti:Sapphire oscillator (Coherent, Vitesse TM 800-2) is used to

seed the Ti:Sapphire regenerative amplifier system. The Ti:Sapphire oscillator

provides ~100 fs laser pulses at 800 nm with repetition rate of 80 MHz. Firstly,

these fs pulses go through the laser pulse stretcher and are stretched to a large

factor (~105). Secondly, the stretched long laser pulses feed into the Ti:Sapphire


50

regenerative amplifier cavity as a seed. At the same time, the gain medium

(Ti:Sapphire crystal) in the cavity is pumped by the Q-switched, Nd:YLF green

pump laser (Coherent, Evolution) at 527 nm with repetition rate of 1 kHz and

pulse duration of 300 ns. In order to synchronize the timing of seed laser pulses,

pump laser pulses and cavity damping, part of the seed laser pulses are collected

by a fast photodiode outside the Coherent Vitesse seed laser. And the photodiode

then provides an input signal to the Pockels Cell Driver to generate the required

reference signal to achieve the synchronization. At last, such cavity-damped,

amplified longer laser pulses are compressed by the pulse compressor to the pulse

duration of ~ 150 fs. The Coherent Libra ultrafast amplifier laser system produces

laser pulses with a pulse energy of ~ 3 mJ, a pulse duration of ~ 150 fs and a

wavelength of 800 nm at a repetition rate of 1 kHz. Figure 2.3 presents the sketch

of the basic layout of the ultrafast amplifier laser system.

Figure 2.3 Sketch of the basic layout of the Coherent Libra ultrafast amplifier

system.

Q-switched, Nd:YLF green pump laser

(Coherent, Evolution)

Mode-locked fs Ti:Sapphire oscillator

(Coherent, Vitesse) Fast photodiode

Pulse strecher

Compressor

Synchronized electronics

Pockles cell driver

Delay

Delay Ti:Sapphire

Polarizer


51

2.2.2 Light-Conversion TOPAS optical parametric amplifier

In order to study the wavelength-dependent nonlinear optical absorption of

graphene and MEPL in MOFs, we utilized the Light-Conversion TOPAS optical

parametric amplifier (OPA) to generate wavelength-tunable laser pulses from 435

nm to 1500 nm. Such OPA is based on second-order nonlinear optical processes

and could provide fs laser pulses of wavelength tunable from 285 nm to 2600 nm.

Essentially, three stages are included in the TOPAS system. Firstly, 10% of the

regeneratively amplified fs laser beam (pump beam) from the ultrafast amplifier

system is employed to generate superfluorescence in the Sapphire crystal.

Secondly, 20% of the remaining strong pump beam is used to amplify the desired

wavelength from the superfluorescence within a β-Barium borate (BBO) crystal

(Preamplifier), where appropriate angle and spatiotemporal overlap between these

two beams are required. In such preamplifier, the optical parametric process is

utilized to amplify the signal beam, and idler photons are also generated in this

process. Finally, the desired wavelength from the pre-amplified signal beam and

the generated idler beam are amplified by the remaining strong pump beam with

appropriate angle and spatiotemporal overlap within another BBO crystal

(Amplifier).

Through selecting the phase match angle of the first BBO crystal and the

generated superfluorescence, the wavelength tuning within the OPA system can be

achieved. Besides this, one additional BBO crystal served as the external mixer

outside the amplification box is utilized to generate the second harmonic


52

generation of the signal and idler beams, and also the sum frequency generation

between the signal or idler beam and the pump beam. Moreover, two additional

BBO crystals served as the external mixers are applied to generate the four

harmonic generation of the signal and idler beams. The average output power

from the TOPAS system is wavelength dependent, and signal beams usually have

much larger power than the idler beams. The pulse durations of the signal and

idler beams from the TOPAS can be slightly longer than the pump beam, but their

repetition rates are the same (1 kHz).

Figure 2.4 (a) Sketch of the basic three stages in the Light-Conversion TOPAS

optical parametric amplifier, SF - superfluorescence; (b) Photos of the layout of

optical components in our Light-Conversion TOPAS optical parametric amplifier;

(c) Photos of the two external mixers and one wavelength separator arranged

Coherent Libra

ultrafast

amplifier system

Preamplifier

Crystal

Power

Amplify

Crystal

Ti: Sapphire

Crystal

10% 800 nm

18% 800 nm

72% 800 nm

SF

Signal

Idler

Signal

Idler

(a)

(b)

External Mixer 1

(c)

External Mixer 2 Wavelength

separator


53

outside the TOPAS box.

2.2.3 TEM00 Gaussian laser beam.

The fs laser pulses are usually focused to a small volume on the samples by an

optical focal lens to achieve the desired high pump intensity for studying the

nonlinear optical properties of materials. For a TEM00 Gaussian laser beam of

beam waist radius w0 traveling in the +z direction, the electric field E can be

expressed as [2.2-2.4]:

where k = 2 / is the wave vector, is the laser wavelength in the free space.

E0(t) is the radiation electric filed at the focus and contains the temporal envelope

of the laser pulse. r = (x2 + y2)1/2 is the radial distance from the center axis.

𝑅(𝑧) = 𝑧(1 + 𝑧02/𝑧2) is the radius of curvature of the wave front at position z.

w(z) is the beam radius at position z and is defined as the half-width of Gaussian

curve at e-1 of its maximum value. w0 is w(z) at the focal point with z = 0. The w(z)

can be related to the w0 by the below equation:

z0 is called the Rayleigh length, and can be expressed as:

Figure 2.5(a) shows the schematic illustration of the propagation profile of the

TEM00 Gaussian laser beam, where is the total angular spread and can be

expressed as:

2 210

0 2

0

( , , ) ( ) exp exp tan (2.1)( ) ( ) 2 ( )

w r kr zE z r t E t ikz i i

w z w z R z z

1/22

0

0

( ) 1 (2.2)z

w z wz

2

00 (2.3)

wz

0

2(2.4)

w


54

The distance between the points z0 is defined as the confocal parameter b (b =

2z0).

Accordingly, the light intensity of a TEM00 Gaussian laser beam can be

expressed as:

where I00 is the on-axis peak intensity at the focus point and p is half of the laser

pulse width at e-1 maximum. Figure 2.5(b) illustrates the two-dimensional

intensity profile of TEM00 Gaussian laser beam along its cross section.

The output TEM00 Gaussian laser beam from the laser system usually has very

large beam waist radius w0 and Rayleigh length z0, and z0 is much longer than the

focal length f of an optical focal lens. In order to achieve the desired high pump

intensity for studying the nonlinear optical properties of materials, we need to

utilize an optical focal lens to focus the laser beam to a small volume on the

samples. Under the condition that z0 >> f, the relationship between beam waist

radius before (w0) and after the focal lens (w01) can be expressed as [2.4]:

Figure 2.5 (a) Schematic illustration of the beam width w(z) of a TEM00 mode

Gaussian laser beam along the propagation direction z. (b) The two-dimensional

intensity profile of a Gaussian beam that is propagating out of the page.

1

2 2 2

00 2 2 2

0

2, , 1 exp exp (2.5)

( ) p

z r tI z r t I

z w z

01

0

(2.6)f

ww

(b) (a)

O

w0 √𝟐w0 z

b w(z)


55

2.3 Z-scan technique

Many experimental techniques have been proposed and developed, in order to

quantitatively determine the nonlinear optical properties of materials in the last

few decades. The typical ones among them are degenerate four-wave mixing [2.5],

nearly degenerate three-wave mixing [2.6], nonlinear interferometry [2.7, 2.8],

ellipse rotation [2.9] and beam-distortion measurements [2.10]. Although these

techniques possess different advantages, the main shortcoming of them is they

require either relatively complex optical alignment or wave propagation analyses.

For example, precise beam scans followed by complicated wave-propagation

analyses is required in the beam-distortion measurements.

Compared with the above five techniques, the Z-scan [2.2, 2.11] is a simple

yet highly sensitive single-beam technique for a much easier and quicker

determination of both the nonlinear refractive index and nonlinear absorption

coefficients of materials. Sheik-Bahae et al. developed and theoretically modeled

the Z-scan technique in 1990 [2.2, 2.11]. The Z-scan technique can easily

determine both the sign and magnitude of nonlinear absorption and nonlinear

refraction based on the transmittance as a function of z position. In the Z-scan

measurements, the transmittance of laser power/energy through a sample is

monitored while translating the sample along the propagation direction of the

laser pulses (z-axis) through the focus with a linear motorized stage. With the

incident laser pulse energies being kept at a constant level, the sample experiences

various laser irradiances I(z) at different z-positions, giving rise to corresponding


56

changes in the sample transmission if the sample absorbs or refracts the light

nonlinearly. The recorded transmission as a function of the z position is analyzed

by the Z-scan theory to extract the nonlinear optical coefficients of the

investigated sample.

Because of its simplicity and high sensitivity, Z-scan technique has been

widely accepted and used as a standard method to measure various nonlinear

optical properties of materials since its first invention. In recent years, scientists

have also developed several modifications based on this method, such as,

reflection Z-scan [2.12, 2.13], eclipsing Z-scan [2.14], two-color Z-scan [2.15,

2.16], Z scan using top-hat beams [2.17], and time-resolved Z-scan [2.18].

2.3.1 Open-aperture Z-scan technique

The experimental set-up for the transmittance open-aperture Z-scan is

schematically illustrated in Figure 2.6. A beam splitter is placed behind both

Aperture 1 and the neutral density filters to split the incoming laser beam into two

equal parts. The reflected part serves as a reference beam for measuring the

transmission and is detected by Detector D1. Another function of the reference

beam is to balance the fluctuation of the laser power and to reduce the noise level

of the transmission signal. On the other hand, the transmitted part serves as the

signal beam and is focused by an optical focal lens onto the sample. In the

open-aperture Z-scan, the aperture 2 is open and all the transmitted laser power

through the sample is collected and measured by Detector D2. Consequently, the

ratio of D2 to D1 is the transmission through the sample and is recorded as a


57

function of the z position (relative to the focal plane), which can be modeled by

the open-aperture Z-scan theory to derive the information of the nonlinear optical

absorption coefficients. Figure 2.7 demonstrates a photo of our Z-scan set-up.

Figure 2.6 Schematic illustration of the open-aperture Z-scan set-up for

measuring nonlinear optical absorption properties.

Figure 2.7 A photograph of our Z-scan setup.

The open-aperture Z-scan technique and its related theoretical analyses are

only valid for “thin” samples. According to Ref. [2.2], “thin” samples are those

with sample length small enough that changes in the beam diameter within the

sample due to either linear diffraction or nonlinear refraction can be neglected.

Based on the analyses in Ref. [2.2], the overall requirement for the thickness of

- Z

PhotoDetector ( D1 )

Power Meter

Sample

+ Z

Photo Detector ( D2 )

Beam

Splitter Lens 1

Fs laser

pulses Translation

stage

Aperture 1

ND

filters

Lens 2 Aperture 2


58

sample L in the Z-scan measurements is L should be smaller than the diffraction

length (L < z0 = w02/λ, w0 is the beam waist).

In a third-order instantaneous nonlinear optical material, the nonlinear

absorption is related to the imaginary part of the third-order nonlinear optical

susceptibility χ(3). The total absorption coefficient dependent on the pump laser

intensity can be expressed as [2.19, 2.20]:

where 0 is the linear absorption coefficient, I is the incident laser intensity; 2 is

the third-order nonlinear optical absorption coefficient and is related to the

imaginary part of χ(3) by 2 = 3Im(χ(3))/(20𝑛02𝑐2).

In the open-aperture Z-scan measurements, as shown by the Z-scan set-up in

Figure 2.6, the sample experiences different irradiance at different z positions due

to the changing of the laser beam area. When the sample is moved towards the

focal point, the absolute value of nonlinear optical absorption 2I will increase

and will reach its maximum at the focal point (z = 0). The sign of the Z-scan

signal (power/energy transmittance change) depends on the sign of α2. For a 1PA

saturation process whose α2 is negative, the energy transmittance change is

positive. On the other hand, the energy transmittance change is negative for a 2PA

process whose α2 is positive. The dashed and solid lines in Figure 2.8 illustrate the

typical open-aperture Z-scan signals for the 1PA saturation process and 2PA

process, respectively.

0 2 (2.7)I


59

-2 -1 0 1 2

No

rmalized

Tra

nsm

itta

nce

1PA saturation

2PA

Z position (cm)

Figure 2.8 Typical open-aperture Z-scan signals for the 1PA saturation (dashed

curve) and 2PA (solid line), respectively.

It should be pointed out here that before performing the open-aperture Z-scan

measurements on any samples, the experimental set-up should be calibrated using

slabs of wide-gap semiconductors such as CdS and ZnS as standard samples.

There are two main purposes for performing such a calibration: the first is to

check the optical alignment of the laser beam and the open-aperture Z-scan set-up;

and the second is to ensure the accuracy of the power detectors. In order to

illustrate such a calibration, we present an example of using a 0.5-mm-thick

hexagonal CdS crystal (Semiconductor Wafer, Inc) to calibrate the experimental

set-up for open-aperture Z-scan at 800 nm in the next section.

2.3.2 Data analyses for two-photon absorption (2PA)

Under the “thin sample” approximation and the slowly varying envelope

approximation (SVEA), the equation describing the relation between irradiance

I(z,r,t) and z’ can be expressed as:

where z’ is the propagation depth in the sample and is different from the sample

0

( , , )( , , ) ( , , ) (2.8)

'

dI z r tI z r t I z r t

dz


60

position z, and is the 2PA coefficient.

By integrating Eq. (2.8) over the whole sample length, we obtain the laser

irradiance at the exit surface of the sample as follows:

where

Here we take account of the reflection from the sample front surface R, and L is

the sample thickness. Ii(z,r,t) is the incident laser beam intensity and can be

expressed by Eq. (2.5).

Through integrating Eq. (2.9) over the spatial and temporal Gaussian laser

pulse, we can obtain the normalized energy transmittance as follows. Firstly, the

laser power at the exit surface of the sample is:

Secondly, the incident laser power on the sample is:

Finally, the energy transmittance is:

02(1 ) ( , , )( , , ) (2.9)

1 ( , , )

L

ie

R I z r t eI z r t

q z r t

( , , ) (1 ) ( , , ) (2.10)i effq z r t R I z r t L

0

0

1(2.11)

L

eff

eL

0

P ( , ) 2 ( , , )e ez t I z r t rdr

0

0

12 2 2

2

00 2 2 2

0

12 2 2

0

00 2 2 2

0

2

2(1 ) 1 exp exp

( )2

21 (1 ) 1 exp exp

( )

(1 ) ( )ln 1 ( ,0, ) (2.12)

2

L

p

eff

p

L

eff

z r tR e I

z w zrdr

z r tR I L

z w z

R w z eq z t

L

0

12 2 2

00 2 2 2

00

2

P ( , ) 2 ( , , )

22 1 exp exp

( )

( )( ,0, ) (2.13)

2(1 )

i i

p

eff

z t I z r t rdr

z r tI rdr

z w z

w zq z t

R L


61

where q(z,0,0) = (1-R) I00 Leff/(1+z2/z02).

For |q(z,0,0)|<1, we can perform the Taylor series expansion for the term

𝑞(𝑧, 0,0)𝑒−𝑥2and the energy transmission can be expressed as:

For most nonlinear optical materials exhibiting two-photon absorption,

|q(z,0,0)| is small. Therefore, we can ignore the high-order terms and only

consider the first two terms. In such a way, the normalized energy transmittance

in the open-aperture Z-scan can be expressed as:

Eq. (2.16) quantitatively describes the relation between the normalized energy

transmittance TOA(z) and the sample position z. As in Eq. (2.16), all the

parameters are measurable except for the 2PA coefficient . Therefore, by fitting

this expression of TOA(z) to the experimental open-aperture Z-scan data, we can

extract the value of the investigated sample.

0

02

2

2

P ( , )

( )

P ( , )

ln 1 ( ,0, )

(1 )

( ,0, )

(1 )ln 1 ( ,0,0) (2.14)

( ,0,0)

e

i

L

Lx

z t dt

T z

z t dt

q z t dt

R e

q z t dt

R eq z e dx

q z

02

0

21 ( 1)

0

2

3/20

(1 ) ( 1)( ) ( ,0,0)

1( ,0,0)

( ( ,0,0))(1 ) (2.15)

( 1)

L jj j x

j

jL

j

R eT z q z e dx

jq z

q zR e

j

00

2 2

0

(1 )( ) ( ,0,0)( ) 1 1 (2.16)

( ) 2 2 2 2 1 /

eff

OA

R I LT z q zT z

T z z


62

Figure 2.9 presents the open-aperture Z-scan traces of the standard sample, a

0.5-mm-thick hexagonal CdS crystal (Semiconductor Wafer, Inc), to calibrate the

set-up at 800 nm. Experimental Z-scan data are the black symbols in Figure 2.9,

and the solid red line corresponds to the theoretical fitting. Firstly, we find the

Z-scan signal in Figure 2.9 is symmetric about the origin of the Z-axis, indicating

a good alignment of the Z-scan set up and the optical path. Secondly, we extract

the value of the CdS at 800 nm by fitting the Z-scan data with Eq. (2.16), and

compare it with the previous experimental and theoretical reports [2.21, 2.22] to

confirm the parameters of our open-aperture Z-scan set up.

-1.0 -0.5 0.0 0.5 1.0

0.95

1.00

CdS

TPA fit

I00

= 0.9 GW/cm2

= 5.3 cm /GW

ex

= 800 nm

0= 16 m

No

rmalized

Tra

nsm

itta

nce

Z (cm)

Figure 2.9 The open-aperture Z-scan signal for 0.5-mm-thick hexagonal CdS

single crystal and the related theoretical fitting.

2.3.3 Data analyses for one-photon absorption (1PA)

saturation

Considering the laser beam propagation in a thin homogeneous broadening

saturable absorber, the optical density loss can be expressed by the differential

equation as follows:

0/ ' ( ) ( ) (2.17)

1 / S

IdI dz f I I I

I I


63

Is denotes the saturation intensity.

Normally, it is hard to provide explicit analytical solutions for Eq. (2.17). The

transmitted optical intensity at the exit surface of the saturable absorber Iout can be

obtained by formally integrating the Eq. (2.17):

Iin is the incident optical intensity at the front surface of the homogeneous

broadening saturable absorber and L is its length.

However, based on the Adomian decomposition (AD) method [2.23, 2.24],

the solution of Iout can always be expressed in terms of the polynomial and the

resultant normalized energy transmittance as a function of z position can be

obtained. Firstly, we express Iout in terms of the polynomial as follows:

Secondly, we can utilzie an infinite series of Adomian’s polynomials to represent

the nonlinear term f(I),

where Aj polynomial is defined by:

In which, is an intermediate variable. Through substituting the expressions in

Eqs. (2.19) and (2.20) into the Eq. (2.18), we can obtain:

From Eq. (2.22) we can easily identify the zero component of uj as u0 = Iin,

therefore, we can obtain uj utilizing the recurrence formula as follows:

0

( ) ' (2.18)

L

out inI I f I dz

0

(2.19)out

j

j

I u

0 1

0

( ) ( , ,..., , ) (2.20)j j

j

f I A u u u

00

1(2.21)

!

j jk

j kjk

dA f u

j d

0 1

0 00

( , ,..., , ) ' (2.22)

L

in

j j j

j j

u I A u u u dz


64

Obviously, we can get all uj from Eq. (2.23) once u0 is known. In such a way, the

exact solution of Iout can be obtained, as 𝐼𝑜𝑢𝑡 = ∑ 𝑢𝑗∞𝑗=0 . Consequently, we can

provide the exact solution of Iout in a series form as below based on Eq. (2.23)：

In which = Iin/Is. The first five terms of y j ( ) are provided as below:

The optical intensity of the incident beam at front surface of the saturable

absorber Iin(z,r,t) can be expressed by Eq. (2.5). Through substituting the Eq. (2.5)

and the expressions of y j ( ) into the Eq. (2.24), we can obtain the transmitted

intensity through the saturable absorber Iout(z,r,t). Consequently, the normalized

energy transmittance as a function of z position can be given by:

At last, we can extract the characteristic parameter of saturable absorber, the

saturation intensity Is, from fitting the open-aperture Z-scan experimental data

with the Eq. (2.26).

1 0 1

0

00

( , ,..., , ) '

(2.23)( 1)!

L

j j j

j jk

kjk

u A u u u dz

L df u

j d

0

2 11

( )1 (2.24)

! (1 )

jjout in

jj

yLI I

j

1

2

3

2

4

2 3

5

1,

1,

1 2 , (2.25)

1 8 6 ,

1 22 58 24 .

y

y

y

y

y

0

0 0

0 0

( , , )

( ) (2.26)

( , , )

out

L in

I z r t rdrdt

T z

e I z r t rdrdt


65

2.3.4 Data analyses for materials exhibiting both 1PA

saturation and 2PA

Many materials are reported to exhibit both 1PA saturation and 2PA

[2.25-2.28], which makes the change of open-aperture Z-scan signals dependent

on the laser intensity applied. Therefore, distinguishing the two nonlinear

absorption effects in these materials and quantitatively evaluating their Is and

values are of great importance. As a result, it is highly necessary to study the

Z-scan theory for materials exhibiting both 1PA saturation and 2PA. Here, similar

to the case of pure 1PA saturation, the open-aperture Z-scan theory for the

simultaneous appearance of both 1PA saturation and 2PA is developed by utilizing

the AD method [2.23, 2.29].

By applying the phenomenological model of the combination of 1PA

saturation and 2PA [2.26, 2.30], the optical intensity loss of the laser beam

propagating through a thin nonlinear optical absorber obeys the differential

equation below:

(I) is the optical absorption coefficient dependent on laser intensity as following:

The first term on the right side of Eq. (2.27) represents the 1PA saturation, and

the second term quantifies 2PA.

The solution of the transmitted laser intensity Iout passing through the

nonlinear optical material with the concurrence of 1PA saturation and 2PA

0/ ' ( ) ( ) (2.27)1 / S

dI dz f I I I I II I

0( ) (2.28)1 / S

I II I


66

processes can be written as an infinite series of polynomials as:

where = Iin/Is, and p() = 0 + (1 + )Is. Therefore, the expression of Iout in Eq.

(2.29) can be further expanded as below:

where

The first four terms of y j ( ) are provided as below:

With x = z/z0, the optical intensity of the incident beam at the front surface of

sample as shown in Eq. (2.5) can be expressed as:

Therefore, the analytical solution of the normalized power transmittance

dependent on the sample relative position x = z/z0 can be derived by substituting

Eq. (2.33) into Eq. (2.30) and performing integration over the cross-section

Gaussian profile. Such derived normalized power transmittance is provided as

follows:

2 1

1

( )( )1 (2.29)

! (1 )

jjout in

jj

p yLI I

j

' ''

0

2 1 2 11 1

( ) ( )1 (2.30)

! (1 ) ! (1 )

j j

j jout in s

j jj j

y yL I LI I

j j

'

1

0

;j

j

j

yy

''

1

(1 )(2.31)

( )j

j

j

s

yy

I

1

2

2 0

2 2 2 2 4 3 2

3 0 0

3 2 2 3 2

4 0 0

2 2 2 2 3 2 3 3 3 6

0

1,

2 ( 1) ,

(1 2 ) 6 ( 1) 2 ( 4 6 3), (2.32)

(6 8 1) 2 (2 6 7)

2 ( 1) (8 29 36 18) 24 ( 1) ,

s

s s

s

s s

y

y I

y I I

y I

I I

2

12

0 2

2( , , ) ( ) 1 exp (2.33)

( )

in rI z r t I t x

w x

0

0

'0 0

1 1

0

( , , )( ) ( )

( , ) 1 ( ) ( ) (2.34)! !

( , , )j

out

j jL s

j

j jL in

I x r t rdrL I L

T x t e q qj j

e I x r t rdr

0

2

( )(2.35)

1s

I t

I x


67

And the first two terms of 𝑞𝑗(𝜌) and 𝑞𝑗′(𝜌) are provided as follows:

Finally, we can deduce the normalized energy transmittance through the

below integration considering the Gaussian temporal envelope of the laser pulse:

Figure 2.10 demonstrates the dependence of the normalized transmittance T (z

= 0) on the peak laser intensity at the focal point I00. In which, the black squares

are for nonlinear optical materials exhibiting only 2PA; the triangles are for the

pure 1PA saturation case; and the circles correspond to the case of the concurrence

of 1PA saturation and 2PA. The utilized parameters for the simulation are as in

Ref. [2.29], where 1PA coefficient 0 = 1.43 cm-1, sample thickness L = 0.2 cm,

saturation intensity Is = 0.0011 GW/cm2 and 2PA coefficient β = 32 cm/GW.

0.00 0.01 0.02 0.03 0.040.9

1.0

1.1

1.2

1.3 1PA saturation

1PA saturation and 2PA

2PA

No

rmalized

T

(z =

0)

I00

(GW/cm2)

Figure 2.10 Dependence of the normalized transmittance T (z = 0) on the peak

laser intensity at the focal point I00 for the pure 1PA saturation (blue triangle),

pure 2PA (black square), and concurrence of both 1PA saturation and 2PA (red

circle) [2.29].

1

1

2 2

0

'

2' 0 02

ln(1 ) / ,

2 ln(1 )1,

2 (1 )

/ 2,

ln(1 ) 2. (2.36)

(1 ) 3

s

s s

q

Iq

q

qI I

2

2

1( ) ( , )exp (2.37)

p

tT x T x t dt


68

2.4 Transient absorption measurement (or pump-probe

technique)

Another important technique that can be utilized to study the nonlinear optical

properties and ultrafast carrier dynamics of materials is the time-resolved

pump-probe technique [2.31]. For short, such technique is also called the transient

absorption measurement or pump-probe technique. Figure 2.11 presents a typical

schematic diagram of the pump-probe experimental set-up. As in Figure 2.11, a

beam splitter is applied to split the incident laser beam into two parts, the strong

pump beam and the weak probe beam. The weak probe beam firstly propagates

through a zero-order quarter wave plate and a linear polarizer in sequence to make

its polarization perpendicular to that of the pump beam. In such a way, we can

eliminate any artificial signals from coherent effects. Subsequently, the weak

probe beam is focused to a small area (~ 20 um) into the sample and its

transmitted energy is detected by a sensitive photodiode. On the other hand, the

strong pump beam is firstly chopped by a chopper and then delayed by a

computer-controlled delay stage. Finally, the strong pump beam is focused to a

relatively large area (~ 50 um) to cover the probe beam spot in the sample. A

blocker is used to block the pump beam after it transmits the sample. Figure 2.12

presents a photo of our pump-probe experimental set-up.


69

Figure 2.11 Schematic diagram of the pump-probe experimental set-up.

Figure 2.12 Photograph of our pump-probe experimental set-up.

In the pump-probe experiment, we obtain the temporal profile of the

photo-excited ultrafast carrier dynamics by acquiring the pump-induced

absorption change of the probe beam as a function of the time delay between the

Attenuator

Photo

Diode

Lock-in

Amplifier

/4

Waveplate Polarizer

Sample

Lens Iris 3

Chopper

Femtosecond

Laser pulse Pump Delay line

Probe

Iris 2

Beam

Splitter

Iris 1


70

pump and probe pulses. Because the absorption change is usually very small and

can be easily swamped by various noises such as the fluctuation of the laser pulse

energy and the environmental noise, it is difficult to get the desired data in real

experiments. The common method to recover the buried minimal signal from the

noises is the lock-in technique. In our experiment, we utilized a chopper to

periodically modulate the pump beam at a frequency (such as 500 Hz) outside the

range of the background noise frequency. As a result, this periodicity would be

reflected in the sample and the transient energy transmittance of the probe beam

would be modulated by this certain periodicity. Then a lock-in amplifier

referenced to this modulation frequency could be used to pick out the desired

signal even from noises orders of magnitude larger. One important requirement in

the pump-probe measurement is that the intensity of probe beam should be much

weaker than that of pump beam (Iprobe/Ipump < 0.1), so that we can neglect the

nonlinear optical effect caused by the probe beam.

In this dissertation, we carried out frequency-degenerate pump-probe

measurements where the wavelengths of the pump and probe beams are the same.

As demonstrated in [2.32], such frequency-degenerate pump-probe technique is

useful in detecting the nonlinear optical absorption, nonlinear refraction and

photo-excited carrier dynamics of nonlinear optical materials.

Calibration performed on the standard semiconductor bulk crystal (CdS) is

needed before our frequency-degenerate pump-probe measurements. Figure 2.13

demonstrates frequency-degenerate pump-probe experimental signal at 800 nm of


71

the standard sample, a 0.5-mm-thick hexagonal CdS crystal (Semiconductor

Wafer, Inc). The black symbols are the experimental data, and the solid black line

corresponds to the two-exponential-component decay fit. The fast relaxation

component accounts for the laser pulse duration, and the much slower relaxation

component is caused by the two-photon absorption induced free carrier absorption

in CdS, indicating the lifetime of the free carriers.

0 2 4 6

0.01

0.1

Pump-probe data

Decay fit

T/T

0 (

a.u

.)

Time Delay (ps)

I00

= 0.6 GW/cm2

0.75 mJ/cm2

CdS , 800nm;

1 <

p ~ 150 fs ,

~ 100ps

Figure 2.13 Frequency-degenerate pump-probe experimental signal of the

standard sample 0.5-mm-thick hexagonal CdS crystal at 800 nm excitation.

2.5 Multiphoton excited photoluminescence (MEPL)

measurement

PL excited by simultaneous multiphoton absorption (MPA) is one of the most

important nonlinear optical properties of materials, and can be applied in various

real applications such as upconversion lasing [2.33, 2.34] and upconversion

bio-imaging [2.35, 2.36]. Three parameters are usually utilized to characterize the

MEPL exhibited by fluorescent nonlinear optical materials, namely (1) the

simultaneously absorbed photons’ number n; (2) the MPA cross-section n; and (3)

the MEPL quantum yield n. Especially, the product of n and n is a direct


72

measurement of the MEPL brightness, and is called the multiphoton action

cross-section nn.

From the excitation intensity dependence of the MEPL signal we can directly

determine the simultaneously absorbed photons’ number n. Moreover, the one

photon excited PL quantum yield 1 can be measured utilizing the absolute

method on a fluorescent spectrometer equipped with a BaSO4-coated integrating

sphere. Normally, at room temperature, n is very close to 1 [2.37, 2.38].

Therefore, we have n ≈ 1 = . Finally, we can obtain the multiphoton action

cross-section n of the investigated material by comparing the MEPL signal with

that of a standard nonlinear optical phosphor under the same experimental

conditions [2.39-2.41]. Therefore, the MPA cross-section n can be derived by

n /.

2.5.1 MEPL measurement for solution sample

2.5.1.1 Experimental setup and related details

Figure 2.14 presents the schematic illustration of the experimental setup

utilized in the MEPL measurement for solution sample. The excitation laser

pulses with tunable wavelengths (1 kHz, 285-2600 nm, pulse width < 150 fs) are

generated by the TOPAS optical parametric amplifier pumped by the Libra

regeneratively amplified fs Ti:Sapphire laser system. The incident laser pulses go

through an aperture with appropriate radius to reduce the beam radius.

Subsequently, an optical focal lens (L1) with focal length of 10 cm is employed to

focus the laser pulses into the centre of the solution sample contained in a 1 cm


73

thick quartz cell. The MEPL signal from the solution sample is collected in the

perpendicular direction of the incident laser beam using a telescope collection

system consisting of a pair of lenses with 10 cm focal length (L2 and L3). In

addition, the scattered excitation laser beam is filtered out by a short-pass filter

(cut at 750 nm), and the obtained pure MEPL signal is directed into a

spectrometer (Avaspec-2048-SPU, Resolution of 0.5 nm). The average power of

the input laser beam is acquired just after the focal lens L1 by using an appropriate

sensor (Detector 919P-003-10, Newport) connected to an optical power meter

(Optical power meter 1917-R, Newport). Moreover, MEPL of standard

fluorescent nonlinear optical solution sample (like Rhodamine 6G in methanol

[2.42]) is measured in the same experimental setup as a calibration.


measurement for solution sample. OPA, WS, and SP are short for optical


respectively.

L1

Libra Laser

(800 nm) OPA

WS

Attenuators

L2

L3

Avaspec

-2048-SPU

Sample

SP Filter cut

at 750 nm

Aperture


74

2.5.1.2 Theoretical data analyses.

Here, we show the theoretical data analyse for the two-, three- and

four-photon excited PL measurements as examples of the quantitative

characterization of MEPL. The MEPL signal within the focused Gaussian laser

beam can be written as [2.39-2.41]:

The factor of 1/n (n = 2, 3, 4) accounts for the fact that n incident photons are

simultaneously absorbed for generating each fluorophore excitation. 𝜙 is the PL

collection efficiency of the experimental setup; is the sample molar

concentration; and 𝐼r(𝑧, 𝑟, 𝑡) is the nearly-constant laser intensity at the small

volume of ds dz, which is given by Eq. (2.5) for a tightly focused TEM00

Gaussian laser beam.

Considering that loss of the incident laser intensity within the sample is

insignificant because of the relatively small MPA cross-section and low sample

concentration, we can obtain the MEPL strength Fn by integrating fn over the

whole laser-focused volume and time (the spatial and temporal profiles of the

laser pulse are Gaussian functions) as [2.39-2.41]:

2 2

2 21/ 2 ( , , ) / ( ) (2.38)rf I z r t ds dz dt

3 3

3 31/ 3 ( , , ) / ( ) (2.39)rf I z r t ds dz dt

4 4

4 41/ 4 ( , , ) / ( ) (2.40)rf I z r t ds dz dt

2 25/22 00 0 0

2 2 2

- - 0

3 25/23 00 0 0

3 3 3

- - 0

4 25/24 00 0 0

4 4 4

- - 0

= 2 (2.41)8 2

= 2 (2.42)36 3

3= 2 (2.43)

512

p

p

p

I w zF f r dr dz dt

I w zF f r dr dz dt

I w zF f r dr dz dt


75

I00 is the on-axis peak intensity at the focus point. The only unknown parameters

in Eqs. (2.41-2.43) are n (n = 2, 3, 4) and 𝜙.

2.5.2 MEPL measurement for solid powder sample

2.5.2.1 Experimental setup and related details

Different from the MEPL measurement for solution sample, in this case the

target sample is compact solid powder and the interaction between the incident

laser beams and the powder sample mainly occurred on the surface with small

interaction length. As a result, to measure the MEPL of the solid powder sample,

a slightly different experimental setup as schematically illustrated in Figure 2.15

has been applied. In the measurement, the well ground powder sample is

compactly packed in a 1-mm-thick quartz cuvette. As in Figure 2.15, first of all,

the incident laser intensity is reduced by inserting a series of ND filters into the

path of the excitation beam just after the output port of the laser system. The

original beam radius of the incident laser beam is reduced to an appropriate value

by inserting an aperture after the ND filters. Subsequently, the incident laser

pulses are focused by a lens (L1’ with focal length of 6 cm). The distance between

the powder sample contained in the 1-mm-thick quartz cuvette and L1’ is kept at a

value (7.5 cm) larger than the focal length, in order to avoid the high excitation

peak intensity on the sample and to have larger excitation area (larger MEPL

signal). The incident angle between the incident laser beam and the sample plane

is maintained at 45, and MEPL signal is collected in the perpendicular direction

to the incident light using a telescope collection system consisting of two optical


76

focal lenses (L2 and L3) with focal length of 10 cm. Finally, the excitation laser

beam is filtered out by a short-pass filter cut at 750 nm and the resultant pure

MEPL signal is coupled into the spectrometer (Avaspec-2048-SPU, Resolution of

0.5 nm). As a calibration, MEPL of a standard solid state sample (like well ground

perylene single crystal (powder) [2.42, 2.43]) is measured under the same

experimental condition. Although this experimental set-up is slightly different

from the ordinary one for solution sample, the applied relative measurement

method utilizing a standard sample can give us reasonable and accurate results.


measurement for solid powder sample. OPA, WS, and SP are short for optical


respectively.

2.5.2.2 Theoretical data analyses.

Theoretical data analyses for the two-, three- and four-photon excited PL

measurements are provided as examples of the quantification for MEPL. MEPL

signal within the small focused Gaussian laser beam volume dsdz and the small

45o

45o

Libra Laser

(800 nm) OPA

WS

Attenuator

s

L2

L3

Avaspec-

2048-SPU

Sample

SP Filter cut

at 750 nm

L1’

Aperture


77

time interval dt can be expressed by Eqs. (2.38-2.40). In addition, in this case the

investigated sample is compact solid powder and the interaction between incident

laser beam and the sample mainly occurs on the sample surface resulting in small

interaction length. Therefore, we can assume this interaction length as a small

constant L0 and hence the Eqs. (2.38-2.40) become:

Considering the experimental setup as demonstrated in Figure 2.15, we define that

the directions of x and y axes are as demonstrated in the following diagram (O is

the original point, y is in the direction perpendicular to the plane of paper and

outward). Consequently, 𝐼r′(𝑧, 𝑟, 𝑡), which is the incident TEM00 Gaussian laser

beam intensity distribution on the sample surface, can be written as:

In which, d is the distance from the central point on the sample to the focal point

of the laser beam.

' '2 2

2 2 01/ 2 / ( ) (2.44)rf L I ds dt

' '3 3

3 3 01/ 3 / ( ) (2.45)rf L I ds dt

' '4 4

4 4 01/ 4 / ( ) (2.46)rf L I ds dt

Solid powder sample

contained in the

1-mm-thick quartz

cuvette.

' '

2 2 2

0 222

0 0

12

00 0

2 2 2

222

0 0

( , , ) ( , y, )

2 2= ( ) exp

1 ( cos( / 4)) /

1 ( cos( / 4)) /

2 2exp (2.47)

1 ( cos( / 4)) /

r r

p

p

I z r t I x t

x y tI d

w d x z

I d x z

x y t

w d x z

y (O)

45o

x

45o

d


78

Based on the fact that the spatial profiles of the input laser pulses are Gaussian

functions, the integration out of the beam radius region at the sample position is

relatively small compared to that within the beam radius, and can be neglected.

Since both the spatial and temporal profiles of the input laser pulses are Gaussian

functions, the totally collected MEPL signal strength 𝐹𝑛′ (n = 2, 3, 4) can be

derived by performing integrations for the Eqs. (2.44-2.46) as below:

(1) First of all, we perform the integration to determine the 2PA excited PL

strength:

' 2

2 0

'

2 2

2

2 0 00 0 2

2

3/2 222

0 00

22

2 0 00 0 32 2

0 0 0

[ ( , , )]

2( )

1

4( )2

1 4exp

1 ( cos( / 4)) /1 ( cos( / 4)) /

1 1 4exp

4( )2 / /

rL I x y t dx dy dt

F

L I w

xdx

w d x zd x z

xL I w

d z w d z

2

23/22 2 0

2 0 00 02(2.48)

8 2( )

dx

zL I w

d

(2) Similarly, we can deduce and obtain the expressions of 3PA and 4PA excited

PL strength as follows:

43/2' 3 2 0

3 3 0 00 03(2.49)

18 3( )

zF L I w

d

63/2' 4 2 0

4 4 0 00 04(2.50)

64( )

zF L I w

d

The fluorescent spectrometer equipped with an integrating sphere can also be

employed to measure the PL quantum yield of the solid powder samples by


79

using the absolute method and suitable sample holder. Therefore, in Eqs.

(2.48-2.50) the only unknown parameters are the PL collection efficiency 𝜙 of

the experimental setup and the MPA cross-sections n (n = 2, 3, 4).

2.6 Transient photoluminescence (PL) characterization

technique

Electrons excited by laser beam will relax to a lower state via radiative

recombination at various times after the excitation. Transient PL measurement (or

called time-resolved PL measurement) acquires the PL intensity as a function of

the time after the laser pulse excitation, and can be utilized to characterize the

radiative relaxation dynamics of the optically excited carriers.

2.6.1 PL lifetime measurement with fast photodiode coupled

with oscilloscope

The experimental set-up utilized in this measurement is similar to that of the

MEPL measurement. However, PL collected by the telescope collection system is

not coupled into a spectrometer. Instead, the collected PL signal firstly goes

through a monochromator (MicroHR, Horiba) and then the resultant PL signal at a

selected wavelength ( 0.25 nm) is detected by a fast silicon photodiode (EOT,

Silicon PIN detector ET-2040, 30 ns). Next, the output signal from the photodiode

is fed into an oscilloscope with 400-MHz bandwidth (CRO, Tektronix TDS 380,

50-ohm-terminate). The time resolution of such a setup is limited by the response

time of the photodiode and is around 30 ns.


80

2.6.2 Time-correlated single photon counting (TCSPC)

technique

TCSPC is another technique that can be applied to measure the PL lifetime

[2.44, 2.45]. Such a technique offers picosecond time resolution, which is much

higher than the above-mentioned one and can be utilized to characterize the fast

PL lifetime exhibited by organic molecules and other organic samples (around

several nanoseconds). The time interval between detecting the first photon

emitted by the sample and the laser pulse excitation is analyzed in the TCSPC

measurements. And the PL decay profile is obtained by repeating such process

many times and then reconstructing the histogram of the detection times from the

individual time measurements. Therefore, TCSPC technique is based on the

detection of single photons of a periodical light signal.

A schematic illustration of the experimental setup applied in the TCSPC

measurements is demonstrated in Figure 2.16. The laser sources are

Orpheus-Twins optical parametric amplifiers (OPAs) (Light Conversion) pumped

by a Pharos-9W fs oscillator/amplifier (Light Conversion). The incident laser

pulses (1MHz, ~ 150 fs) are split by a beam splitter into two parts. The first part is

used as the excitation laser source and is focused onto the sample. The second

part goes through a photodiode, a delay line, and then is directed into the TCSPC

counter (PicoHarp 300, PicoQuant) acting as the start signal. The PL signal at a

selected wavelength is collected by a monochromator (MicroHR, Horiba) coupled

with a single photon counting avalanched photodiode (MPD PDM series), and


81

then is input to the TCSPC counter serving as the stop signal. With both the start

and stop signals being detected by the TCSPC counter, the full PL decay profile,

and consequently, the lifetime of the excited states can be acquired.

Figure 2.16 Schematic illustration of the experimental setup for TCSPC

measurement. OPA, WS, PD and SPAD are short for optical parametric amplifier,

wavelength separator, photodiode and single photon counting avalanched

photodiode, respectively.

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Beam Splitter

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PD

Aperture

Orpheus Twins Laser

OPA

Attenuator

s

Lens

Lens

Filter

45o

45o

Sample

Monochromator

SAPD

Counter

Computer

Delay

Stop Signal


82

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Chapter 3 One-photon absorption of CVD-grown graphene films

86

Chapter 3

One-photon absorption of CVD-grown graphene films

3.1 Introduction to CVD-grown graphene films

As a special allotrope of carbon, graphene has an atomic-scale,

two-dimensional, hexagonal lattice structure in which the carbon atoms are

sp2-bonded with a bond length of 0.142 nm. Graphene was proposed theoretically

long time ago [3.1] and was thought as thermodynamically unstable. Until 2004,

Andre Geim and Konstantin Novoselov firstly extracted the single layer graphene

from bulk graphite via the micromechanical cleavage technique [3.2, 3.3].

Thereafter, various methods have been developed to synthesize graphene films

with high quality and large area, and also to simplify the synthesis procedure and

to reduce the cost. Until now, there are five main methods available for preparing

graphene films, namely, (1) micromechanical exfoliation of graphene from highly

oriented pyrolytic graphite (HOPG) [3.2-3.8]; (2) carbon segregation from silicon

carbide (SiC) (or called epitaxial growth of graphene on SiC) [3.9-3.18]; (3)

chemical vapor deposition (CVD) of graphene on metal substrate [3.19-3.25]; (4)

reduction of graphene oxide [3.26-3.28] and (5) liquid-phase exfoliation of

graphite powder using ultrasonication [3.29-3.32].

Graphene films synthesized by micromechanical exfoliation of HOPG possess

the highest quality in terms of purity, defects level and crystallinity. The high

quality graphene films obtained via this method exhibit many important electrical


87

and optical properties, such as the ultrahigh room-temperature carrier mobility (~

10,000 cm2V-1s-1) [3.2]; room temperature quantum Hall effect [3.4]; and giant

third-order optical nonlinearity demonstrated by Four-Wave-Mixing

measurements [3.8], and so on. However, they have a disadvantage with regard to

their limited size (around few tens of micrometers). Furthermore, the low yield

and throughput of this method indicates that it is impractical for large-scale

applications.

Another method for producing high-quality graphene films is through thermal

decomposition of SiC surface at high temperatures [3.9-3.18]. Epitaxial graphene

films grown via this method are demonstrated to exhibit high purity, low defect

level and high crystallinity. As a result, high low-temperature carrier mobility

comparable to the exfoliated graphene has been demonstrated in such epitaxial

graphene films [3.13]. Compared to the small size exfoliated graphene, epitaxial

graphene synthesized via this technique offers the advantage of scalability with

size ~ 1 cm. However, both the requirement of expensive SiC substrate and

incapability to change substrate have greatly limited its real applications.

Reducing exfoliated graphene oxide is one of the productive and

cost-effective synthesis methods for graphene [3.26-3.28]. However, because the

existing reduction methods cannot remove many structural defects and various

functional groups introduced in the synthesis process, graphene films prepared via

this method exhibit low quality with disrupted band structure and degraded

electronic properties.


88

To address the problems induced by the oxidation and reduction processes in

the above method, another productive and cost-effective synthesis technique for

graphene has been developed, which utilizes liquid-phase exfoliation of graphite

powder with ultrasonication [3.29-3.32]. Both the exfoliation and stabilization of

graphene in this method are carried out using special solvents of surfactants, and

almost no oxidation or defect formation is introduced. However, graphene flakes

prepared by this method still suffer from several problems, including the small

size (around several micrometers); the layer number inconsistency and the

influence from the solvent.

Chemical vapor deposition (CVD) opens an attractive route to large-scale

production of high-quality graphene films [3.19-3.25], which provides the merits

of cost effectiveness, absence of intense mechanical or chemical treatment and

convenience of deterministic placement of graphene films on pre-defined

positions on a substrate of choice. Utilizing this synthesis technique, large area

graphene films with size about several centimeters or even larger and high quality

can be obtained [3.19-3.22]. Large area CVD graphene based electrical devices

have also been successfully demonstrated [3.21, 3.22]. The advantages of

large-scale production, low cost and relatively high quality make CVD a

promising method for synthesizing graphene films for practical applications.

Table 3.1 summarizes the advantages and disadvantages of the above

presented synthesis methods of graphene. We can conclude that CVD method is

the most promising method for real applications. Consequently, we choose


89

CVD-grown graphene films as the research targets in this dissertation.

Table 3.1 Advantages and disadvantages of various graphene synthesis methods

Graphene synthesis

methods Advantages Disadvantages

Micromechanical

exfoliation

Highest quality

Cost-effective Limited size ~ Tens of m

Epitaxial method High quality

Large scale ~ 1 cm

Expensive

Incapable to change substrate

Reduction of GO Productive

Cost-effective

Low quality

Disrupted band structure

Degraded electronic property.

Liquid-phase exfoliation

of graphite powder

using ultrasonication

Productive

Cost-effective

Small size ~ few m

Layer number inconsistency

Influence from the solvent.

CVD

Productive

Cost-effective

Large size ~ few cm

Relatively high quality

Moderate crystalline quality

compared to the 1st and 2nd

methods, but much better

than the 3rd

and 4th methods.

The CVD graphene films investigated in this dissertation were prepared by

our collaborator Dr. Wang Yu in the Institute of Process Engineering, Chinese

Academy of Sciences, China. Large-area (0.8 × 1.0 cm2), both mono-layer and

5-layer graphene films were synthesized in a thermal CVD furnace (Thermo

Scientific™ Lindberg/Blue M™ Mini-Mite™ Tube Furnaces, TF55035C-1) using

thermally annealed copper foil as substrate [3.20-3.22]. Subsequently, the normal

wet-transfer technology [3.20-3.22] was applied to transfer the as-synthesized

CVD graphene films onto quartz substrates. The 5-layer CVD graphene films

were also stacked sequentially in order to obtain 10-, 15-, or 20-layer

superimposed graphene films. Figure 3.1 depicts photos of the CVD-grown


90

mono-, 5-, and superimposed 10-, 15-, 20-layer graphene films on quartz substrate

at a larger scale. The characterization for these CVD graphene films will be

described in detail in the following sections.

Figure 3.1 Larger-scale optical images of mono-, 5-, and superimposed 10-, 15-,

20-layer graphene films on quartz substrate. (a) Monolayer graphene on quartz; (b)

5-layer graphene on quartz; (c) superimposed 10-layer graphene on quartz; (d)

superimposed 15- and 20-layer graphene on quartz.

3.2 Characterization of the CVD-grown graphene films

3.2.1 Introduction

We have applied following experimental techniques: (i) optical microscopy, (ii)

micro-Raman spectroscopy, (iii) reflection contrast spectroscopy, and (iv)

UV-VIS-NIR 1PA spectroscopy to characterize the fundamental properties of

these CVD graphene films. These characterizations are aimed to the evaluation of

homogeneity, number of layers, crystallinity, density of defect states and

interlayer coupling. Because the graphene films have a large size of ~ 8 × 10 mm2,

we randomly selected 10 areas of 1 × 1 mm2 on each film for micro-Raman

spectroscopy, reflection contrast spectroscopy and UV-VIS-NIR 1PA

spectroscopy measurements to ensure their spatial uniformity (for 15-layer

(a) (b)

(c) (d)

Superimposed

15 layers

Superimposed

20 layers


91

graphene film, 6 areas were selected due to its relatively smaller size).

3.2.2 Optical microscopic characterization for homogeneity

A Nikon Eclipse Ti optical microscope with a 50 objective lens and a colour

camera was applied to examine the homogeneity of the CVD-grown graphene

films on quartz substrate. As examples, the optical microscope images which

were zoomed on the edge of the mono-, 5- and 10-layer graphene films were

displayed in Figure 3.2 (a), (b) and (c), respectively. All these images clearly

illustrate the continuous smoothness of the CVD graphene films.

Figure 3.2 (a), (b) and (c) show the optical microscopic images of the single-, 5-

and 10-layer graphene films on quartz, respectively.

The edge between

graphene film and

quartz

The edge between

superimposed

graphene stacks

10 m

(b)

10 m

(a)

10 m

(c)


92

3.2.3 Micro-Raman spectroscopic characterization for

crystallinity, density of defect states, layer number and

interlayer coupling

Raman spectroscopy is a technique which detects the inelastic scattering of

monochromatic laser light in the visible, near infrared or near ultraviolet range

from a material. The interaction between the incident laser photons and the

phonons (vibrations) or other low-frequency modes in the material generates

Raman signals, which provides insight into the vibration modes in the material.

Figure 3.3 illustrates a typical energy diagram of the Raman scattering process.

Figure 3.4 shows the schematic illustration of the experimental setup in a typical

Raman spectrometer. The reflected light from the sample is collected by the

objective lens and then directed to a long-pass filter to remove the excitation laser

beam which comes from the elastic Rayleigh scattering. The remaining pure

Raman signal is focused by an optical focal lens and then sent through a

monochromator which is coupled to an appropriate detector (CCD or PMT).

Figure 3.3 Schematic illustration of a typical energy diagram of the Raman

scattering process.

Excited state

Vibrational energy levels

Ground state

Vibrational energy levels

Virtual states

Rayleigh

Scattering

Stokes

Scattering


93

Figure 3.4 Schematic illustration of the experimental setup in a typical Raman

spectrometer

In this dissertation, we employed a micro-Raman spectrometer (WITec

Alpha300 R) with excitation laser wavelength at 532 nm and a 50 objective lens

to measure the Raman spectra of the CVD-grown graphene films on quartz

substrate. The focused laser spot size on the sample was around 1 m in diameter.

In order to ensure the spatial uniformity of our graphene films which have large

size of ~ 8 × 10 mm2, we selected 10 areas of 1 × 1 mm2 on each graphene film

and focused on their centers for micro-Raman inspection. These areas were also

utilized for the linear and nonlinear optical absorption measurements described in

the following sections and chapters. No significant difference in these acquired

Raman spectra was found, which indicated high spatial uniformity in our

graphene films.

Figure 3.5 shows the measured Raman spectra of monolayer, 5-layer and

superimposed 10-, 15-, 20-layer graphene films. In Figure 3.5 (a), a representative

micro-Raman spectrum of the monolayer graphene on quartz is illustrated by the

Laser

Sample

Monochromator CCD Mirror

Dichroic mirror

Objective lens

Long-pass

filter

Focal lens


94

black curve. In which, two primary features are pronounced, including (i) a G

peak located at ~ 1580 cm-1 corresponding to the in-plane optical vibration

(degenerate zone center E2g mode) and (ii) a 2D peak located at ~ 2700 cm-1

induced by the second-order zone boundary phonons. Both results are close to the

reported values [3.19-3.22, 3.33-3.36]. In addition, the peak intensity ratio

between 2D and G peaks I2D/IG of the Raman spectrum is found to be ~ 2.1 and

the full width at half-maximum (FWHM) of the symmetric 2D band

(single-Lorentzian profile as shown in the bottom inset of Figure 3.5 (a)) is ~ 32

cm-1. These two features support that the graphene is a single layer as reported

before [3.19-3.22, 3.33-3.36]. The disorder-induced D peak (at ~ 1350 cm-1) is

absent in the Raman spectrum of such single-layer graphene, which indicates very

low defect density and very high crystalline quality in this monolayer graphene

film as in Ref. [3.33, 3.37].

Similar to previous reports [3.19-3.21, 3.34-3.36] on the Raman spectra of

CVD graphene, an increase in G peak and also a decrease in 2D peak as

demonstrated by the red curve in Figure 3.5 (a) indicate the formation of

multilayer graphene. Furthermore, in the Raman spectrum shown by the red curve,

the 2D to G peak intensity ratio I2D/IG decreases to ~ 0.45 < 1 and the FWHM of

the symmetric 2D band (single-Lorentzian profile as shown in the top inset of

Figure 3.5(a)) increases to ~ 70 cm-1, revealing the layer number of the graphene

film should be larger than three [3.19-3.21, 3.34-3.36]. This finding is consistent

with the experimental data acquired in the optical reflection contrast spectroscopy


95

and the NIR 1PA spectroscopy measurements as demonstrated below. The exact

layer number of this multilayer graphene is determined to be 5 by the combination

of the micro-Raman spectra result, optical reflection contrast spectra result and

the NIR 1PA spectra result.

Figure 3.5 (a) shows the micro-Raman spectra of the monolayer (black) and

5-layer (red) graphene films on quartz; and (b) displays the micro-Raman spectra

of the 5-layer (black), 10-layer (red), 15-layer (blue), and 20-layer (dark cyan)

graphene films on quartz.

A weak disorder-induced D peak appears in the 5-layer graphene film, the

intensity ratio between D and G peaks ID/IG is only ~ 0.09 < 0.1, indicating both

high crystalline quality and low density of defects [3.19-3.22, 3.34-3.36]. Despite

its multilayer nature, however, we did not observe the multi-peaked and

"shouldered" 2D peak in the Raman spectra of the 5-layer graphene film, which

(a)

(b)


96

results from strong interlayer coupling and is the hallmark of

HOPG-mechanically exfoliated multilayer graphene films [3.33, 3.34, 3.37-3.39].

Furthermore, as demonstrated by the top inset of Figure 3.5(a), the 2D peak

shows a single-Lorentzian line shape. These experimentally observed features

support that in the 5-layer graphene film, interlayer coupling is very weak and can

be neglected [3.19, 3.34, 3.37]. The 5-layer graphene film resembles the

multilayer turbostratic graphene with turbostratic random stacking [3.34, 3.40,

3.41]. Consequently, such 5-layer graphene film exhibits electronic properties

similar to those of a monolayer graphene [3.19, 3.34, 3.37, 3.40-3.42]. In addition,

similar to the previously reported Raman spectra on CVD-grown multilayer

graphene [3.19-3.22, 3.34-3.36] and turbostratic graphite [3.43], its 2D peak has a

slight up-shift (~ 20 cm-1) relative to that of the monolayer graphene, further

demonstrating the insignificance of interlayer coupling.

In Figure 3.5(b), we compare the micro-Raman spectra of 5-layer graphene

film and the superimposed 10-, 15-, and 20-layer graphene films. As the 5-layer

graphene films are stacked sequentially [3.21, 3.22, 3.36], the intensities of the G-

and 2D-band peaks increase, but no significant change in the intensity ratios

between G and 2D peaks is found. These observed features are similar to the

previous report on CVD graphene [3.22], and support that between the stacked

5-layer graphene films there is nearly-zero interlayer coupling. Therefore, the

electronic properties of the superimposed 10-, 15-, and 20-layer graphene films

are also similar to those of a monolayer graphene [3.22, 3.42, 3.44].


97

3.2.4 Optical reflection contrast spectra for characterization

of layer number

In order to quantitatively determine the layer number of the CVD-grown

multilayer graphene films, we applied the optical reflection contrast spectroscopy

[3.45, 3.46]. In the optical reflection contrast spectroscopy, the optical reflection

spectra from the bare substrate R0() and from the graphene film on substrate R()

are acquired to study the thickness of the graphene films. Based on the Fresnel’s

equations [3.45-3.47], the optical reflection contrast spectra C() which represents

the reflectance difference induced by the presence of graphene film can be

utilized to directly determine the thickness of the graphene film. The contrast

spectra, C(), is defined by [3.45, 3.46]:

C(λ) =R0(λ) − R(λ)

R0(λ) (3.1)

It has been reported [3.48, 3.49] that the contrast spectra for multilayer graphene

films on quartz substrate are nearly flat in the spectral range of 450-600 nm and

the contrast values are around N (-0.068) for these multilayer graphene films. N

is the graphene layer number and N = 1, 2, ..., to 10.

In this dissertation, we measured the optical reflection spectra R0() from bare

quartz substrate and R() from our graphene films on quartz substrate through

utilizing an optical microscope (Nikon Eclipse Ti), a white light source (tungsten

halogen lamp) and a spectrometer (Avaspec-2048-SPU). A 50× objective lens

with a numerical aperture of 0.80 was used and the spot size of the focused

incident light on the sample was estimated to be ~ 1.5 µm determined by a


98

scanning edge method [3.50]. The reflected light was collected by using

backscattering configuration. Similar to our micro-Raman spectra measurements,

we acquired the optical reflection contrast spectra on the centres of the selected 10

areas of 1 × 1 mm2 on each graphene film and no significant difference between

them was found.

In Figure 3.6, we showed the acquired optical reflection contrast spectra of the

5-layer and 10-layer graphene films on quartz substrate in the spectral range of

450-600 nm as examples. As in Refs. [3.48, 3.49], these contrast spectra were

nearly flat in this spectral range. Moreover, we compared our measured contrast

values (-0.32 and -0.65) to the reported results in Ref. [3.48, 3.49] and the layer

numbers of these graphene films were determined to be 5 and 10, respectively.

This result is consistent with the conclusion of the micro-Raman spectra

measurements in Section 3.2.3 and also agrees with experimental data acquired in

the NIR 1PA spectra measurements in the next section. In the following section,

the 1PA spectra of the mono-, 5- and 10-layer graphene films on the quartz were

measured and the obtained spectra were shown in the Figure 3.7. It was known

that monolayer graphene should absorb an amount of 2.3% of incident light

power across the NIR spectral region [3.5, 3.6]. Therefore, we obtained the

number of graphene layers by taking into account the percentage of absorbed NIR

light power in these graphene films and considering each graphene layer in the

films behaved like a monolayer. We found the acquired layer numbers of the


99

investigated graphene films were in agreement with the results from the

above-said optical reflection contrast spectroscopy.

Figure 3.6 Optical reflection contrast spectra of the 5- and 10-layer graphene

films on quartz.

3.3 1PA of graphene in the UV-VIS-NIR spectral range

3.3.1 Introduction

1PA spectroscopy is a technique which characterizes the interaction between

relatively low intensity light and the material by measuring the absorption as a

function of light frequency. In 1PA, each electron in the ground state of the

material absorbs the energy of one photon and is then excited to a higher-energy

level (excited state). Therefore, density of states of the related transition energy

levels determines the amplitude of the 1PA at a specific frequency. And the

electronic structure of the investigated material can be characterized by the 1PA

spectrum.

1PA measurements on graphene have been reported in Refs. [3.5, 3.6], which

revealed that monolayer graphene film absorbed a fraction of = 2.3% of the

incident light power across the NIR and Short-wavelength infrared spectral


100

regions (from 0.5 eV – 1.2 eV), where = e2/ ħc ≈ 1/137 is the fine structure

constant. Such spectrally flat 1PA was attributed to graphene’s unique electronic

structure and was further confirmed by the theoretical calculations based on the

independent particle theory [3.51-3.53], which considered only the optical

transitions near the Dirac point (K point). In addition, studies in Refs. [3.54-3.56]

both theoretically and experimentally demonstrated that strong optical transitions

around the saddle point due to the divergent density of states at such a van Hove

singularity and electron-hole interactions around the saddle point could lead to the

excitonic Fano resonance feature in the 1PA spectra of graphene in the visible and

UV spectral regions. In the THz spectral range, Drude-model-like frequency

dependence was observed for the 1PA spectra of graphene resulting from the

intraband transitions [3.57].

3.3.2 1PA of graphene enhanced by the excitonic Fano

resonance in the UV-VIS spectral range

We measured the UV-VIS-NIR 1PA spectra of the graphene films by

utilization of the SHIMADZU UV-3600 UV-VIS-NIR spectrophotometer. The

spectral resolution of the utilized SHIMADZU spectrophotometer is 0.1 nm and

its measureable spectral range is from 185 nm to 3300 nm. The light beam in the

spectrometer was at normal incidence to the graphene samples. By inserting an

extra iron plate with a 1-mm-diameter aperture into the beam path of the

spectrophotometer, we acquired the 1PA spectra at the previously–mentioned 10

locations on each graphene film and found no significant difference,


101

demonstrating high spatial uniformity of the graphene films. We conducted the

calibration for the measured 1PA spectra of graphene films by subtracting the

1PA spectrum of a blank quartz slide from all the measurements.

Figure 3.7 presents the 1PA spectra of mono-, 5- and 10-layer graphene films

on quartz substrate and the associated theoretical modellings. As for the

monolayer sample, Figure 3.7(a) shows a resonance peaked at Eexp ≈ 4.65 eV. The

ab initio GW calculation predicted that the band-to-band transition energy, EGW, at

the M-point of E-k diagram should be 5.2 eV for mono-layer graphene [3.54, 3.58,

3.59]. Our measurement reveals a redshift (EGW - Eexp = 0.55 eV). In addition,

Figure 3.7(a) shows an asymmetric line shape with higher absorption on the low

energy side. Both these features unambiguously indicating the interaction

between excitonic transitions and band-to-band transitions in the graphene film

were reported in detail in Refs. [3.54-3.56]. We compare our measured 1PA

spectrum of monolayer graphene with the previous report [3.56] in which

graphene films were prepared by mechanical exfoliation of graphite and then

deposited on SiO2 substrate. As shown in Figure 3.7(a), good agreement can be

found, showing no difference between the CVD-grown and

mechanically-exfoliated graphene on substrate. Note that the optical conductivity

reported in Ref. [3.56] was converted to the absorbance by multiplying 4/c.


102

Figure 3.7 (a) Comparison between the measured 1PA spectra of CVD-grown

monolayer graphene on quartz substrate and that of micromechanically exfoliated

monolayer graphene on SiO2 substrate in Ref. [3.56]; (b) and (c) theoretical

modeling of Fano resonance based on the ab initio GW calculation and JDOS

method to fit the measured 1PA spectra of the monolayer graphene; and (d) the

1PA spectra of 5- and 10-layer graphene on quartz substrate and the

corresponding theoretical modeling with JDOS method.

Figure 3.7 also includes our theoretical modeling explained in the following

steps. First, without considering the interference with exciton, we adopted the ab

initio GW calculation published in Ref. [3.54] for the unperturbed band-to-band

1PA, Acont(). In Figure 3.7(b), we reproduced the ab initio GW calculation

convoluted with a Lorentzian broadening of 250 meV by Mak et al [3.56]. Second,

considering the interference between unperturbed band-to-band 1PA and exciton,

we calculated the resultant 1PA spectrum near (and at) the saddle point by [3.56]:

2

2

( )( ) ( )

1cont

qA A

(3.2)


103

where = (ħ -Eres)/(/2) is the normalized energy by width relative to the

resonance energy Eres of the perturbed exciton, and q2 denotes the ratio of the

strength of the excitonic transition to the unperturbed band-to-band transition. As

indicated by the red line in Figure 3.7(b), excellent agreement between Eq. (3.2)

and our measurement can be obtained by using q = -1, Eres = 5.02 eV, and = 780

meV. These parameters are consistent with those utilized by Mak et al [3.56].

Third, we also employed the JDOS method [3.60] to quantify the optical

transitions near the saddle-point (or M-point) singularity. By neglecting the

interband transitions near the K-point (or Dirac point) of E-k diagram, the JDOS

method has an advantage of being simpler in comparison with the ab initio GW

calculation, because it can show that Acont() has an explicit form, (-ln|1-ħ/E0|),

instead of numerical results, for the unperturbed band-to-band transition [3.60].

By taking E0 = 5.20 eV and a Lorentzian broadening width of 400-meV in the

convolution of -ln|1-ħ/E0|, accounting for the broadening effect, we calculated

the resultant spectrum, as shown by the cyan line in Figure 3.7(c). By taking Eq.

(3.2) and applying the fitting parameters in Ref. [3.56], we produced the magenta

line in Figure 3.7(c). This theory is also in good agreement with the experiment

near the M-point singularity in the spectral range (3.0 - 5.5 eV). And the

discrepancy in the range of ħ < 3.0 eV is expected due to the assumption that the

interband transitions near the K-point are totally ignored.

Similar conclusions can be drawn from both the 5- and 10-layer graphene films

in Figure 3.7(d). The larger widths ( = 950 meV and 1150 meV for the 5- and


104

10-layer films, respectively) were required for the best fit, indicating shorter

exciton lifetimes in these graphene samples. This is attributed to the relatively

higher density of defects in these films, as evidenced by their Raman spectra

demonstrated in Figure 3.5, where relatively stronger D peaks in comparison to

the monolayer sample were observed.

3.4 Conclusion

First, by utilizing the CVD method with thermally annealed copper foil as

substrate, both monolayer and 5-layer graphene films with large-area of ~ 0.8 ×

1.0 cm2 were synthesized in a thermal CVD furnace. Such monolayer and 5-layer

graphene films were then transferred onto quartz substrates using normal

wet-transfer technology. Furthermore, 10-, 15-, and 20-layer superimposed

graphene films were obtained by stacking the 5-layer graphene films.

Secondly, we employed micro-Raman spectroscopy to characterize the

crystallinity, density of defect states and interlayer coupling of the synthesized

graphene films on quartz. Moreover, we applied the combination of the optical

reflection contrast spectroscopy, micro-Raman spectroscopy and NIR 1PA

spectroscopy to determine the exact layer numbers of the multilayer graphene

films. The spatial uniformity (or homogeneity) of these graphene films was

examined by the optical microscopy, and the above-mentioned three

spectroscopic techniques. The characterization results demonstrated that the

CVD-grown graphene films utilized in this dissertation possessed high spatial


105

uniformity (homogeneity) with well-defined number of layers, high crystallinity

and low density of defects, and nearly-zero interlayer coupling.

Finally, the measured 1PA spectra of the synthesized graphene films on quartz

in the UV-VIS-NIR spectral range demonstrated excitonic Fano resonance feature,

which could be explained by the cooperative effects of the strong optical

transitions and the electron-hole interactions around the saddle point, similar to

previous reports [3.54-3.56]. Through applying both theoretical modellings based

on the ab initio GW calculation [3.54-3.56] and the JDOS method [3.60] to fit our

experimental results, we found: (i) the theoretical modelling based on ab initio

GW calculation can well fit the experimental data over the whole studied spectral

range; (ii) the modelling based on JDOS method is in good agreement with the

experimental result near the M-point singularity in the spectral range of 3.0 - 5.5

eV and cannot fit to the experimental data in the range of ħ < 3.0 eV, since it

ignores the contribution from the interband transitions near the K-point. Therefore,

both theoretical modellings based on the ab initio GW calculation and the JDOS

method can well explain the excitonic Fano resonance feature in the measured

1PA spectra of graphene near the saddle point. Since the JDOS method has the

advantage of being much simpler than the ab initio GW calculation and can

provide explicit forms for both the 1PA and two-photon absorption (2PA)

[3.60-3.62] near the saddle point, the theoretical modeling based on JDOS method

is preferred to analyze both the 1PA and 2PA spectra near the saddle point. In

Chapter 4, we will take this advantage to study 2PA spectrum in graphene.


106

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112


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Chapter 4 2PA and 1PA saturation of graphene in the visible range

113

Chapter 4

Two-photon absorption and one-photon absorption

saturation of graphene in the visible spectral range

4.1 Introduction

The interaction between graphene and femtosecond laser pulses is of

relevance to many practical applications in photonics and optoelectronics. One of

the successful applications is that saturation in interband transitions induced by

one-photon absorption (1PA) in graphene has been utilized for mode-locking

technology [4.1-4.5]. In which, graphene is used as an effective saturable absorber

for generating ultrashort laser pulses because of its efficient photo-excited carrier

dynamics that were confirmed by experimental measurements [4.6-4.11] and

underpinned by theoretical modeling [4.12-4.15]. Although 1PA saturation in

graphene have been intensively studied [4.3, 4.5, 4.12-4.17], it should be pointed

out that the previous studies, either experimental or theoretical, focused on the

light intensity dependence of absorption saturation in graphene at wavelengths of

800 nm and 1550 nm. Little is known about its spectral dependence which is

desirable for both realistic applications and fundamental understanding, except for

the theoretical estimation by Vasko [4.12], and a recent experimental report [4.17].

In Ref. [4.12], the saturation intensities of graphene at photon energies of ћω ≈

0.12, 0.8 and 1.5 eV has been theoretically calculated by Vasko. However, his

theoretical results underestimated the thresholds, because the Coulomb-scattering


114

was completely neglected in the calculations. Coulomb-scattering has been

recently demonstrated to be an important underlying mechanism for interband

1PA saturation in graphene at high photo-carrier densities by Winzer, et al [4.15].

In Ref. [4.17], 1PA in epitaxial graphene has been observed in the spectral range

from 0.03 to 0.245 eV (or, from 5 to 41 µm) and its quadratic photon energy

dependence has been established in a phenomenological way. But until now, no

investigation has been performed on the spectral dependence of 1PA saturation in

graphene in the spectral range from visible to near-infrared (NIR). Furthermore,

all the above reports except the study in Ref. [4.16] have ignored the presence of

two-photon absorption (2PA). It has been experimentally confirmed that 2PA

plays an important role in saturable absorber mirrors made of InGaAs quantum

wells [4.18]. The theoretical simulations have showed that the presence of 2PA

has a significant impact on the stability of continuous-wave, mode-locking

operation [4.18].

Interestingly, apart from 1PA saturation, two-photon-induced interband

transitions in graphene also have potential for photonic applications. In Ref.

[4.19], coherent control and noncontact generation of ballistic photocurrents in

multilayer epitaxial graphene at wavelengths of 3.2 m / 1.6 m and 4.8 m / 2.4

m have been demonstrated by utilizing the quantum interference between one-

and two-photon-induced interband transitions. Utilizing such a noncontact method

for generating electrical currents can overcome the difficulty of making reliable

contacts for future graphene-based electronic devices, which have drawn


115

intensive research interest [4.20-4.22] due to the superior electron transport

properties of graphene [4.23-4.25]. Moreover, such a method eliminates the

parasitic effects due to electrical contacts on graphene in potential applications.

Therefore, 2PA is of importance to graphene photonics and optoelectronics.

From the fundamental point of material properties, 2PA of graphene has not

been systematically investigated in the visible spectral region. Previously Yang et

al demonstrated, both theoretically and experimentally, that 2PA is as important

as 1PA saturation in AB-stacking bilayer epitaxial graphene in the NIR spectral

range [4.16]. In the report, only the optical transitions near the Dirac point (K

point) were considered in the theoretical calculation, and no significant

contributions from the optical transitions around the saddle point (M point) of

graphene was experimentally observed in this NIR spectral range. Strong optical

transitions around the saddle point due to the divergent density of states at such a

van Hove singularity and electron-hole interactions around the saddle point have

been demonstrated to lead to the excitonic Fano resonance feature in the 1PA

spectra of graphene in the visible (VIS) and ultraviolet (UV) spectral region, both

theoretically [4.26] and experimentally [4.27, 4.28]. Such effect has also been

observed in our 1PA spectra measurements on the synthesized CVD graphene

films on quartz in the UV-VIS spectral range, as demonstrated in Chapter 3

Section 3.3. There, we have also introduced a much simpler theoretical modelling

based on the joint density of states (JDOS) method [4.29] (compared to that based

on the ab initio GW calculation [4.27, 4.28]) to fit the experimental results, since


116

the JDOS method can provide explicit forms for the 1PA (also for the 2PA) near

the saddle point. And we have found such modelling could well fit the

experimental data near the saddle point singularity in the spectral range of 3.0 -

5.5 eV, despite its simplicity. Recently, strong third-harmonic generation (THG)

has been demonstrated in CVD-grown monolayer graphene at photon energy in

three-photon resonance with the exciton-shifted van Hove singularity at the

saddle point of graphene [4.30]. All these reports lead us to speculate that the

excitonic Fano resonance should be anticipated in the 2PA spectrum of graphene.

Up to date, however, no such investigations have been carried out. Moreover,

recently Hanczyc el al. [4.31] have successfully demonstrated the interestingly

large 2PA and multiphoton absorption properties of amyloid protein fibres in

experiment. And they further proposed that the cooperative effects due to

excitonic interactions [4.32] could efficiently enhance the 2PA and multiphoton

absorption in the amyloid protein fibres. In all, all these have drawn us to study

the excitonic Fano resonance effect on the 2PA spectrum of graphene.

Here, we present our unambiguous determination of interband 2PA and 1PA

saturation in high-quality, CVD-grown graphene films over the NIR and visible

spectral range (435-1100nm) using Z-scan technique with femtosecond laser

pulses. First of all, we systematically study the interband 2PA of graphene in the

visible spectrum (435-700 nm) and report our observation of 2PA enhanced by

the excitonic Fano resonance at the saddle point of graphene. Based on the

second-order, time-dependent perturbation theory, we develop a semi-empirical


117

model in which interband transitions among three states near the saddle point of

graphene are taken into consideration, together with interference between

band-to-band transitions and excitons. We find that the model is in agreement

with the photon-energy dependence of the observed 2PA spectrum with a scaling

factor of B = (1~5) × 102 cm/MW/eV5. Our results verify, for the first time, that

excitonic Fano resonance plays an important role for the 2PA of graphene in the

visible spectrum. The resultant 2PA coefficients of graphene in the visible

spectral range no longer follow the -4 scaling law ( is the photon angular

frequency) as predicted before [4.16]. And their magnitudes are comparable to

that in the NIR spectral region, making graphene a broadband two-photon

absorber. The obtained 2PA coefficients of graphene in the visible spectrum are

around 600 cm/GW, which is about 2 orders of magnitude larger than the typical

semiconductors like ZnO, CdS and ZnS whose 2PA coefficients in the visible

spectral range are less than 5 cm/GW [4.33, 4.34]. In addition, it is the first time

that 2PA spectrum has been characterized in the large-scale, high-quality and

relatively cheap CVD-grown graphene compared to the previously utilized

expensive epitaxial graphene, which is of direct relevance to practical

applications.

As for interband 1PA saturation of graphene, our data revealed a quadratic

photon energy dependence of 1PA saturation in graphene in the investigated

spectral region (435-1100 nm). This could be explained by the linear dependence

of density of state on energy in graphene combined with its linear increase of


118

carrier scattering rate out of the excited state with increasing energy, similar to the

previous report [4.17] in the infrared spectral range (5 - 41 µm).

This Chapter is organized in the following way. Section 4.2 details our

open-aperture Z-scan measurements on CVD graphene and the related theoretical

data analyses. Section 4.3 demonstrates the experimentally obtained 2PA

spectrum of graphene in the visible range enhanced by the excitonic Fano

resonance, and presents our theoretical modelling based on the second-order,

time-dependent perturbation theory. Section 4.4 reports the measured 1PA

saturation intensities in the NIR and visible spectral range, and compares our

findings to other reports. Section 4.5 provides a conclusion.

4.2 Open-aperture Z-scan measurements on CVD graphene

and the related theoretical data analyses

To investigate both 2PA and 1PA saturation of graphene in the NIR and visible

spectral range, we performed the open-aperture Z-scan measurements [4.35] on

the CVD-grown graphene films. The operational principles and theoretical data

analyses method of the open-aperture Z-scan have been detailedly introduced in

Chapter 2. Moreover, characterization and 1PA measurements of the CVD-grown

graphene films utilized in this chapter have been detailed in Chapter 3.

The excitation laser pulses (1 kHz, 435-1100 nm, pulse width ~ 150 fs, exact

duration depends on laser wavelength) were employed and all the open-aperture

Z-scan measurements were carried out at room temperature. Our open-aperture

Z-scan set-up was used previously [4.16]. As displayed in Figure 4.1(a), in the


119

present Z-scans, the laser pulses were focused on the sample using a lens of

15-cm focal length and the beam waist radius of the focused laser beam was in the

range from 25 2 to 35 3 µm, depending on the laser wavelength used and the

size of an aperture placed before the lens. The set-up was calibrated by using

slabs of wide-gap semiconductors (like CdS and ZnS). The transmitted laser pulse

energies were monitored while translating the graphene sample along the

propagation direction of the laser pulses (z-axis) through the focus with a linearly

motorized stage.

Figure 4.1 (a) Schematic open-aperture Z-scan set-up; and (b) open-aperture

Z-scans on the 10-layer sample measured at a maximum on-axis irradiance (I00 at

z = 0) of 4.0 ± 0.5 GW/cm2. The symbols are the experimental data and the solid

curves are the numerical simulations based on Eq. (4.1). The z position is

normalized to z0 which is the Rayleigh range.

(b)

Reference

Detector

Femtosecond

Laser

Pulses

Z

Signal

Detector

(a)

Aperture


120

In order not to cause laser-induced damage in the graphene samples, the

maximum on-axis irradiance (I00 at z = 0) of the laser pulses for all the Z-scans

reported here was controlled to be in the range of 0.4 ~ 20 GW/cm2. No damage

was induced by laser illumination during the Z-scans performed in this intensity

range. Since the laser-induced damage on the sample would result in the

asymmetry of Z-scan traces [4.36] due to the irreversible nature of the damage, it

can be excluded from the symmetry and repeatability of the obtained Z-scan

traces, as demonstrated in Figures 4.1(b), 4.3 and 4.5. The Z-scans on the

monolayer graphene sample at 800 and 535 nm as demonstrated by Figures 4.2,

show the signal-to-noise ratio is less than 2 even under the maximum intensity of

20 GW/cm2 and less than 1 when intensity 10 GW/cm2. Hence, the 2PA cannot

be accurately determined from the monolayer graphene sample. In order to

enhance the Z-scan signal and to have Z-scan signal reasonably larger than the

experimental error, we used 5-, 10-, 15- and 20-layer graphene samples which

have nearly-zero interlayer coupling and electronic properties similar to that of

monolayer graphene (as demonstrated by the micro-Raman spectra measurements

in Chapter 3), for the Z-scan measurements. The results are shown in Figures 4.1

(b), 4.3 and 4.5. Specifically, Figures 4.1(b) and 4.3 display the Z-scans on

10-layer graphene sample at the selected wavelengths in the range from 435 to

1100 nm, from which 2PA spectrum was determined. And Figure 4.5 shows

Z-scans on 5-, 10-, 15- and 20-layer graphene samples at 800 and 535 nm,

demonstrating the layer number independence of mono and Is (The definition of


121

mono and Is will be introduced in the theoretical data analyses part). These Z-scans

show larger signal-to-noise ratios. Therefore, the superimposed two 5-layer (or

10-layer) graphene film was utilized to study the spectral dependence of 2PA and

1PA saturation.

Figure 4.1(b) displays Z-scans recorded at wavelengths from 435 to 1100 nm

on the 10-layer graphene sample under a maximum on-axis irradiance (I00 at z = 0)

of 4.0 ± 0.5 GW/cm2. As the sample was scanned along the z-axis through the

focus with the incident laser pulse energies being kept at a constant level, the

sample experienced various laser irradiances I(z) at different z-positions, giving

rise to corresponding changes in the sample transmission if the sample absorbs

light nonlinearly. More data measured on graphene samples with different layer

numbers and at various values of I00 are also available. Figure 4.3 demonstrates

the measured Z-scans (colored symbols) on the 10-layer graphene film on quartz

at selected wavelengths in the range from 435 to 1100 nm and with various peak

intensities (I00) of the excitation laser pulses. Figure 4.5 illustrates the Z-scans

(colored symbols) acquired at 800 and 535 nm on the 5-, and superimposed 10-,

15- and 20-layer graphene films. From these Z-scans, we obtain their

corresponding plots of normalized transmittance change ΔT/T0 at z = 0 as a

function of I00. The black symbols in Figure 4.4 are the corresponding plots of

normalized transmittance change ΔT/T0 vs. I00 obtained from the Z-scans in

Figure 4.3. Similarly, plots of normalized transmittance change ΔT/T0 vs. I00

corresponding to the Z-scans in Figure 4.5 are demonstrated in Figure 4.6.


122

Figure 4.2 (a, b) Open-aperture Z-scans on the monolayer graphene sample at

800 and 535 nm, respectively. The symbols are the experimental data at various

values of I00. The green lines are Z-scans on quartz substrate at I00 = 20 GW/cm2.


123

Figure 4.3 Z-scans on the 10-layer graphene sample at selected wavelengths

in the range (a) from 1100 to 640 nm and (b) from 575 to 435 nm. The

symbols are the experimental data at various values of I00. The solid curves are

the theoretical fits based on Eq. (4.1). The green lines are Z-scans on quartz

substrate at I00 = 20 GW/cm2.

Figure 4.4 Plots of ΔT/T0 vs. I00 at z = 0. The symbols are the experimental data

at various values of I00. The solid and dashed curves are the modeling with 𝛽 ≠ 0

and = 0, respectively.


124

Figure 4.5 Open-aperture Z-scan measurements on the 5- and superimposed

10-, 15- and 20-layer CVD-grown graphene films on the quartz substrate at

800 and 535 nm. The symbols are the experimental Z-scan data at various values

of I00. The solid curves are the theoretical fits based on Eq. (4.1). The green lines

are Z-scans on quartz substrate at I00 = 20 GW/cm2.

Figure 4.6 Plots of ΔT/T0 (at z = 0) vs. I00 corresponding to the Z-scan

measurements in Figure 4.5. The symbols are the experimental data at various

values of I00. The solid and dashed curves are the modeling with and without the

term of two-photon absorption, respectively.


125

Both measured Z-scans and plots of ΔT/T0 vs. I00 were analyzed by using the

nonlinear propagation equation:

0

' 1 / s

dII I

dz I I

(4.1)

where z' is the propagation depth in the graphene sample, different from z which

is the sample position along the laser propagation direction (z-axis); I(z,r,t) is the

intensity of laser pulses within the graphene sample at position z, time t, and r is

radial distance from the center axis. The first term on the right side of Eq. (4.1) is

a phenomenological expression for saturation in 1PA with 0 being the

small-signal (or linear) absorption coefficient and Is being the saturation

irradiance; and the second term quantifies 2PA with being the 2PA coefficient.

Equation (4.1) was solved numerically based on the AD method as detailed in

Chapter 2 to obtain the transmitted light intensity. Next, the transmitted light

intensity was integrated over space and time to obtain the transmitted laser pulse

energy by assuming Gaussian profiles for temporal and spatial dependence of the

incident laser beam intensity (

2 2

2 2

2

( )

0( , , ) ( ) p

r t

w zI z r t I z e

, where p is related to the

laser pulse duration and w(z) is the beam radius at a given z position) and I00 = I0(z

= 0). As such, both 1PA saturation intensity and 2PA coefficient were

unambiguously determined. In the numerical simulation for the best fit to the

experimental data, both 0-value and -value used in Eq. (4.1) take account of

multilayer effects. The 0-value is related to monolayer graphene value mono by

0 = Nmono where N is the layer number. The -value is given by

2 8/ (1 0.023 / 2)mono N N , see Ref. [4.37], where mono is the 2PA efficient for


126

monolayer graphene, which is proportional to the imaginary part of χ(3). From the

best fits between the numerical solutions of Eq. (4.1) and the measured Z-scans,

we extracted unambiguously both Is-values and mono-values in the range from

435 to 1100 nm. Both the extracted Is-values and mono-values in the range from

435 to 1100 nm were summarized in Table 4.1. Moreover, Tables 4.2 and 4.3

summarized the extracted mano and Is values of the best fits to both the Z-scans

and their corresponding plots of ΔT/T0 (at z = 0) vs. I00 on 5-, and superimposed

10-, 15- and 20-layer graphene films at 800 and 535 nm, respectively.

In Figures 4.1(b) and 4.3-4.6, the symbols are the experimental data and the

solid curves are the modeling with total absorption coefficient of 0/[1+I/Is] +

I, as in the Eq. (4.1). On the other hand, the dashed curves in Figures 4.4 and

4.6 are the modeling of the above equation without the 2PA term using =

0/[1+I/Is] and = 0, which corresponds to pure saturation modeling. The

parameters used in the pure saturation modeling corresponding to the dashed

curves in Figures 4.4 and 4.6 are also listed in Tables 4.1-4.3. As shown clearly

by Figures 4.4 and 4.6, the nonlinear signals (ΔT/T0) are dominated by 1PA

saturation at relatively lower excitation (I00 < 5 GW/cm2, or below the saturation

intensity, Is). However, the 2PA manifests itself in the higher excitation regime,

which can be identified from the deviation of the measurements in Figures 4.4

and 4.6 from the dashed curves in the higher excitation regime, demonstrating

that both 1PA saturation and 2PA should contribute to the overall nonlinear

signal.


127

Table 4.1 Fitting parameters used in the modeling of Z-scans on the 10-layer

graphene sample at selected wavelengths in the range from 1100 to 435 nm as in

Figure 4.3 and their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.4.

ex (nm)

Wavelen

gth

mono (cm-1

)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

1100

mono =

7.1 0.8 10-5

Is = 2.3 0.3

mono = 0.86 0.09

Is = 2.3 0.3

mono = 0

Is = 4.7 0.6

mono = 0

1000

mono =

7.2 0.8 10-5

Is = 3.1 0.4

mono =0.79 0.08

cm/MW

Is = 3.1 0.4

mono = 0

Is = 6.5 0.8

mono = 0

900

mono =

7.4 0.9 10-5

Is = 5.7 0.7

mono = 0.69 0.07

cm/MW

Is = 5.7 0.7

mono = 0

Is = 11.01.4

mono = 0

800

mono =

7.7 0.9 10-5

Is = 7.5 1.0

mono = 0.60 0.06

cm/MW

Is = 7.5 1.0

mono = 0

Is = 16.02.1

mono = 0

700

mono =

8.1 0.9 10-5

Is = 9.0 1.2

mono = 0.43 0.05

cm/MW

Is = 9.0 1.2

mono = 0

Is = 17.02.2

mono = 0

640

mono =

8.4 1.0 10-5

Is = 10.0 1.3

mono = 0.55 0.06

cm/MW

Is = 10.01.3

mono = 0

Is = 22.02.9

mono = 0

575 mono =

8.7 1.0 10-5

Is = 13.0 1.7

mono = 0.67 0.07

cm/MW

Is = 13.00.4

mono = 0

Is = 29.03.8

mono = 0

535

mono =

9.1 1.0 10-5

Is = 12.5 1.6

mono = 0.81 0.09

cm/MW

Is =12.5 1.6

mono = 0

Is = 29.03.8

mono = 0

500

mono =

9.5 1.1 10-5

Is = 17.0 2.2

mono = 0.62 0.07

cm/MW

Is =17.0 2.2

mono = 0

Is = 41.05.3

mono = 0

470

mono =

9.9 1.1 10-5

Is = 18.0 2.3

mono = 0.550.06

cm/MW

Is =18.0 2.3

mono = 0

Is = 41.05.3

mono = 0

435

mono =

10.5 1.210-5

Is = 21.5 2.8

mono = 0.36 0.04

cm/MW

Is =21.5 2.8

mono = 0

Is = 40.05.2

mono = 0


128


and superimposed 10-, 15- and 20-layer graphene samples as in Figure 4.5(a) and

their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.6(a).

Layer

Number

Fitting

Layer

Number

mono (cm-1

)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

5 layers

mono =

7.5 0.9 10-5

cm-1

Is = 6.7 0.9

mono = 0.63 0.07

cm/MW

Is = 6.7 0.9

mono = 0

Is = 13.01.7

mono = 0

10 layers

mono =

7.7 0.9 10-5

cm-1

Is = 7.5 1.0

mono = 0.60 0.06

cm/MW

Is =7.5 1.0

mono = 0

Is = 16.02.1

mono = 0

15 layers

mono =

7.8 0.9 10-5

cm-1

Is = 7.7 1.0

mono = 0.57 0.06

cm/MW

Is = 7.7 1.0

mono = 0

Is = 18.02.3

mono = 0

20 layers

mono =

7.8 0.9 10-5

cm-1

Is = 8.2 1.1

mono = 0.58 0.06

cm/MW

Is = 8.2 1.1

mono = 0

Is = 21.02.7

mono = 0


and superimposed 10-, 15- and 20-layer graphene samples as in Figure 4.5(b) and

their corresponding plots of ΔT/T0 vs. I00 at z = 0 as in Figure 4.6(b).

Layer

Number

Fitting

Layer

Number

mono (cm-1

)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

Is (GW/cm2)

mono (cm/MW)

5 layers

mono =

8.7 1.0 10-5

cm-1

Is = 11.5 1.5

mono = 0.85 0.09

Is = 11.51.5

mono = 0

Is = 26.03.4

mono = 0

10 layers

mono =

9.1 1.0 10-5

cm-1

Is = 12.5 1.6

mono = 0.81 0.09

cm/MW

Is =12.51.6

mono = 0

Is = 29.03.8

mono = 0

15 layers

mono =

9.2 1.1 10-5

cm-1

Is = 13.1 1.7

mono = 0.80 0.08

Is = 13.11.7

mono = 0

Is = 31.04.0

mono = 0

20 layers

mono =

8.9 1.0 10-5

cm-1

Is = 14.5 1.9

mono = 0.84 0.06

cm/MW

Is = 14.51.9

mono = 0

Is = 35.04.6

mono = 0


129

4.3 2PA spectrum of graphene in the visible range enhanced

by the excitonic Fano resonance

In this section, we emphasize our demonstrations and discussions on the

excitonic Fano resonance effect at the saddle point (M point) of graphene on the

obtained mono spectrum. From Table 4.1, we plotted the measured mono spectrum,

as demonstrated in Figure 4.7. Here, the experimental error of 10-15% results

mainly from the uncertainty in fluctuation of the input laser pulse energy and

determination of the laser beam characteristics such as minimum beam waist and

pulse duration.


130

Figure 4.7 (a) mono spectrum of graphene. The symbols ( ) are the

experimental data. The solid curves are theoretical modeling: (i) the blue curve

( ) is expressed by Eq. (4) in Ref. [4.16]; and (ii) the cyan curve ( ) and

red curve ( ) are given by Eq. (4.4) and Eq. (4.6), respectively. (b) Modeling

by using Eq. (4.6) with = 0, 0.5 and 5 eV.

Under the assumption of linear E-k dispersion with the Fermi energy being at

the Dirac point, a quantum perturbation theory was developed previously by Yang

et al to derive an analytic expression for mono [4.16], showing that it is inversely

proportional to ω4 (ω is photon frequency). At photon energies less than ~1.5 eV

(two-photon energy 2ħ < 3.0 eV), the measured mono-values are close to it,

within one order of magnitude. If we extrapolate the measured mono-values to the

mid infrared (MIR) spectral region, we find that the extrapolated values are less

than the theoretical values. This is expected as the theory is derived with the

Fermi energy (Ef ) at the Dirac point (i.e., Ef = 0). The samples that we used in

this investigation are known to contain unintentional doping, which results in

Fermi energy (~ 200 meV or less) above the Dirac point. As a consequence, there

should be an effective bandgap. With the presence of this effective bandgap, the

available amount of intermediate states involved in two-photon transitions is

decreased as compared to the case of Ef = 0, thereby giving a reduction in the

strength of the measured mono.

In the visible region from 1.8 to 2.9 eV (two-photon energy 3.6 eV < 2ħ <

5.8 eV), however, the measured 2PA spectrum clearly deviates from the

above-mentioned theory. This is anticipated as the theory is invalid in the

spectrum far away from the Dirac point. As the photon energy is varied away


131

from the Dirac point and approaches the saddle-point singularity (M-point) in the

Brillouin zone of graphene, another strong resonance feature appears. In 1970,

Bassani and Hassan developed a theoretical model to describe 2PA near or at the

saddle point of the electronic band structure in a two-dimensional semiconductor

[4.29, 4.38, 4.39]. In their model, they completely ignored the contributions from

the K-point, similar to the JDOS method in the 1PA case. And they also excluded

the interference between electron-hole (or exciton) and band-to-band transitions.

By assuming three states (one initial, one intermediate and one excited state), they

derived an analytical expression, predicting that the 2PA spectrum should be

dominated by a sharp logarithmic singularity at the saddle point, analogous to the

case for 1PA processes. In the case of degenerate 2PA (in which two photons

having the same energy, ħ1 = ħ2 = ħ are simultaneously absorbed), the

Bassani-Hasan model gives an analytical expression for mono near the M-point as

follows [4.29, 4.38, 4.39]:

0

int 3 2

0

21 1 5( ) 1

( ) 4 ' '

4log (4.2)

2' '

n nsaddle po

n n

E

M M

M

E

where 𝑀 = 𝐸0 + ∆ + (𝛼n/𝛼′)(2ℏω − 𝐸0) − ℏω; E0 is the energy gap at the

saddle point M (and E0 ≈ 5.2 eV in graphene); ∆ is the energy difference

between the intermediate state and the excited state; 𝛼′ , 𝛼n , 𝛽′ , 𝛽n are the

second-order Taylor expansion coefficients of the energy difference in terms of k

relative to the M-point, and they are essentially related to the reduced effective


132

masses of the electron and the hole at the M-point of the Brillouin zone. 𝛼′ and

𝛽′ are related to the energy difference between the excited state and initial state;

and 𝛼n, 𝛽n corresponding to the intermediate state. In the case of graphene, we

have 𝛼n = 𝛼′ = 4.5a2, 𝛽n = 𝛽′ = 1.5a2 (a is the carbon-carbon distance and

is the nearest-neighbor hopping energy in graphene [4.40]).

We first consider the case of ∆ = 0 in which the three-state model becomes a

two-state model, and Eq. (4.2) becomes:

0

int 5

0

21 5 2( ) 1 log (4.3)

( ) 2 2saddle po

E

E

To take the broadening effect from carrier relaxation into account, we convolute

Eq. (4.3) with a Lorentzian line shape of width of = 350 meV, which is a little

sharper than the 1PA case as expected according to Ref. [4.29, 4.38, 4.39]. And

the resultant 2PA spectrum around the saddle point (M) can be expressed as:

0

int 25

0 0

2

21 5 2 1( ) 1 log (4.4)

( ) 2 2 21

/ 2

saddle po

EB

E E

where B is an overall scaling factor. As shown in Figure 4.7 where B = 1 102

cm/MW/eV5, Eq. (4.4) exhibits a symmetric profile, resulting from the exclusion

from electron-hole (or exciton) interaction.

Analogous to the 1PA case [4.27, 4.28], the experimentally observed peak

photon energy (ℏωmax ≈ 2.32 eV) is redshifted from E0/2 = 2.6 eV; and the

measured resonance feature possesses an asymmetric line shape with larger mono

-values on the low-energy side. Both the features indicate that the Bassani-Hassan


133

model fails and the exciton (or electron-hole) interaction with the continuum band

near such a saddle point should be taken into account. In a similar approach to the

1PA case [4.27, 4.28], we adopt the well-established phenomenological Fano

interference model [4.41-4.43] to explain the measured mono spectrum with an

emphasis of spectral profile (or photon-energy dependence). Then, by the best fit

to our experimental results, the extracted scaling factor that accounts for the mono

magnitude should shed some light for future theoretical investigations.

When applying the Fano interference model into the 2PA case, the ratio of

two-photon transition probability from the interferential excitonic transition to the

unperturbed band-to-band transition can be derived as:

(4.5)

where |E⟩ is the coupled electronic states between the excitonic state at the

M-point and the existing continuum of electronic states, |𝑛⟩ is the intermediate

state, |𝑖⟩ and |𝑓⟩ are the initial and excited states, respectively. Similarly to the

1PA case, = (ħ - 𝐸res′ )/(/2) is the normalized energy by width relative to

the resonance energy 𝐸res′ between the intermediate state and the excitonic state;

q2 denotes the ratio of the strength of the excitonic transition to the unperturbed

band-to-band transition.

In order to completely describe the measured mono spectrum from NIR to

visible (ħ = 1.1 ~ 2.9 eV; 2ħ = 2.2 ~ 5.8 eV), contributions from both

two-photon transitions at the linear E-k dispersion near the Dirac point [4.16] and

22

2

int

ˆ ˆ( ) ( )

ˆ ˆ( ) 1

excitonic Fano E

saddle po

T n n T i q

f T n n T i


134

around the saddle-point (M) singularity should be taken into account. There is a

good agreement between the red curve and the experimental data in Figure 4.7 if

we plot a linear summation of Eq. (4) in Ref. [4.16] and Eq. (4.5), which gives

rise to:

int( ) ( ) ( )mono K po excitonic Fano (4.6)

where 𝛽K−point(𝜔) is the ω-4-dependent 2PA coefficient derived in Ref. [4.16];

and 𝛽excitonic Fano(𝜔) is given by Eqs. (4.4) and (4.5). The best fit yields B = 1

102 cm/MW/eV5. Furthermore, the ratio q = -1; resonance energy 𝐸res′ = 2.4 eV

is nearly the same as half of the energy Eres in the 1PA case; and the width is

1000 meV. These parameters are consistent with the 1PA measurement analyses,

as demonstrated in Chapter 3. We also consider the three-state model in which

≠ 0. Figure 4.7 shows the modeling with various values of . These curves

demonstrates no significant difference in the spectral profiles between the

two-state and three-state model. But, the scaling factor of B varies from 100 to

450 cm/MW/eV5.

In conclusion, we have observed the 2PA enhanced by the excitonic Fano

resonance of graphene with femotosecond laser pulses in the visible spectral

range. Based on the second-order, time-dependent perturbation theory, we have

developed a semi-empirical model in which interband transitions among three

states at the saddle point of graphene are taken into consideration, together with

excitonic interference. We find that the model is in agreement with the


135

photon-energy dependence of the observed 2PA spectrum with a scaling factor of

B = (1~5) × 102 cm/MW/eV5.

From Tables 4.2 and 4.3, the obtained mono values as a function of the layer

number at 800 and 535 nm were displayed in Figures 4.8(a) and (b), respectively,

revealing the independence of mono values on the layer number within the

experimental uncertainty. This is consistent with the micro-Raman results in

Figures 3.5(a) and (b), as detailed in Chapter 3 and is due to the fact that

inter-layer interaction in our samples is too weak to be observed.

Figure 4.8 mono values measured at 800 nm and 535 nm as a function of layer

number. The black symbols are the obtained βmono values at 800 nm and 535 nm,

and the solid red lines are guidelines.

4.4 1PA saturation in graphene in the NIR and visible

spectral range

From Table 4.2, we plotted the spectral dependence of the 1PA saturation

intensities, as demonstrated in Figure 4.9. Interestingly, our experimentally

obtained 1PA saturation intensities on the superimposed 10-layer CVD graphene

revealed a quadratic dependence on the photon energy in the spectral range from

1.1 to 2.9 eV, as can be seen in Figure 4.9. Furthermore, with ultrafast excitation,


136

i.e. the laser pulse duration is less than the photo-excited carrier relaxation time (~

1 ps, determined by our degenerate pump-and-probe measurements as shown in

Figure 4.11), the saturation fluence can be approximately expressed as Fs ≈ Is ×

τFWHM, where τFWHM is the full width at half maximum (FWHM) of the temporal

Gaussian laser pulse distribution. We converted our experimentally obtained 1PA

saturation intensities to the above-defined saturation fluences. And we found our

results were in agreement with the previous reports [4.3, 4.5, 4.13, 4.15-4.17]

obtained in the mid-infrared (MIR) and NIR spectral range on graphene samples

made by various techniques, with light pulse duration being less than the carrier

relaxation time. Graphene samples applied in Ref. [4.3, 4.5, 4.13, 4.15-4.17]

include epitaxial graphene on SiC substrate, and graphene made by CVD,

liquid-phase exfoliation, or mechanical exfoliation on transparent substrates. The

comparison between our results and the previous reports from six other research

groups is displayed in Figure 4.10(a) (colored symbols). Figure 4.10(a) clearly

demonstrates that the quadratic photon energy dependence of the saturation

fluence is valid over a wide range of photon energies (0.03 to 2.9 eV). The solid

curves in Figures 4.9 and 4.10 are corresponding to the quadratic fits. And

especially, the solid curves in Figure 4.10 represent a phenomenological

expression for the photon energy dependence of the saturation fluence:

𝐹𝑠 = (ℏ𝜔)2/𝐴 , with A = 2.4 × 103 (eV cm)2 / J. Within one order of magnitude,

all the experimentally data are in agreement with this phenomenological

expression. The deviation of the experimental results from the quadratic fit in


137

Figure 4.9 Quadratic photon energy dependence of the obtained 1PA saturation

intensities in the spectral range from 1.1 to 2.9 eV. The black symbols are

experimental data and the solid curve is quadratic fit.

Figure 4.10 (a) Measured saturation fluence (symbols) as a function of photon

energy and (b) comparison with theoretical modeling. The solid line ( ) is a fit

with a slope of 2. The symbols ( ) are our measurements in this study, and

other symbols are the data from previous reports by various groups [4.3, 4.5,

4.12-4.17].


138

Figure 4.10(a) can be due to that different kinds of graphene samples have been

used in different reports and different laser sources have been applied by different

groups. Additionally, the deviation in the mid-infrared part can also be induced by

the intraband transitions.

Most of the currently available theoretical reports on investigating the 1PA

saturation in graphene were carried out at a photon energy of ħ ≈ 1.55 eV (or ex

≈ 800nm) [4.13-4.15], the main three of them are briefly discussed and compared

with the experimental results in the following. A semiclassical method, which

focuses on valence-band depletion, conduction-band filling and ultrafast intraband

carrier thermalization, was applied in Ref. [4.13]. In order to fit to their

experimental data, the theoretical calculations resulted in an ultrafast decay

constant of 8 (± 3) fs. However, this decay constant is considerably shorter than

the one measured in differential transmission experiments [4.6-4.11].

In the second model [4.14], numerical calculations within a

quantum-mechanical, full-band steady-state density-matrix approach showed that

saturation intensity strongly depends on the carrier relaxation time, τ1 (Is = 1.53

GW/cm2 , 5.27 GW/cm2 and 11.8 GW/cm2 for τ1 = 500 fs, 250 fs and 125 fs,

respectively). Revealed by the numerical modeling, a clear trend is that the

shorter the relaxation time, the larger is the saturation intensity. This can be

explained by that with shorter carrier relaxation time, the optically generated

carriers can be more efficiently spread over an energetically broader range leading

to a more considerable reduction of Pauli-blocking. In a stringent term, this model


139

cannot be applied to our experiment due to it requires that laser pulse duration P

should be longer than the carrier relaxation timescale τ1, but P < τ1 ~ 1 ps in our

case. Nevertheless, if we assume that τ1 = 0.5 ps and the laser pulse duration is 0.5

ps, we converted the calculated saturation intensity (1.53 GW/cm2) to saturation

fluence, and displayed it in Figure 4.10(b) for comparison.

The third model simulates time-, momentum-, and angle-resolved microscopic

photo-carrier dynamics in optically excited graphene at ћω = 1.5 eV for 10-fs and

56-fs pulse excitations [4.15]. It demonstrates that Coulomb scattering is the

predominant microscopic mechanism for the absorption saturation at high laser

irradiances due to its shorter timescale. It points out that the saturation fluence is

determined by competition between absorption saturation via Pauli blocking and

carrier-out scattering from optically pumping states. Figure 4.10(b) shows that the

theoretical calculations for both 10-fs and 56-fs pulse excitations are comparable

to our experimental data around 1.5 eV.

Theoretical studies on the photon energy dependence of 1PA saturation in

graphene are unavailable in literature, except for one report by Vasko [4.12]. In

Ref. [4.12], Vasko theoretically investigated the saturation effect of graphene

within the framework of the “temporally local approach” for photon energies of

ћω ≈ 0.12, 0.8 and 1.5 eV, respectively (three typical wavelengths in the MIR,

NIR and visible spectral regions). He estimated the thresholds of absorption

saturation which are about 1~2 orders of magnitude smaller than the solid line in

Figure 4.10(b). This can be due to that the author completely neglected


140

Coulomb-scattering in his theoretical calculation, which is one of the important

underlying mechanisms for interband absorption saturation at high photo-carrier

densities, as pointed out recently by Winzer, et al [4.15].

Since quantitative theoretical investigations on the photon energy dependence

of 1PA saturation in graphene are unavailable in literature, we would like to cite

the qualitative explanation given in Ref. [4.17], where the quadratic photon

energy dependence of saturation fluence in graphene was believed to result from

the linear dependence of density of states on energy in graphene combined with

its linear increase of carrier scattering rate out of the excited state with increasing

energy.

Figure 4.11 displays the transient absorption signals (colored symbols) at 800

nm measured by a degenerate pump-and-probe technique on the 10-layer

graphene sample under the excitation of pump beams with various peak

intensities (I00). The solid curves in Figure 4.11 are the corresponding

biexponential fits, indicating the ultrafast photo-excited carrier relaxation time ~ 1

ps in our CVD graphene samples which is comparable to other reports [4.6-4.9,

4.16]. The values of I00 are in the range from 1 to 20 GW/cm2. Note that the

pump-and-probe experiment was calibrated by utilizing a standard sample (CdS)

as mentioned in Chapter 2, section 2.4. Figure 4.12 shows the transient absorption

signals (black symbols) at 800 nm on 0.5-mm-thick CdS crystal, together with

biexponential fits. The slow carrier dynamics ~ 0.1 ns shown in the degenerate

pump-probe signals of CdS corresponds to 2PA excited free carrier absorption.


141

Figure 4.11 Degenerate pump-and-probe measurements on the 10-layer

graphene film at 800 nm. The symbols are the experimental data and the solid

curves are the biexponential fits.

Figure 4.12 Degenerate pump-and-probe measurements on CdS at 800 nm.

The symbols are the experimental data and the solid curves are the biexponential

fits.

From Tables 4.2 and 4.3, we plotted the layer number dependence of 1PA

saturation intensities Is of graphene at 800 nm and 535 nm, as demonstrated in

Figures 4.13 (a) and (b), respectively. The black symbols in Figure 4.13 show the

measured layer number dependence of the 1PA saturation intensities Is.

Theoretical trends based on the analysis method in Ref. [4.15] are also

demonstrated in Figure 4.13 (solid curves), which assumes that each graphene

layer in the samples behaves like a saturable monolayer and neglects the influence


142

of the reflection. From Figure 4.13, we find the experimentally obtained layer

number dependence of Is values are in agreement with the theoretical trends,

which is anticipated due to the nearly-zero inter-layer interaction in our samples

as demonstrated by the micro-Raman results in Chapter 3. Furthermore, as

indicated by Figure 4.13, both the experimentally obtained and the theoretically

predicted Is values are found to be relatively larger in thicker graphene samples,

which is expected due to the buried layers are exposed to lower laser irradiance.

However, such small difference is within the experimental uncertainty here as

demonstrated in Figure 4.13.

Figure 4.13 Is values measured at 800 nm and 535 nm as a function of layer

number. (a) and (b) display the layer number dependence of the obtained 1PA

saturation intensities Is at 800 nm and 535 nm (black symbols), the solid curves

are the theoretical modeling based on the analysis method given in Ref. [4.15].

4.5 Conclusion

In this chapter, we investigated the photon-energy dependence of nonlinear

optical absorption in graphene with femtosecond laser pulses in the NIR and

visible spectral range. Firstly, both interband 2PA and 1PA saturation in

high-quality, CVD-grown graphene films were unambiguously determined over


143

the near-infrared (NIR) and visible spectral range (435-1100nm) using Z-scan

technique. Secondly, we observed the 2PA enhanced by the excitonic Fano

resonance of graphene in the visible spectral range. Based on the second-order,

time-dependent perturbation theory, we developed a semi-empirical model in

which interband transitions among three states at the saddle point of graphene are

taken into consideration, together with excitonic interference. We found that the

model was in agreement with the photon-energy dependence of the observed 2PA

spectrum with a scaling factor of B = (1~5) × 102 cm/MW/eV5. Thirdly, the

experimentally obtained 1PA saturation intensities in the investigated spectral

range (435-1100 nm) revealed a quadratic photon energy dependence.

Furthermore, by converting the obtained 1PA saturation intensities to saturation

fluences, our results were in agreement with the previous reports obtained in the

mid-infrared (MIR) and NIR spectral range with light pulse duration being less

than the carrier relaxation time. A qualitative explanation was utilized to explain

the observed quadratic photon energy dependence of 1PA saturation fluence and a

phenomenological expression was provided. This quantitative expression is valid

with a laser pulse duration less than the photo-excited carrier relaxation time and

should shed light on further theoretical investigations into understanding the

spectral dependence of 1PA saturation in graphene.

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Chapter 5 Structural and linear optical properties of MOFs and ligands

148

Chapter 5

Structural and linear optical properties of

metal-organic frameworks (MOFs) and ligands

5.1 Introduction

In recent times, materials based on metal-organic frameworks (MOFs) [5.1]

have been extensively investigated as they hold the key for promising hybrid

materials with unique properties. MOFs consisting of metal ions coordinated to

organic ligands can have one-, two-, or three-dimensional crystalline structures.

By taking advantage of the combined properties of the metal ions and the organic

ligands, many functional materials suitable for gas sorption [5.2], separation [5.3],

luminescence [5.4], catalysis [5.5], magnetism [5.6] and conductivity [5.7] can be

constructed. Moreover, in nonlinear optics, taking advantage of the highly

directional metal-ligand coordination bonds and the well-defined geometry of

metal centers, noncentrosymmetric MOFs exhibiting large second-order nonlinear

optical properties (mostly second-harmonic generation (SHG)) can be rationally

designed and synthesized in a systematic way with the combination of synthetic

chemistry and crystal engineering [5.8, 5.9].

Nowadays six main approaches have been proposed and developed to

synthesize MOFs, namely, (1) solvothermal technique [5.10]; (2) slow

evaporation method [5.11]; (3) microwave-assisted synthesis [5.12]; (4)

electrochemical synthesis [5.13]; (5) mechanochemical synthesis [5.14] and (6)


149

sonochemical synthesis [5.15]. All these syntheses methods are liquid-phase

syntheses, in which solvent is added to a mixture of solid salt and ligand or

separate metal salt and ligand solutions are mixed together in a reaction vial.

Different aspects such as reactivity, solubility, redox potential, stability constant

and so on can influence the choice of an appropriate solvent for the liquid-phase

reaction [5.16]. Among these liquid-phase synthesis methods, the solvothermal

method is mostly utilized and is involved in the routine synthesis of MOFs [5.16].

Moreover, compared to other liquid-phase synthesis methods, solvothermal

method provides the highest yield of synthesized MOFs (~ 70%) [5.16]. On the

other hand, many researchers have also tried solid-state syntheses of MOFs as

contrast to the liquid-phase ones. Although solid-state syntheses are faster and

easier compared to liquid-phases syntheses, they usually suffer from difficulties in

obtaining single crystals and hence, determining product structures [5.16].

In addition, MOF composites/hybrids (also called as MOFs) can be obtained

by controllable integration of MOFs and plenty of functional materials [5.17].

Especially, active species such as metal nanoparticles/nanorods, quantum dots

(QDs), organic polymers, cabon nanotubes, graphene, biomolecules and other

molecular species have been successfully incorporated into the MOFs to achieve

supreme performance unattainable by the individual constituents [5.18-5.20].

In this dissertation, we have selected the ligand based on the well-established

guiding principles in the architecting of chromophore with relatively large

nonlinear optical properties to synthesize MOF with multiphoton excited


150

photoluminescence (MEPL) properties, utilizing the solvothermal method. The

main organic ligand is trans, trans-9, 10-bis (4-pyridylethenyl) anthracene

(An2Py). The choice of this organic ligand is based on the correlation between

nonlinear optical properties and molecular structure. It has been shown that

organic molecules with symmetrical conjugated substituted structures of

Donor-π-Acceptor-π-Donor (D-π-A-π-D) or Acceptor-π-Donor-π-Acceptor

(A-π-D-π-A) arrangement can have relatively large nonlinear optical properties

[5.21]. The main ligand (An2Py) and co-ligand trans,trans-4,4

stilbenedicarboxylic acid (H2SDC) have been synthesized by our collaborator Mr.

Quah Hong Sheng, according to literature [5.22-5.25] in the Department of

Chemistry in National University of Singapore (NUS). Zinc cation has been

employed as the metal ion. We selected zinc cation as the metal ion in MOFs in

order to achieve high PL quantum yield [5.26]. Transition metals (e.g. Cu, Zn),

alkaline earth elements (e.g. Sr, Ba), p-block elements (e. g. In, Ga), actinides (e.g.

U, Th), and even mix metals have been used for the synthesis of MOFs [5.16].

MOFs containing transition-metal ions in the framework typically exhibit PL

centered on the linker rather than on the metal [5.26]. Using transition metals

which have partially filled d orbitals, ligand-filed transitions (d-d) can lead to

strong reabsorption and/or quenching of fluorescence generated from the organic

molecule, which can occur via electron or energy transfer through the partially

filled d-orbitals [5.27]. On the contrary, MOFs containing transition-metal ions

without unpaired electrons, especially those with d10 configurations, can yield


151

ligand-based highly emissive materials [5.26]. Zinc atom has an electron

configuration of 3d104s2, and its ion is +2 with electronic configuration of 3d104s0.

The d orbital of Zn2+ is fully filled and it does not have unpaired electrons.

Therefore, zinc cation has been utilized as the metal ion of our MOFs.

The systematic solvothermal synthesis of the zinc(II) MOF with An2Py,

H2SDC has also been carried out by our collaborator, yielding

[Zn2(SDC)2(An2Py)]∙ DMF∙4H2O (MOF 1). MOF 1 slowly became powdery

with the guest solvents removed even upon exposure to air. The framework was

still intact and formed a new crystalline phase [Zn2(SDC)2(An2Py)] (MOF 1a). In

our experiments, this dehydrated compound MOF 1a was obtained by grinding

MOF 1 and heating it at 100˚C for 2 h under vacuum. The MEPL character of the

main ligand An2Py has been successfully translated into the synthesized MOF 1a.

And the solid-state MEPL of the MOF 1a is enhanced compared to that of its

organic ligand in the solid-state form due to the rigidifying effect in the MOF

framework. Moreover, by encapsulating two high quantum yielding guest

molecules perylene and anthracence into the voids of the MOF 1a, [Zn2

(SDC)2(An2Py)]∙perylene (MOF 2) and [Zn2 (SDC)2 (An2Py)]∙anthracene

(MOF 3) have been obtained. MOFs 2 and 3 have been prepared utilizing the

solvothermal method by our collaborator as well, with An2Py, H2SDC and two

guest molecules perylene and anthracence, respectively. Taking advantage of the

Förster resonance energy transfer (FRET) between the host MOF and the guest

molecules, we have achieved further enhanced MEPL in the MOFs 2 and 3.

https://en.wikipedia.org/wiki/F%C3%B6rster_resonance_energy_transfer


152

5.2 Characterization for the ligands and MOFs

Figure 5.1 demonstrates the optimized molecular structures of the organic

ligands An2Py and H2SDC in the ground state. The ground-state geometry were

optimized at the density functional theory (DFT) level using the Gaussian 09

package [5.28], where coulomb-attenuated CAM-B3LYP exchange correlation

functional [5.29] was utilized to properly take account of long-range coulombic

effects [5.30, 5.31]. The applied basis set for description of electrons of all the

atoms here is 6-31+G*.

Figure 5.1 (a) Optimized molecular structure of the organic ligand An2Py in

the ground state and (b) Optimized molecular structure of the organic ligand

H2SDC in the ground state.

The Frontier Molecular Orbitals (FMOs) of the An2Py molecule has been

calculated and displayed in Figure 5.2. As revealed by Figure 5.2, the electron

distribution in the HOMO-1 and the LUMO+1 in An2Py molecule localizes at

conjugated anthracene center and the two side pyridine terminals, respectively.

This electron transfer from the anthracene center to the side pyridine terminals

(a)

(b)


153

demonstrates the electron acceptor - - electron donor - - electron acceptor

(A--D--A) distribution in the conjugated pyridine-anthracene-pyridine system

(An2Py) [5.32].

Figure 5.2 The theoretically calculated Frontier Molecular Orbitals of An2Py

molecule.

The structural characterizations for the synthesized MOFs have been

performed by our cooperator Mr. Quah Hong Sheng in the Department of

Chemistry in NUS. Single Crystal X-Ray Diffraction (SCXRD) techniques were

applied to determine the solid-state structures of MOFs 1-3. SCXRD studies

revealed that MOF 1 crystallized in the monoclinic space group C2/c with Z = 4,

whereas MOFs 2 and 3 crystallized in monoclinic space group P21/n with Z = 2.

Nonetheless, all the three MOFs shared the same fourfold interpenetrating pcu

topology rendering them essentially analogous, as demonstrated by Figures 5.3.

HOMO-1 HOMO

LUMO LUMO+1


154

Table 5.1 displays the obtained crystal cells data of MOFs 1-3. (MOF 1 in both

Figure 5.3 and Table 5.1 does not include the guest solvent DMF∙4H2O) MOF 1

is assembled such that the anthracene moiety of An2Py is stacked alternating

along the c-axis with the closest edge to edge C28-C28 distance between the

anthracenes to be 4.55 Å. As for MOF 2, the tilting and π-stacking are similar to

MOF 3, but differing slightly from the vinyl C7 of the ligand to the centroid of

the perylene guest distance, 3.48 Å. The anthracene guest molecules in MOF 3

are π-stacked in between the An2Py along a-axis and are tilted in the direction of

(101) plane with a distance of 3.51 Å from the vinyl C23 of the ligand to the

centroid of the guest. Topological study revealed MOF 3 is slightly compressed

as compared to MOF 1. This is reflected in the diagonal distances of the (4,4)

plane (Zn∙∙∙Zn, 27.43 and 20.78 Å in MOF 1 and 30.48 and 16.02 Å in MOF 3).

a) b) c)

e) f)

g) h) i)

d)


155

Figure 5.3 Crystal structure packing. (a-c) A view of a portion of MOFs 1, 2

and 3. (d-f) Pcu packing of MOFs 1, 2 and 3. (g-i) Packing of MOFs 1, 2 and 3.

(j-l) Simplified toplogical net of MOFs 1-3 showing 4-fold interpenetrating pcu

nets.

Table 5.1 Crystal cells data of MOFs 1-3.

Compound MOF 1 MOF 2 MOF 3

Formula C60H40N2O8Zn2 C80H52N2O8Zn2 C74H50N2O8Zn2

Formula weight 1047.75 1299.97 1225.90

Crystal system Monoclinic Monoclinic Monoclinic

Space Group C2/c P21/n P21/n

a, Å 15.084(13) 9.190(3) 9.3342(7)

b, Å 27.43(2) 17.557(5) 16.2033(13)

c, Å 15.799(13) 19.107(6) 19.0664(13)

β 95.447(14)° 102.375(7)° 101.826(2)°

V, Å3 6508(9) 3011.1(15) 2822.5(4)

Z 4 2 2

Upon removal of the guest solvents, MOF 1 does not retain single

crystallinity and it slowly became powdery even upon exposure to air. But the

framework is still intact as the resultant powder remained insoluble in DMSO.

After the guest solvents were fully removed, the framework formed a new

crystalline phase MOF 1a, which is revealed by the Powder X-Ray Diffraction

(PXRD) pattern. This new phase, MOF 1a is similar to that of the compressed

framework of MOF 3 upon comparison. It is likely that such a flexible

paddlewheel framework undergoes contraction [5.33] during the solvent removal.

j) k) l)


156

Hence, we have simulated the crystal structure of the compressed framework,

MOF 1a by removing the anthracene guest and lowering the symmetry of crystal

structure MOF 3 to Pī. Using total pattern and analysis solution (Figure 5.4), the

powder data were refined to reveal a new phase ascertaining the phase

compression. Despite attempts to obtain a 100% framework compressed phase,

the framework absorbs moisture from the air to regain partially the original

framework of MOF 1. It was found that the powder used for subsequent analysis

consists of 92.23% of the compressed phase MOF 1a and 7.77% of the original

uncompressed phase MOF 1. For subsequent measurements of single-photon and

multi-photon excited PL, this dehydrated compound (MOF 1a) was used for

consistency. Through grinding MOF 1 and heating it at 100˚C for 2 h under

vacuum, we obtained the dehydrated compound MOF 1a for our measurements.

Figure 5.4 illustrates the PXRD patterns of MOF 1 and MOF 1a, and

structure solution by total pattern and analysis solution (TOP). The PXRD

patterns of MOFs 2 and 3 have also been measured to confirm their purities, as

shown by Figures 5.5 and 5.6. The PXRD measurements and the refinement of

the powder data with total pattern and analysis solution were conducted by our

collaborator Quah Hong Sheng from Department of Chemistry in NUS and

Martin K. Schreyer from Institute of Chemical & Engineering Sciences in

A*STAR, respectively.


157

Figure 5.4 X-ray powder patterns of MOF 1 and MOF 1a, and structure

solution by total pattern and analysis solution. (TOP) Structure solution of the

desolvated compound MOF 1a by rietveld refinements. Despite efforts to fully

remove the solvent molecule, the reabsorption of moisture from the atmosphere

led to the sample retaining 7.77% of the uncompressed phase. (Bottom) The

pictorial representation of the framework compression of MOF 1 to MOF 1a due

to desolvation.


MOF 3

MOF 1

MOF 1

MOF 1a

MOF 1a


158


Figures 5.7 (a-c) display the photos of the compact well powdered single

crystals of the MOFs 1a, 2 and 3, which are packed in a 1-mm-thick quartz

cuvette.

Figure 5.7 (a), (b) and (c) Photos of compact well powdered single crystals of

MOFs 1a, 2 and 3 packed in a 1-mm-thick quartz cuvette, respectively.

In addition, several other measurements including: 1H-NMR spectra;

Thermogravimetric analysis (TGA), the C, H, N analysis and electron

paramagnetic resonance (EPR) spectroscopy have also been utilized for the

characterization of the MOFs and ligands. These measurements were conducted

by our collaborator Mr. Quah Hong Sheng.

5.3 Linear optical properties of ligands and MOFs

For the linear optical characterization of the organic ligands and guest

molecules in solution, we have measured their UV-VIS absorption spectra, linear

a) b) c)


159

PL spectra excited by UV light and absolute PL quantum yields. For the linear

optical characterization of the solid-state MOFs, we have acquired their linear PL

spectra excited by UV light, excitation spectra at the peak PL wavelength and the

absolute PL quantum yields. Moreover, the absolute PL quantum yield of the

main ligand An2Py in the solid-state form has been obtained. The linear PL

spectra excited by UV light and excitation spectra at the peak PL wavelength of

the main ligand An2Py in the solid-state form have also been collected and

compared to the UV-VIS absorption spectra of its solution. The details are

demonstrated as follows.

UV-VIS absorption spectra of the organic ligands An2Py and H2SDC

dissolved in chloroform solvent and contained in a 1-cm-thick quartz cuvette were

measured using the SHIMADZU UV-3600 UV-VIS-NIR spectrophotometer with

spectral resolution of 0.1 nm. The UV-VIS absorption spectra of the chloroform

solutions of the guest molecules perylene and anthracene were also collected

using the same setup. The concentration of the An2Py, perylene and anthracene

was controlled to be 10-4 M, but the concentration of H2SDC was 10-3 M due to its

small absorbance. The results are shown in Figure 5.8. The linear PL spectra of

these solution samples excited by UV light at 350 nm were measured utilizing the

Cary Eclipse Spectrophotometer. The acquired linear PL spectra are demonstrated

in Figure 5.9.


160

Figure 5.8 Solution UV-VIS absorption spectra of organic compounds used.

Figure 5.9 Solution linear photoluminescence spectra of organic compounds

used.

In addition, we employed a Horiba Jobin-Yvon FluoroMax-4

Spectrofluorometer with appropriate sample holder to measure the linear PL

spectra of the MOFs 1a-3 and the main ligand An2Py in the solid-state form

(well ground powder) with excitation wavelength at 400 nm. The comparison

between the normalized linear PL spectra of the organic ligands in solutions and

that of MOF 1a is demonstrated in Figure 5.10, where the excitation wavelengths

were at 400 nm for An2Py solution and solid-state MOF 1a but was selected to

be 350 nm for H2SDC solution due to its blue-shift absorption spectra and


161

negligible absorption at 400 nm. The normalized linear PL spectra of the main

ligand An2Py in solid-state form is also displayed in Figure 5.10 for comparison.

As indicated by Figure 5.10, the normalized linear PL spectrum of the MOF 1a is

almost the same as that of the ligand An2Py in chloroform solution, and is very

different from that of the H2SDC solution. This could be due to the small

absorption and emission of H2SDC (as demonstrated above and in the absolute

quantum yield measurement), and also the strut-to-strut [5.34] energy transfer

between An2Py and H2SDC within the MOF 1a since the UV-VIS absorption

spectrum of An2Py and the emission spectrum of H2SDC partially coincide as

demonstrated in Figure 5.11. Therefore, we can attribute the main of the linear

and nonlinear PL emission properties of the MOF 1a to its ligand An2Py, while

the other ligand H2SDC only serves as a structural component. Moreover, the

linear PL spectra of the ligand An2Py in solid-state was found to be slightly

blue-shifted (~ 10 nm) compared to that of An2Py in solution, as in Figure 5.10.

This can be due to the packing effect (‘crystal property’) in the solid-state An2Py,

which also induces the difference between the measured one-photon excitation

spectra (acquired at peak PL wavelength) of An2Py in solid-state form and the

one-photon absorption spectra of the An2Py solution as shown in the following.


162

Figure 5.10 Comparison of the linear PL spectra of MOF 1a with those of two

ligands An2Py and H2SDC in solutions, revealing that the PL of MOF 1a mainly

originates from one of its ligands, An2Py. The linear PL spectra of An2Py in

solid-state was found to be slightly blue-shifted (~ 10 nm) from that of An2Py in

solution, which is believed to be caused by the packing effect (‘crystal property’)

in the solid-state An2Py.

Figure 5.11 Comparison of the UV-VIS absorption spectra of the main ligand

An2Py in chloroform and the linear PL spectra of the co-ligand H2SDC in

chloroform, showing the partial spectral overlap.

Figure 5.12 illustrates the obtained normalized linear PL spectra of MOFs

1a-3. As shown in Figure 5.12, all the three MOFs emit light in the spectral range

from 470 nm to 700 nm with the PL peak centered at ~ 560 nm. Furthermore, the

normalized PL spectra of MOFs 2-3 are similar to that of MOF 1a (consequently


163

similar to that of ligand An2Py) with only a small blue-shift (~15 nm) being

observed for MOF 3. And the emission of the guest molecules perylene and

anthracene in MOFs 2 and 3 seem to be quenched upon excitation. This is caused

by the FRET between the host MOF 1a and the guest molecules, which is further

evidenced by the close proximity between the guest molecules and ligand An2Py

within the MOFs (3.48 Å and 3.51 Å for MOFs 2 and 3, respectively, as shown in

section 5.2), the spectra overlap of the guest emission and the excitation of the

MOF 1a as in following and in the time-resolved PL measurements in Chapter 6.

Figure 5.12 Comparison of the linear PL spectra of the three MOFs 1a-3, which

are similar to each other. And it indicates that the emission of the guest molecules

perylene and anthracene in MOFs 2 and 3 seem to be quenched upon excitation.

Furthermore, we measured the one-photon excitation spectra of the solid-sate

MOFs and An2Py at their peak PL emission wavelengths by using the same

Horiba Jobin-Yvon FluoroMax-4 Spectrofluorometer. The acquired normalized

excitation spectra of the MOFs 1a-3 and An2Py in solid-state form are

demonstrated in Figure 5.13, revealing a broad excitation peak range from ~ 365

nm to ~ 485 nm with the centre peak wavelength at ~ 425 nm . The excitation


164

spectra of these three MOFs are similar to each other and are close to that of the

main ligand An2Py in solid-state form as in Figure 5.13, which further confirms

that the linear and nonlinear PL emission properties of the MOFs originates from

the ligand An2Py. Figure 5.14 illustrates the comparison between the UV-VIS

one-photon absorption spectra of the ligand An2Py in chloroform solution and the

one-photon excitation spectra of An2Py in solid-state form. Although both spectra

show centre absorption peak wavelength is at ~ 420 nm, one-photon excitation

spectrum of An2Py in solid-state form is found to be much broadened than that in

solution. Such broadening can be attributed to the packing effect (‘crystal

property’) in the solid-state An2Py as mentioned. All the observed difference in

linear PL spectra and one-photon excitation spectra of the ligand An2Py in

solution and in solid-state form can serve as the possible explanations for the

difference in the measured 2PA spectra as detailed in the Chapter 6.

Figure 5.13 Comparison of the one-photon excitation spectra of the MOFs 1a-3

and An2Py in solid-sate, which are collected at their peak PL emission

wavelength. It reveals that the one-photon excitation spectra of the MOFs 1a-3

are similar to each other, and are similar to that of the main ligand An2Py in

solid-state.


165

Figure 5.14 Comparison between the UV-VIS one-photon absorption spectra of

the ligand An2Py in chloroform solution and the one-photon excitation spectra of

An2Py in solid-state acquired at its peak PL emission wavelength.

Figure 5.15 shows the comparisons between the PL emission spectra of the

guest molecules perylene and anthracene and the excitation spectra of the host

MOF 1a. The PL emission spectra of the MOFs 2 and 3 are also presented in the

Figure 5.15 for the comparison. As illustrated by Figure 5.15, these guest

molecules have PL emissions in the excitation region of MOF 1a, and the

emission of the guest molecules does not show in the resultant MOFs 2 and 3.

Both the spectra overlap between the guest emission and the excitation of the

MOF 1a and the quenched emission of the guest molecules in MOFs 2 and 3

here suggest the occurrence of FRET between the host MOF 1a and the guest

molecules. Such energy transfer process was further confirmed by the close

proximity between the guest molecules and the ligand An2Py within the MOFs

(3.48 Å and 3.51 Å for MOFs 2 and 3, respectively, as shown in section 5.2), and

the time-resolved PL measurements shown in Chapter 6.


166

Figure 5.15 Emission spectra of the guests and MOFs 2, 3 together with the

excitation spectra of parent MOF 1a showing the occurrence of FRET. (a)

The emission spectrum of the perylene dye coincides with the excitation region of

the parent MOF 1a leading to an emission at 570 nm. The emission of perylene is

not observed in MOF 2. (b) The emission spectrum of the anthracene dye

coincides with the excitation region of the parent MOF 1a leading to an emission

at 560 nm. The emission of anthracene is not observed in MOF 3.

Finally, we have obtained the solid-state absolute PL quantum yields of the

MOFs 1a, 2, 3 and ligand An2Py through utilizing a steady-state and

phosphorescence lifetime spectrometer (FSP920, Edinburgh) coupled with an

integrating sphere (150 mm; internally coated with barium sulphate) with the

excitation at 400 nm. The solution absolute PL quantum yields of the ligands

An2Py and H2SDC have also been acquired using the same experimental setup

with different sample holder, where the excitation wavelength for H2SDC solution

(b)

(a)


167

was set at 350 nm due to its blue shift absorption spectra and small absorption at

400 nm. Table 5.2 summarizes the experimentally obtained absolute PL quantum

yields of the MOFs and ligands. As demonstrated in Table 5.1, the absolute PL

quantum yield of the chloroform solution of An2Py (10-4 M) excited at 400 nm is

35.7%, whereas quantum yield of the chloroform solution of H2SDC (10-4 M)

excited at 350 nm is much smaller only 4.3%, revealing that ligand An2Py

possess much better emission property than ligand H2SDC. Moreover, the

solid-state absolute PL quantum yield of An2Py is only 6.2%, which is much

smaller than its solution counterpart (35.7%) due to the PL quenching caused by

the aggregation effect. Interestingly, solid-state MOF 1a possesses three times

higher quantum efficiency (17.3%) compared to that of the solid-state ligand

An2Py (6.2%). This is due to the increased rigidity sustained by the MOF

framework which minimizes the aggregation-caused quenching in the solid-state

ligand. Furthermore, the measured absolute PL quantum yields of MOF 2 (25.4%)

and MOF 3 (26.2%) were found to be better than MOF 1a due to the FRET

between the host MOF 1a and the guest molecules.

Table 5.2 Absolute PL quantum yield measurements.

An2Py in

Chloroform

(10-4M)

H2SDC in

Chloroform

(10-4M)

An2Py

in solid

state

MOF 1a

in solid

state

MOF 2

in solid

state

MOF 3

in solid

state

Absolute

PL

quantum

yield

35.7%

4.3%

6.2%

17.3%

25.4%

26.2%


168

5.4 Conclusion

Based on the well-established guiding principles in the architecting of

chromophore with relatively large nonlinear optical properties, we have chosen

the An2Py as the main ligand for the systematic solvothermal synthesis of a

zinc(II) MOF (MOF 1). H2SDC was utilized as the co-ligand. MOF 1 was further

finely ground and heated at 100˚C for 2 h under vacuum to obtain the dehydrated

compound MOF 1a. In addition, through encapsulating two high quantum

yielding guest molecules perylene and anthracence into the pore spaces of MOF

1a, MOFs 2 and 3 have been obtained.

We have measured the linear PL spectra of the ligands and guest molecules in

solution, and the MOFs and main ligand An2Py in the solid-state form. The

comparison between the normalized linear PL spectra of the ligands and that of

MOFs revealed that the PL emission properties of the MOFs were mainly

contributed by ligand An2Py. The linear PL spectrum of the ligand An2Py in the

solid-state form was found to be slightly blue-shifted (~ 10 nm) compared to that

of its solution because of the packing effect (‘crystal property’). In addition, the

emission of the guest molecules in MOFs 2 and 3 were observed to be quenched

upon excitation, indicating the FRET between the guest molecules and the host

MOF 1a. We have also acquired the UV-VIS one-photon absorption spectra of

the ligands and guest molecules in solution, and the one-photon excitation spectra

at the peak PL wavelength of the MOFs and main ligand An2Py in the solid-state

form. The excitation spectra of the MOFs were similar to each other and very


169

close to that of the An2Py in the solid-state form. On the other hand, the

excitation spectrum of the An2Py in the solid-state form was much broadened

compared to the UV-VIS one-photon absorption spectrum of its solution, which

was induced by the packing effect in the solid-state An2Py. We further compared

the PL emission spectra of the guest molecules with the excitation spectrum of the

host MOF 1a, which revealed that these guest molecules had PL emissions in the

excitation region of MOF 1a. Such spectra overlap between guest emission and

the excitation of the host suggested the occurrence of the FRET.

We have performed the absolute PL quantum yield measurements for ligands

in solution. The An2Py solution possessed much higher PL quantum yield (35.7%)

than that of the H2SDC solution (4.3%). More importantly, we have carried out

the solid-state absolute PL quantum yield measurements for the MOFs and main

ligand An2Py. The solid-state PL quantum yield of An2Py was only 6.2% much

smaller than its solution counterpart due to the PL quenching induced by the

aggregation effect. On the contrary, solid-state MOF 1a held three times larger

quantum efficiency (17.3%) compared to that of the main ligand An2Py resulting

from the rigidifying effect sustained by the framework which minimized the

aggregation-caused quenching in the solid-state ligand. Furthermore, MOFs 2 and

3 were found to possess better PL quantum yields (25.4% and 26.2%, respectively)

than that of MOF 1a, which stemmed from the FRET between the guest

molecules and the host MOF 1a.


170

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Chapter 6 Efficient upconversion PL of MOFs excited by simultaneous MPA

174

Chapter 6

Efficient frequency-upconverted photoluminescence of

metal-organic frameworks (MOFs) excited by

simultaneous multiphoton absorption

6.1 Introduction

Multiphoton-excited, frequency-upconverted photoluminescence (PL) is a

process where an electron is excited by simultaneously absorbing more than one

incident photon and subsequently relaxes to the original unexcited state by

emitting light at photon energy larger than that of the incident photons. This is

particularly an enticing property suitable for a variety of applications in nonlinear

optics, phonics, and bio-photonics, such as optical limiting [6.1], lasing [6.2],

optical data storage [6.3] and high contrast bio-imaging [6.4]. Until now, many

organic molecules with large multiphoton absorption (MPA) cross-sections and

efficient PL quantum yield have been designed and synthesized in order to realize

these applications [6.5]. Moreover, various guiding principles on the

structure-property relationship have been developed to synthesize organic

molecules with relatively large nonlinear optical properties [6.6-6.13]. Recently,

multi-photon harvesting (up to five photons) arose from the simultaneous

absorption of multiple, identical and energized photons was observed in

(E)-3-(4-(2-(1-hexyl-4-methyl-1H-imidazol-5-yl)vinyl) pyridinium-1-yl)propyl

sulphate [6.14]. Compared to the lower-order nonlinear optical absorption, the PL


175

excited by simultaneous five-photon absorption in the short-wavelength infrared

(SWIR) range would possess stronger spatial confinement, deeper penetration

length, improved sensitivity and resolution [6.14].

Although organic molecules with large nonlinear optical properties are in

great demand for a variety of applications, frequency up-converted PL or lasing

exhibited by organic molecules in solution is usually quenched in the solid-state

form due to the aggregation effects [6.15]. However, efficient frequency

up-converted luminescent materials excited by MPA in the solid-state form are

highly preferable in real applications due to a higher resistance to photobleaching.

Despite reports on two-photon excited PL in a zinc(II)-based metal organic

polymer [6.16, 6.17], the lack of solid-state structure and the difficulty in

synthesizing the organic polymer constrained its tunability. Serving as host

matrices, MOFs with solid-state crystal structures can offer a practical solution to

the aggregation-caused quenching in the multiphoton excited PL (MEPL) of

organic molecules in solid-sate form.

In the last decade, extensive research works have been conducted to

investigate materials based on metal-organic frameworks (MOFs) since they hold

the key for promising hybrid materials with unique properties [6.18]. Especially,

by taking advantage of traditional organic and inorganic PL materials, MOFs with

unique and superior luminescent properties have been successfully synthesized

[6.19]. In MOFs, both the organic linkers and the metal ions/clusters can serve as

the platforms to generate PL. Furthermore, the luminescent properties of MOFs


176

can be further tuned by encapsulating guest molecules or ions into their pore

spaces, which can directly emit PL or induce PL through the interactions with host

MOFs [6.19-6.21]. Nowadays, plenty of luminescent MOFs have been

synthesized and developed, however, most of them exhibit linear PL with the

photon energy of emission light smaller than that of the excitation light.

There have been reports on frequency up-converted PL from lanthanides [6.22,

6.23] and lanthanides-based MOFs [6.21]. However, the absorption and

consequential PL response do not originate from the ligand in the framework but

the lanthanide cation, thus restricting amenability to the metal ion. Furthermore,

the lanthanide MOFs exhibit sequential stepwise multi-photon excitation but not

simultaneous multi-photon absorption which enables higher contrast in

bio-imaging. By encapsulating suitable dyes in the solvent accessible void of

MOFs to minimize aggregation-caused quenching, two-photon imaging [6.24]

and lasing [6.25] from solid-state MOFs were documented one and two years ago,

respectively. However, the two-photon absorption (2PA) and resultant PL

response do not originate from the ligands in the framework but the guest dyes,

which limits the amenability as the ability of encapsulating molecules is restricted

by the pore sizes of MOFs. In order to break this restriction and to enhance the

amenability, we have tried the strategy of immobilizing a nonlinear optically

active chromophore as the ligand and successfully minimized the

aggregation-caused quenching, resulting in significant MEPL in the

as-synthesized MOF. Moreover, by encapsulating high quantum yielding dye


177

molecules into the MOF as guest molecules, we demonstrated that the MEPL can

be further enhanced through Förster resonance energy transfer (FRET) between

the host MOF and the guest molecules.

In all, the predictability of structural property relationship in MOFs has drawn

us to work on this project. During the period when our work was reviewed by

reviewers, Qian et al reported the incorporation of a zwitterionic ligand into a

MOF which displayed two-photon excited PL via the multivariate strategy [6.26].

In order to rationally synthesize MOFs with efficient MPA property, we have

selected the ligand based on well-established guiding principles in the architecting

of chromophore with relatively large MPA cross sections (n). We have

synthesized the nonlinear optically active organic ligand An2Py and transferred

its MEPL character into the MOF 1a ([Zn2(SDC)2(An2Py)]), which has been

obtained by the solvothermal method. It has been demonstrated that the solid-state

MEPL of the MOF is enhanced compared to its organic ligand due to the

rigidifying effect provided by the MOF framework. Moreover, we have achieved

further enhancement of the MEPL by encapsulating high quantum yielding guest

molecules perylene and anthracene into the voids of MOF 1a, which formed

MOFs 2 ([Zn2(SDC)2(An2Py)]∙perylene) and 3 ([Zn2(SDC)2(An2Py)]∙

anthracene), providing an additional synthetic possibility to amend the

up-conversion property. Such enhancement is believed to be caused by the FRET

between the host MOF and the guest molecules. Our initial results suggest that

utilizing the above two strategies could make MOF a promising frequency


178

up-converted, efficiently luminescent material in the solid-state form.

To clearly present this work, the content of this chapter is organized in the

following manner. Section 6.2 details the two-, three and four-photon excited PL

measurements on MOFs and the related theoretical data analyses. Experimentally

obtained multiphoton action cross-sections of the ligand An2Py and the MOFs in

the solid-sate form are presented and discussed in Section 6.3. Section 6.4

presents the experimental and theoretical studies on the 2PA properties of the

main ligand An2Py in the molecule level (i.e. in solution), and its comparison

with that of An2Py in the solid-state form. A summary is given in Section 6.5.

6.2 Two-, three-, and four-photon excited PL measurements

on MOFs and data analyses

In order to study the MEPL of the synthesized MOFs, we carried out the two-,

three-, and four-photon excited PL measurements on the MOFs with femtosecond

laser pulses (~ 150 fs, 1 kHz repetition rate) and compared the results with that of

the ligand An2Py in the solid-state form. Characterization and linear optical

properties of the MOFs and ligands have been detailed in Chapter 5. The

experimental setup, operational principles and data analysis for the MEPL

measurements for solid powder samples have been introduced in Chapter 2. In

this section, we will focus on experimental results from the MEPL measurements

for the solid-state MOFs and ligand An2Py and the related theoretical data

analysis.


179

6.2.1 Multiphoton excited frequency-upconverted PL

measurements on MOFs and ligands in the solid-state form

The MEPL measurements were performed at room temperature in the

wavelength range of 800-1500 nm. In our measurements, the compact well

powdered single crystals of the MOFs and ligands were packed in a 1-mm-thick

quartz cuvette. As in Figure 2.15, in the MEPL measurements, the incident laser

pulses were focused by a lens (L1) with a focal length of 6 cm. The distance

between the powder samples contained in the 1-mm-thick quartz cuvette and L1

was kept at 7.5 cm, in order to avoid the high excitation peak intensity on the

samples and to have larger excitation area (larger MEPL signal). The spot size of

the incident laser beam on the samples was controlled to be at around 1.5 0.2

mm by an iris before L1. As a calibration, we measured the two-photon excited

PL for a standard solid state sample, well ground perylene single crystal (powder)

which shows two-photon excited PL at 800 nm [6.27, 6.28], in the same

experimental set-up at 800 nm excitation. The applied relative measurement

method utilizing a standard sample can give us reasonable and accurate results. It

should be pointed out that we applied the measurements of third harmonic

generation (THG) signals of a quartz plate at higher excitation intensities to

confirm the wavelengths of the infrared incident laser beams at the range of

1150-1500 nm, as displayed in Figure 6.1.


180

800 900 1000 1100

0.0

0.5

1.0

No

rma

lize

d In

ten

sit

y (

a.u

.)

Wavelength (nm)

Incident laser beams spectra

ex

= 800-1100nm(a)

375 400 425 450 475 500 525

0.0

0.5

1.0

No

rma

lzie

d I

nte

ns

ity

(a

.u.)

Wavelength (nm)

THG from Quartz generated by incident laser

beams for ex

= 1150-1500nm(b)

Figure 6.1 Spectra of the excitation laser source at various wavelengths (a)

Incident laser spectra at wavelengths of 800, 850, 900, 950, 1000, 1070, and 1100

nm, and (b) third-harmonic generation (THG) spectral profiles of the excitation

laser beams (with higher intensities) passing through a 1-mm-thick quartz plate at

wavelengths of 1150, 1200, 1250, 1300, 1350, 1400, 1450, and 1500 nm.

Photos in Figure 6.2 clearly demonstrate the MEPL when the MOFs are

illuminated with near-infrared (NIR) femtosecond laser pulses, where the MEPL

of the solid-state MOFs and ligands at 800, 1200, and 1500 nm femtosecond

pulsed laser excitation are presented as examples. The one-photon excitation

spectra of the MOFs acquired at the peak PL emission wavelength as

demonstrated in Chapter 5 indicate the absorption maxima at around 400 nm.

Correspondingly, the MEPL spectra of the MOF samples collected at 800 nm for

two-photon absorption (2PA), 1200 nm for three-photon absorption (3PA), and

1500 nm for four-photon absorption (4PA) are displayed in Figure 6.3 (Note:

different samples have different molar concentrations used for the determination

of n as recorded in the Table 6.1), as examples of all the experimentally

obtained two-, three- and four-photon excited PL spectra of the MOFs. Excitation

intensity dependences of the MEPL signal (shown in the inset of Figure 6.3)

further justify that 2PA, 3PA and 4PA are responsible for the PL excitation on

MOFs at 800 nm, 1200 nm and 1500 nm, respectively. Figure 6.4 shows the


181

excitation intensity dependence of MEPL signal for both the MOFs and the

ligands in the solid-state form at 800 nm, 1200 nm and 1500 nm, where the slopes

clearly indicated the occurrence of MPA processes. The excitation intensity

dependence of two-photon excited PL signal for the used standard solid state

sample (perylene in powder) at 800nm is also displayed in Figure 6.4. Moreover,

as shown by Figure 6.5, the comparisons between one-photon-excited PL spectra

and MEPL spectra of the MOFs at 800 nm, 1200 nm and 1500 nm demonstrate

the same PL spectra profiles, indicating that the emission involves the same

electronic state of the MOFs and is independent of the excitation wavelength.

The slopes indicative of the order of absorption process from the excitation

intensity dependence of MEPL signals (An2Py and three MOFs in the solid-state

form) across different wavelengths are summarized in Figure 6.6. In the short

wavelength range from 800 nm to 900 nm, the slopes of PL from the samples are

around 2, clearly indicating 2PA. 3PA processes with slopes increasing to around

3 appears to dominate as the excitation wavelength is increased from 950 to 1400

nm. As excitation wavelengths are increased to the range from 1450 to 1500 nm,

the slopes are around 4, signalling the dominance of 4PA processes.

As for the co-ligand H2SDC, its one-photon absorption peak is at ~ 384 nm.

As such, the wavelength range in which n-photon absorption process occurs

differs from An2Py and the MOFs, as evidenced by its excitation intensity

dependence of MEPL signal at 800 nm and 1200 nm demonstrated in Figure 6.4.

For H2SDC, 3PA fluorescence is dominant in the wavelength range of 800-1150


182

nm with slope 3. While at longer wavelengths of 1200-1350 nm, a 4PA process

occurs.

Figure 6.2 Multi-photon excited photoluminescence images of the MOFs 1a-3

and ligands in the solid-state form (well ground powder) at 800, 1200, and 1500

nm femtosecond pulsed laser excitation.

Figure 6.3 Photoluminescence spectra of the three MOFs in the solid-state

form (well ground powder) with femtosecond pulsed laser excitation. The

inset shows the dependence on laser intensity. (a) Two-photon excited emission

at 800 nm of MOFs 1a-3. (b) Three-photon excited emission at 1200 nm of

MOFs 1a-3. (c) Four-photon excited emission at 1500 nm of MOFs 1a-3.

Definition of peak excitation laser intensity on the sample surface I0(d) is as Eq.

(2.47) in the Chapter 2.


183

Figure 6.4 Excitation intensity dependence of MEPL peak intensity for the MOFs

and ligands An2Py, H2SDC at excitation wavelengths of 800, 1200 and 1500 nm.

As a calibration, excitation intensity dependence of perylene was measured at 800

nm. Definition of peak excitation laser intensity on the sample surface I0(d) is as

Eq. (2.47) in the Chapter 2.

2 3 4

103

Slope = 2.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

11 12 13 14 15

5x102 Slope = 3.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

22 24 26

5x102

Slope = 3.9

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

1 1.5 2

103

Slope = 2.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GWcm

-2)

8 10 12 14

103 Slope = 3.0

PL

In

ten

sit

y (

a.u

.)I0(d) (GWcm

-2)

14 16 18

103

Slope = 4.2

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

0.5 1 1.5

103

Slope = 2.1

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

8 10 12 14

103

Slope = 3.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

10 12 14 16

103

Slope = 3.9

PL

In

ten

sit

y (

a.u

.)

I0(d)(GW cm

-2)

1 2 310

2

103

Slope = 2.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

10 12 14 16

103 Slope = 3.1

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

16 18 20

5x102

Slope = 3.8

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

0.5 1 1.5

103

Slope = 2.2

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

5 6 7 8 9 10

103

Slope = 3.0

PL

In

ten

sit

y (

a.u

.)

I0(d) (GW cm

-2)

6 7 8 9 10

103

I0(d) (GW cm

-2)

Slope = 3.8

PL

In

ten

sit

y (

a.u

.)

MOF 1a

MOF 2

MOF 3

An2Py

Perylene

H2SDC

ex = 800 nm ex = 1200 nm ex = 1500 nm


184

Figure 6.5 Comparison of one-photon-excited and multiphoton-excite PL spectra

of MOFs 1a, 2 and 3.

Figure 6.6 Slopes n plotted as a function of laser excitation wavelength, where n

is defined by the excitation intensity dependence of the MEPL signals of MOFs

1a, 2 and 3 and ligand An2Py that is proportional to (excitation intensity)n.

6.2.2 Data analyses to determine the multiphoton action

cross-sections of the investigated samples.

Multiphoton action cross section, which is the product of MPA cross section

(n) and PL quantum yield (n), is a direct measurement of the MEPL brightness.

As in Chapter 2, at room temperature the multiphoton excited PL quantum yield

400 600 800

0.0

0.5

1.0 ex

= 400nm

ex

= 800nm

ex

= 1200nm

ex

= 1500nm

3

Inte

ns

ity

(a

.u.)

Wavelength (nm)

(c)

400 600 800

0.0

0.5

1.0

ex = 400nm

ex

= 800nm

ex

= 1200nm

ex

= 1500nm

1a

Inte

ns

ity

(a

.u.)

Wavelength (nm)

(a)

400 600 800

0.0

0.5

1.0 ex

= 400nm

ex

= 800nm

ex

= 1200nm

ex

= 1500nm

2

Inte

nsit

y(a

.u.)

Wavelength (nm)

(b)


185

n is very close to the one photon excited PL quantum yield 1 [6.5, 6.29] (n ≈

1 = ). In order to determine the n values of the investigated samples, we

applied the theoretical data analysis method and Eqs. (2.48-2.50) in Chapter 2,

and utilized perylene in the solid-state form as the standard sample [6.27, 6.28],

which shows two-photon emission upon exciting with 800 nm laser beam.

In order to determine the multiphoton action cross-sections of the investigated

samples, two-photon excited PL of a standard sample, perylene in the solid-state

form (well ground powder), has been measured at 800 nm utilizing the same

experimental setup. 2PA cross-section of perylene is reported to be 3.0 GM at 800

nm and its quantum yield in the solid-state form (well ground powder) is ~ 0.18

[6.27, 6.28]. Two-photon action cross-sections of our samples at 800 nm can be

obtained from the ratio of the measured PL strengths from the perylene to the

samples (𝐹2(Py)/𝐹2(x)) = [(𝜂𝜎2)Py ∙ 𝜌Py ∙ (𝐼002 )Py]/[(𝜂𝜎2)x ∙ 𝜌x ∙ (𝐼00

2 )x] , where

𝐹2(Py) and 𝐹2(x) are the measured PL strengths. Similarly, three-photon action

cross-sections of the investigated samples at different wavelengths can be

obtained from (𝐹2(x)800nm/𝐹3(x)2) = {9√3ℏ𝜔[(𝜂𝜎2) ∙ (𝐼002 )𝑤0

2𝑧02]x(800nm)} /

{4√2[(𝜂𝜎3) ∙ (𝐼003 )𝑤0

2𝑧04/𝑑2]x(𝜆2)}, where 𝐹2(x)800nm is their two-photon excited

PL strength measured at 800 nm and 𝐹3(x)2 is the three-photon excited PL

strength at 2. Four-photon action cross-sections of the samples are determined

from the ratio between the four-photon excited PL strength at 3 and the

two-photon excited PL strength at 800 nm, as:

(𝐹2(x)800nm/𝐹4(x)3) = 4√2(ℏ𝜔)2[(𝜂𝜎2) ∙ (𝐼002 )𝑤0

2𝑧02]x(800nm)/[(𝜂𝜎4) ∙


186

(𝐼004 )𝑤0

2𝑧06/𝑑4]x(𝜆3) . Through applying the various experimental parameters

(including the molar concentrations of different samples as shown in Table 6.1)

into the above expressions, two-, three- and four-photon action cross-sections of

the investigated samples can be unambiguously determined.

Table 6.1 Molar concentration calculations of our samples and standard sample

enclosed in the cuvette used for MEPL measurements.

Samples Weight

(mg)

Molar Weight

(g mol-1)

Volume

(cm3 )

Molar concentration

(10-4 mol cm-3 )

MOF 1a 9.2 1047 10.310.1 2.8

MOF 2 19.4 1299 10.370.1 4.0

MOF 3 27.9 1225 10.520.1 4.4

An2Py 19.5 384 10.370.1 14

H2SDC 35.5 268 10.850.1 16

Standard

(Perylene) 30.1 252 10.400.1 30

6.3 Results and discussion

Based on the two-, three-, and four-photon excited PL measurements on

MOFs and ligands demonstrated in Section 6.2.1 and the subsequent theoretical

data analyses provided in section 6.2.2, we obtained the multiphoton action

cross-sections, i.e. the n (n = nth order photon absorption) values of the MOFs

and An2Py as shown in Figures 6.7-6.9.


187

Figure 6.7 Two-photon action cross-sections of An2Py, MOFs 1a, 2, 3.

Figure 6.8 Three-photon action cross-sections of An2Py, MOFs 1a, 2, 3.

Figure 6.9 Four-photon action cross-sections of An2Py, MOFs 1a, 2, 3.


188

As demonstrated in Figure 6.7, within the region of 2PA process, the measured

(2) are in the range of 0.2-7.2 GM with a maximum at 850 nm for all the

samples. Moreover, Figure 6.7 indicates that MOF 1a has larger two-photon

action cross sections than An2Py, which is about three-times greater. This

difference can be mainly attributed to that MOF 1a possessing about three times

higher fluorescence quantum yield (17.3%) than An2Py (6.2%) shown in Chapter

5, as a result of the increased rigidity sustained by MOF. This trend is similar to

the linearly excited PL. Enhanced 2 observed in MOFs 2 and 3 came from

FRET occurring between the encapsulated guests and the host MOF. Overall, the

measured 2 is relatively small compared to that of the usual solution samples

expected from laser dyes. This can be due to reabsorption and scattering effects of

solid samples which is present during the collection process.

As illustrated by Figure 6.8, in the wavelength range of the dominant 3PA

process (950-1400 nm), a maximum (3) at 950 nm is revealed for all the

samples and it decreases with increasing wavelength. The maximum 3 obtained

amongst the compounds is (3.9 0.6) 10-79 cm6 s2 photon-2 for MOF 3 at 950

nm. However, similar to 2PA, the 3 value could be underestimated with the

measurement setup. Noteworthyly, this behavior of 3 decreasing with the

increasing wavelength is similar to typical semiconductor crystals. It is

documented that 3PA coefficient of semiconductor crystals is a function of the

photon energy as (3ℏω/Eg − 1)5/2(3ℏω/Eg)−9 where Eg is the bandgap for the

semiconductor crystals [6.30]. Strikingly, though MOF 1a has almost the same 3


189

as that of An2Py it demonstrates thrice as large PL (3) than An2Py due to its

three times higher PL quantum yield (), as in the 2PA case. On a separate note,

similar enhancements in 3 are obtained in MOFs 2 and 3 as a result of FRET

between the host MOF and guest molecules perylene or anthracene.

As shown in Figure 6.9, the four photon process is further demonstrated at

1450 nm and 1500 nm, and similar trends to that of 2PA and 3PA are observed.

Although it is underestimated, the maximum 4 obtained amongst the

compounds is (5.7 0.8) 10-110 cm8s3photon-3 for MOF 3 at 1450 nm. Across

all wavelengths, it is evident (Figures 6.7-6.9) that MOF 3 possessed the highest

multiphoton action cross sections amongst the MOFs synthesized. This could be

due to the better overlap of the anthracene emission with the excitation of MOF

1a compared to the perylene guest. Nevertheless, MOF 2 exhibits larger excited

PL than MOF 1a at all wavelengths due to FRET while the enhancement

demonstrated by all the MOFs over the ligand is due to the rigidity sustained by

the MOF framework.

FRET is a nonradiative energy transfer mechanism and is utilized to describe

the energy transfer between two chromophores [6.31]. FRET is named after the

German Scientist Theodor Förster [6.32]. The energy transfer between the donor

and acceptor in FRET is through nonradiative dipole-dipole coupling [6.33]. The

FRET efficiency relies on both the distance between the acceptor and the donor,

and the spectral overlap of the acceptor absorption spectrum and the donor

emission spectrum. Especially, the efficiency is inversely proportional to the sixth

https://en.wikipedia.org/wiki/Theodor_F%C3%B6rster


190

power of the separation distance between acceptor and donor, because of its

dipole-dipole coupling mechanism [6.34]. The large spectra overlap between the

guest emission and the excitation of the MOF 1a, the quenched emission of the

guest molecules in MOFs 2 and 3, and the close proximity between the guest

molecules and the ligand An2Py within the MOFs (3.48 Å and 3.51 Å for MOFs

2 and 3, respectively) demonstrated in Chapter 5 suggest the occurrence of FRET

between the host MOF 1a and the guest molecules. Figure 6.10 displays the

schematic illustrations of the FRET processes in MOFs 2 and 3.

Figure 6.10 (a) and (b) Schematic illustrations of the FRET processes in MOFs 2

and 3, respectively.

In order to confirm the occurrence of the FRET between the encapsulated

guests and the host MOF and to know the FRET efficiency in MOF 3 which

possesses the highest multiphoton action cross sections across all the investigated

wavelengths, time-resolve PL measurements have been carried out to study the PL

lifetime of the MOF 3 and its guest molecule anthracene. Time-resolved

measurements for the 2PA excited PL were performed with the time-correlated

Excited state E3

Ground state G3

Anthracence

Absorption

Relaxation (b)

FRET

Ground state G1

Excited state E1

MOF 1a

Emission

Ground state G1

Excited state E1

MOF 1a

Emission

Ground state G2

Excited state E2

Perylene

Absorption

FRET

Relaxation (a)


191

single photon counting (TCSPC) technique utilizing femtosecond laser pulses

(1MHz, ~ 150 fs) excitation. The experimental setup and operational principles of

the TCSPC technique have been detailed in Chapter 2. The excitation and

detection wavelengths for MOF 3 are at 800 nm and at 570 nm, respectively. And

for the guest anthracene they are at 650 nm and 410 nm, respectively, duo to its

blue-shift absorption and PL spectra. The basic operational principles of the

TCSPC technique were detailed in Chapter 2. Figure 6.11 demonstrates the

experimentally obtained PL decay curves of the MOF 3 (green line) and its guest

anthracene (black line). The red curves correspond to the

mono-exponential-component decay fits, which reveal the PL lifetimes of the

MOF 3 and its guest anthracene are 1.67 ns and 3.96 ns, respectively. Therefore,

we can determine FRET efficiency within the MOF 3 by applying the formula E

= 1- MOF-3/anthracene , resulting in E = 1- 1.67/3.96 ≈ 58%. This relatively high

FRET efficiency led to the enhanced MEPL observed in the MOF 3.

Figure 6.11 Time resolved PL measurements. PL decay curves of the MOF 3

(green line) and its guest anthracene (black line), the red curves are the fitting

with mono-exponential decays of 1.67 ns and 3.96 ns, respectively. This result


192

indicates the FRET efficiency in MOF 3 is E = 1- compound 3/Anthracene = 1-

1.67/3.96 ≈ 58%.

6.4 Experimental and theoretical studies on the 2PA

properties of the ligand An2Py in the molecule level

We have also carried out investigations on the 2PA properties of the main

ligand An2Py in the molecule level (i.e. in solution). Unfortunately, we are unable

to conduct studies on the 3PA and 4PA properties of the An2Py solution due to the

limit solubility of An2Py in organic solvents (even in DMSO, the solubility is

only about 2 mM). Both the experimental and theoretical studies have been

performed to study the 2PA properties of An2Py. Open-aperture Z-scan and

two-photon excited PL measurements were applied for the experimental study.

We conducted open-aperture Z-scan measurements for the An2Py solution in the

wavelength range of 560 – 680 nm. At 800 nm, two-photon excited PL

measurements were used due to the small 2PA at this wavelength. The basic

operational principles and theoretical data analysis method of these two

experimental measurements have been introduced in detail in Chapter 2. In

addition, the response theory calculations based on the time-dependent

perturbation theory have been carried out to theoretically study the 2PA properties

of the An2Py solution.


193

6.4.1 Experimental studies on the 2PA properties of the

ligand An2Py in the molecule level

Open-aperture Z-scan technique [6.35] was employed to characterize the 2PA

spectrum of the An2Py solution (in DMSO) contained in a 1-mm-thick quartz

cuvette in the visible wavelength range from 560 to 680 nm. The excitation laser

pulses are generated from the Coherent Libra ultrafast laser system combined

with the Light-Conversion TOPAS optical parametric amplifier and have pulse

duration ~ 150 fs, repetition rate of 1 kHz. Figure 6.12 (a) presents the schematic

illustration of the experimental set-up and also the photo of the investigated

An2Py in DMSO contained in 1-mm-thick cuvette. In the current Z-scan, a lens of

10-cm focal length was used to focus the laser pulses into the sample and the

beam waist radius was in the range from 15 1.5 to 20 2 µm, depending on the

laser wavelength used and the size of an aperture placed before the lens. As in

Chapter 2, the setup was calibrated by using slabs of wide-gap semiconductors

(CdS). The transmitted laser pulse energies were monitored while translating the

sample along the propagation direction of the laser pulses (z-axis) through the

focus with a linear motorized stage.

Figure 6.12(b) demonstrates the acquired open-aperture Z-scans (symbols) on

the An2Py in DMSO at selected wavelengths in the range from 560 to 680 nm

and under a maximum on-axis irradiance of 250 ± 30 GW/cm2. The molar

concentration of An2Py solution is 2 mM. Open-aperture Z-scan measurements

with the same laser intensity on the pure DMSO solvent were also performed at


194

each wavelength, no signal was observed as demonstrated by the flat dashed lines

in Figure 6.12(b). The corresponding theoretical data analyses for the Z-scan

results were conducted and illustrated as solid curves in Figure 6.12(b). In which,

the expression for the normalized energy transmittance in the open-aperture

Z-scan Eq. (2.16) was applied. By taking the reflectance R as 0.04 (from the

quartz) and effective thickness Leff = L= 0.1 cm (no linear absorption), we

extracted the 2PA coefficients () of the An2Py solution at the selected

wavelengths and summarized them in Table 6.2. Correspondingly, 2PA cross

sections (2) at these wavelengths were obtained by taking account the relation

between and 2 as indicated by Eq. (1.13). The acquired 2 values have also

been summarized in Table 6.2. The 2 values as a function of the wavelength are

demonstrated in Figure 6.14.

Reference

Detector

Femtosecond

Laser

Pulses

Z

Signal

Detector

Detecto

r

(a)

Aperture


195

-1 0 10.9

1.0

1.1

1.2

1.3

1.4

No

rmalized

Tra

nsm

itta

nce

Z (cm)

F

H

J

L

N

P

R

T

V

X

ex

= 560 nm

ex

= 590 nm

ex

= 620 nm

ex

= 650 nm

ex

= 680 nm

Figure 6.12 (a) Schematic illustration of the open-aperture Z-scan set-up, photos

of the An2Py solution and pure DMSO solvent contained in a 1-mm-thick cuvette

are also shown, the left is the An2Py solution, and the right is the pure DMSO

solvent; (b) open-aperture Z-scans on the An2Py solution measured at a

maximum on-axis irradiance (I00 at z = 0) of 250 ± 30 GW/cm2. The symbols are

the experimental data and the solid curves are the theoretical fit based on Eq.

(2.16).

Table 6.2 2PA coefficients and cross sections at selected wavelengths in the

wavelength range of 560 – 680 nm,.

An2Py in

DMSO

(2 mM)

ex: 560

nm

ex: 590

nm

ex: 620

nm

ex: 650

nm

ex: 680

nm

(10-3cm/GW)

5.6 0.7

8.7 1.0

12.4 1.5

10.5 1.3

7.2 0.9

2 (GM)

131 16

196 23

263 31

213 25

138 16

Since the two-photon excited PL measurements for the solid-sate MOFs and

ligand An2Py as demonstrated in Section 6.2 were limited by the available

experimental setup (short-pass filter cut at 600 nm is not available, only have one

cut at 750 nm and another cut at 500 nm) and were conducted at 800 nm. In

order to have a direct comparison, we needed to perform 2PA study for the An2Py

solution at 800 nm. But the Z-scan at 800 nm with laser peak intensity of ~ 250

(b)


196

GW/cm2 didn’t give any signal due to the small 2PA at this wavelength and low

concentration. Therefore, we tried the two-photon excited PL measurements

[6.36-6.38] on the An2Py solution at 800 nm. The An2Py solution was contained

in a 1-cm-thick quartz cuvette. In this measurement, the laser pulses were focused

by a lens of 10-cm focal length into the sample and the beam waist radius was

about 25 2.5µm. As detailed in Chapter 2, the two-photon excited PL signal was

collected in the direction perpendicular to the excitation beam path by a telescope

system and the scattered excitation beam was filtered out by the short-pass filter

cut at 750 nm. In order to calibrate the experimental setup and also to

quantitatively determine the 2PA properties of the An2Py solution at 800 nm,

Rhodamine 6G solution in methanol which presented two-photon excited PL

[6.27, 6.39] at 800 nm was used as the standard sample.

Figure 6.13(a) presents the two-photon excited PL signals of the An2Py in

DMSO and the standard sample, Rhodamine 6G in methanol, which were

acquired at 800 nm with peak laser irradiance of 200 ± 25 GW/cm2 and under the

same experimental conditions. The molar concentrations of the An2Py and

Rhodamine solutions were 2 mM and 0.35 mM, respectively. Through applying

the expression of the strength of two-photon excited PL signal as in Eq. (2.41), we

can have the ratio of the acquired two-photo excited PL from Rhodamine 6G to

An2Py as:

𝐹2(𝑅6𝐺)

𝐹2(𝐴𝑛2𝑃𝑦)

=𝜂𝑅6𝐺𝜎2(𝑅6𝐺)𝜌𝑅6𝐺

𝜂𝐴𝑛2𝑃𝑦𝜎2(𝐴𝑛2𝑃𝑦)𝜌𝐴𝑛2𝑃𝑦

(6.1)


197

The absolute PL quantum yield of Rhodamine 6G in methanol is 0.95, and its

2PA cross section at 800 nm has been reported to be 65 GM [6.27]. Therefore, we

can obtain the two-photon action cross-section of An2Py in DMSO at 800 nm to

be ~ 2.9 GM. Since the absolute PL quantum yield of An2Py in DMSO is almost

the same as An2Py in chloroform, i.e. 𝜂𝐴𝑛2𝑃𝑦 = 0.357, the 2PA cross-section 2

of An2Py solution at 800 nm is ~ 8.1 GM. This 2 of An2Py solution at 800 nm is

displayed in Figure 6.14 for comparison. Figure 6.13(b) illustrates the intensity

dependence of acquired 2PA excited PL signals of An2Py solution, which is

plotted in a log-log scale. The slope is ~ 2.1, further confirming the occurrence of

2PA process. The inset of Figure 6.13(a) displays a photo of the 2PA excited PL

measurement on An2Py solution.

400 500 600 700

0.0

0.5

1.0

PL

In

ten

sit

y (

a.u

.)

Wavelength (nm)

An2Py in DMSO

Concentration: 2 mM

R6G in methanol

Concentration: 0.35 mM

I00

= 200 GW/cm2

exc

= 800nm

50 100 150 20010

2

103

Ligand-An2Pyex

= 800nm

Two-photon

Slope = 2.00

An2Py in DMSO

Concentration: 2 mM

Slope = 2.1

ex

= 800 nm

PL

In

ten

sit

y (

a.u

.)

I00

(GW/cm2)

Model

Equation

Reduced Chi-Sqr

Adj. R-Square

B

(a)

(b)


198

Figure 6.13 (a) Two-photon excited PL signals of the An2Py and the Rhodamine

6G solutions excited at 800 nm with peak laser irradiance of 200 ± 25 GW/cm2;

Inset: photograph of the 2PA excited PL measurement on An2Py solution

contained in a 1-cm-thick cuvette; (b) Intensity dependence of acquired 2PA

excited PL signals of An2Py solution at 800nm in log-log scale.

550 600 650 700 750 8000

100

200

300

2P

A c

ros

s-s

ec

tio

n

2 (

GM

)

Wavelength (nm)

An2Py in DMSO

Concentration: 2 mM

Figure 6.14 The measured 2 spectrum of the An2Py solution.

6.4.2 Theoretical investigations on the 2PA properties of the

ligand An2Py in the molecule level

In this section, we have applied the response theory method based on the

time-dependent perturbation theory to theoretically provide insight on the 2PA

properties of the ligand An2Py.

We first applied the time-dependent density function theory (TDDFT) [6.40]

to obtain the energy levels and electronic distribution of the An2Py molecule in

solution. 1PA properties of the An2Py molecule in solution was obtained and

compared to the experimental result. To achieve this, we employed the Gaussian

09 package [6.41] with coulomb-attenuated CAM-B3LYP exchange correlation

functional [6.42] which was demonstrated to be able to properly take account of

long-range coulombic effects [6.43,6.44] in the calculations. Moreover, the


199

solvent effects were taken care of by the polarized continuum model (PCM) of

Tomasi [6.45] and the basis set for description of electrons of all the atoms here is

6-31+G*. Firstly, we acquired the optimized molecular structures of the organic

ligands An2Py and H2SDC in the ground state, as demonstrated in Figure 5.1.

Secondly, the Frontier Molecular Orbitals (FMOs) of the An2Py molecule were

calculated, and changes of the electron distributions from HOMO-1 to LUMO+1

revealed an electron transfer from the anthracene center to the side pyridine

terminals demonstrating the electron acceptor - - electron donor - - electron

acceptor (A--D--A) distribution in the conjugated pyridine-anthracene-pyridine

system (An2Py) [6.46], as illustrated by Figure 5.2 in Chapter 5. Thirdly, the

excitation energies and oscillator strengths of the first five excited states of the

An2Py in DMSO were calculated and listed in Table 6.3. Considering the

Gaussian broadening with band width of 0.4 eV, we obtained the theoretically

calculated 1PA spectra of An2Py in DMSO and compared it with the experimental

result as shown in Figure 6.15, indicating good agreement. Theoretically

calculated 1PA peak is slightly blue-shifted by ~ 15 nm from experimental one.

Table 6.3 The excitation energies and oscillator strengths of the first five excited

states of the An2Py molecule in DMSO.

Excited states

(Singlet)

1

2

3

4

5

Excitation

energies (eV)

3.117 3.963 4.117 4.119 4.787

Oscillator

strength (a.u.)

0.6384 0.0004 0.1579 0.0000 0.5169


200

300 400 500 600

0.0

0.5

1.0 An2Py in DMSO

Theoretical calculation

No

rma

lize

d A

bs

orb

an

ce

Wavelength (nm)

Figure 6.15 The comparison between the experimental and theoretical 1PA

spectra of An2Py in DMSO. The 1PA of An2Py in DMSO is almost the same as

that in chloroform. Gaussian broadening with half-width of 0.4 eV is considered

for the theoretical results.

(i) Theoretical calculations of the 2PA properties of An2Py

molecule in DMSO utilizing the response theory method

Consider the time-dependent Schrödinger equation :

iℏ𝜕𝜓(𝑟, 𝑡)

𝜕𝑡 = �̂�𝜓(𝑟, 𝑡) (6.2)

where the Hamiltonian operator contains both the original one of isolated

molecule and the interaction one as:

�̂� = �̂�0 + �̂�(𝑡) (6.3)

Take the microscopic form of the interaction Hamiltonian operator:

�̂�(𝑡) = −�̂� ∙ �⃗⃗�(𝑡) (6.4)

where �̂� = −𝑒�̂�(𝑡) is the electric dipole moment operator. Therefore, after the

calculations based on the second-order perturbation approximation [6.47-6.49],

we can obtain the two-photon transition matrix element as [6.47-6.49]:

0 0(6.5)

/ 2 / 2

i j j i

ij

m m f m f

m m f m m fS

https://www.google.com.sg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CBsQFjAAahUKEwj7nrTv2YfIAhXHcY4KHRndC4k&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSchr%25C3%25B6dinger_equation&usg=AFQjCNEEEa9JmGJ86q71vfGGZrmonfOefQ


201

where the i, j denote x, y, z molecular axis. |0> represents the initial state and is

usually taken as the ground state. |m> is all the possible intermediate states. |f> is

the final state of the two-photon transition. ℏ𝜔𝑚 is the energy difference

between the intermediate state and the ground state, and ℏ𝜔𝑓 is the energy

difference between the final state and the ground state. The summations extend

over all possible intermediate states and the exact calculation through Eq. (6.5) is

referred as the sum-over-states (SOS) calculations [6.5, 6.50].

Two-photon transition probability which is related to the two-photon

transition matrix can be expressed as:

δ2 = |𝑒1 ∙ �̂� ∙ 𝑒2| (6.6)

where 𝑒1 and 𝑒2 are the unit vector of the polarization of the applied optical

fields. Considering the orientations of the molecules in the solution are random

and performing average on the orientations of the molecules, two-photon

transition probability is:

* * *

2 (6.7)ii jj ij ij ij ji

ij

F S S G S S H S S

Moreover, for linearly polarized incident laser beam in our case, F = G = H = 2.

Finally, the 2PA cross-section can be calculated from the two-photon transition

probability as:

a0 is the Bohr radius; is the fine structure constant; g() provide the spectral

line profile, which can be taken as either Gaussian or Lorentzian linewidth

2 5 2

02 2

4 ( )(6.8)

15 f

a g

c


202

function; and f is the broadening factor of the final state and is related to its

lifetime. f is usually taken as 0.1eV for molecules in solution.

Since it is very challenging and almost impossible to perform the summations

over all possible intermediate states to calculate the 2PA cross-section using the

Eqs. (6.5), (6.7) and (6.8), we applied the response theory method to effectively

convert the summation calculations to solving a system of equations about the

investigated molecule, which does not need the information of all the excited

states [6.51, 6.52]. Moreover, the calculation with the response theory method is

also based on the time-dependent perturbation theory and is an accurate

calculation as compared to the approximation calculation in few-state models

[6.53, 6.54]. The idea of the response theory method is: 1) firstly obtain the

time-dependent expectation value of a physical quantity which describes the

system’s property (such as the electric dipole moment here); 2) secondly such

time-dependent expectation value can be expanded by a series of response

function, and all these response functions can describe the response of the system

to the external perturbation. For example, when the applied physical quantity is

the electric dipole moment, the linear, second-order and higher-order response

functions can be directly related to the molecule’s linear, second-order and

higher-order nonlinear optical susceptibilities. Furthermore, the residue of the

different order response functions can be directly utilized to calculate the

corresponding multiphoton transition matrix elements. Especially, the single

residue of the second-order response function can be applied to calculate the


203

two-photon transition matrix element. In which, the third-order nonlinear optical

susceptibilities can be obtained from the residue of second-order response

function resulting in largely simplified calculations. More details are referred to

the Refs. [6.51, 6.52].

In this dissertation, we applied the DALTON program package [6.55] to

accurately calculate the 2 values of the An2Py molecule in DMSO. Similar to the

1PA calculation, coulomb-attenuated CAM-B3LYP exchange correlation

functional was applied to properly take account of long-range coulombic effects,

the solvent effects were taken care of by the polarized continuum model (PCM) of

Tomasi and the basis set for description of electrons of all the atoms here is

6-31+G*. The calculated 2 values of the first five excited states are displayed in

Table 6.4. As expected, the calculated 2 values of the first, third and fifth excited

states are negligible due to the different selection rule for 2PA in molecules [6.56,

6.57]. In addition, the obtained 2 value of the second excited state is also very

small, indicating the small two-photon transitions to this state. In contrast,

reasonably large 2PA cross-section (2 = 391 GM) was obtained for the

fourth-excited state. Figure 6.16 demonstrates the comparison between the

theoretically calculated 2 spectrum of An2Py in DMSO and the experimental

results, where the Gaussian broadening with band width of 0.4 eV is applied as in

the 1PA analysis. As indicted by Figure 6.16, although the theoretically calculated

results is larger than the experimental obtained values, relative good agreement

was obtained between them with the theoretical results less than 1.5 times of the


204

experimental values. In addition, the spectral distribution of the theoretically

calculated 2 spectrum is similar to that of the experimental one. The theoretical

estimated peak position is slightly blue-shifted (~ 15 nm) from the experimental

one. The difference between the theoretical calculation results and the

experimental measurements can be due to that: (1) The theoretical calculations

only focus on the contributions from the electrons and does not consider the

molecular vibration effect, which has non-negligible contribution to the molecules’

2PA [6.58]; (2) The theoretical calculation is performed on single molecule and

does not consider the effect of inter-molecular interaction, although it is small in

solution sample; (3) The applied solvent model of polarized continuum model

(PCM) only consider the long-term interaction, and no short term interaction is

included [6.45, 6.59].

Table 6.4 Calculated 2PA cross-sections of the first five excited states of An2Py

molecule in DMSO.

Excited states

(Singlet)

1

2

3

4

5

Excitation

energies (eV) 3.117 3.963 4.117 4.119 4.787

2 (GM)

1.310-9

210-7

3.510-4

391

1.210-5


205

500 550 600 650 700 750 800 850

0

100

200

300

400 An2Py in DMSO

Experiemental data

Response Theory

2P

A c

ross-s

ecti

on

2 (

GM

)

Wavelength (nm)

Figure 6.16 The comparison between the experimentally measured 2 spectrum

of the An2Py solution and the theoretical calculated one utilizing the response

theory.

We compared the experimentally acquired 2PA spectra of the ligand An2Py in

solution and in the solid-state form. As indicated in Figure 6.7, although the

experimentally obtained 2 value of the ligand An2Py in solid-state form at 800

nm is 2 = 2 / ~ 4.8 GM and is quite similar (larger than half) to that of the

solution An2Py (~ 8.1 GM), the obtained 2PA spectrum of solid-state An2Py is

different from that of the solution one with a peak at 850 nm. Moreover, the

obtained 2 value of the solid-state An2Py is believed to be underestimated due to

the reabsorption and scattering effects in solid samples which is present during the

collection process. Therefore, we propose that the observed difference between

the measured 2PA spectrum of solid-state An2Py and that of the An2Py solution is

due to the packing effect (‘crystal property’) in the solid-state sample. Such

packing effect also induced the much broader one-photon excitation spectra of the

solid state An2Py than that of its solution, as demonstrated in Figure 5.14 in

Chapter 5. In which, broad peak of the one-photon excitation spectra of the solid


206

state An2Py was revealed with a center peak wavelength at 425 cm compared to

the narrow peak at ~ 410 nm observed in An2Py solution. Besides these, the

packing effect resulted in the measured different EPR results for An2Py in

solid-state form and in solution, where EPR result for solid-state An2Py shows a

singlet biradical character whereas it is silent for An2Py solution. Unfortunately,

details about this packing effect are still unknown and need further experimental

and theoretical investigations. Since we don’t have a short-pass filter cut at 600

nm and only have one cut at 750 and another cut at 500 nm in our lab, we are

unable to experimentally measure the two-photon excited PL of the solid-state

An2Py in the visible range. Nonetheless, largely enhanced two-photon excited PL

and two-photon action cross-sections are observed in the three MOFs in

solid-state compared to that of the solid-state An2Py.

6.5 Conclusion

In summary, usually MEPL exhibited by organic molecules in solution is

quenched in the solid-state due to aggregation. However, efficient

frequency-upconverted luminescent materials in the solid-state form are highly

preferable in many photonic applications such as up-conversion lasing and light

emission due to a higher resistance to photobleaching. In this Chapter, we

demonstrated that MOFs with efficient nonlinear optical response and enhanced

MEPL can be designed by rational choice of ligands with relatively strong

nonlinear optical properties. Firstly, with A-π-D-π-A structure, nonlinear optically

active and luminescent An2Py was selected as the ligand of MOF 1a. Secondly,


207

the property of the ligand An2Py was duly expressed in MOF 1a that formed.

This showed a successful incorporation of a multiphoton excited emissive organic

chromophore into a MOF which resulted in solid-state MEPL. Furthermore, the

rigidifying of the chromophore in the MOF framework led to the enhancement in

MEPL. Thirdly, through incorporating suitable high quantum yielding

chromophores into the voids of MOF 1a, MOFs 2 and 3 were obtained. MOFs 2

and 3 displayed further enhancement on the solid-state MEPL signal due to the

FRET between the encapsulated guest chromophores and the host MOF. These

two strategies described above should disclose a fresh route for the future

production of solid-state MEPL materials and devices.

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Chapter 7 Conclusions

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Chapter 7

Conclusions

7.1 Summary of results

In this dissertation, we focus on the investigations of the nonlinear optical

absorption properties of two novel materials: namely, (1) graphene and (2)

metal-organic frameworks (MOFs). Due to its unique electronic structure,

graphene has been demonstrated to possess unique optical properties. Especially,

intriguing nonlinear optical properties of graphene have been revealed in the

infrared spectral range. Saturation in interband transitions of graphene induced by

one-photon absorption (1PA) has been utilized for mode-locking technology, and

the saturation intensity has been characterized in the infrared spectral range.

However, little is known about the spectral dependence of 1PA saturation in

graphene which is essential for both realistic applications and fundamental

understanding. Until now, no studies have been carried out on the spectral

dependence of 1PA saturation in graphene the spectral range from visible to

near-infrared (NIR).

Apart from 1PA saturation, two-photon-induced interband transitions in

graphene are also very important to various practical applications in photonics

and optoelectronics. The presence of two-photon absorption (2PA) in graphene

will have an important impact on the stability of the continuous-wave,

mode-locking operation, which has been both experimentally and theoretically


215

confirmed in saturable absorber mirrors made of InGaAs quantum wells.

Furthermore, 2PA in graphene in the infrared range has been applied to realize the

coherent control and noncontact generation of ballistic photocurrents in graphene,

where the quantum interference between one- and two-photon-induced interband

transitions has been utilized. Previously, Yang et al demonstrated, both

theoretically and experimentally, that 2PA was as important as 1PA saturation in

AB-stacking bilayer epitaxial graphene in the NIR spectral range. However, until

now 2PA of graphene around the saddle point (M point) with one-photon energy

(ħ) lying in the visible spectral range has not been investigated.

To systematically investigate the interband 2PA and 1PA saturation of

graphene over the visible and NIR spectral range (435-1100 nm), we have carried

out Z-scan measurements on CVD graphene films with femtosecond laser pulses

as detailed in Chapter 4. In Chapter 4, firstly we present our unambiguous

determination of interband 1PA saturation and 2PA in high-quality, CVD-grown

graphene films over the studied spectral range. As for 2PA in graphene, we find

that the measured 2PA coefficients in the NIR spectral range of 800 to 1100 nm

can be explained by the theoretical model reported by Yang et al, which is based

on the optical transitions near the Dirac point (K point). We also systematically

investigate the interband 2PA of graphene in the visible spectrum (435-700 nm)

and report our observation of an enhancement induced by the excitonic Fano

resonance at the saddle point (M point) of graphene. By applying the second-order,

time-dependent perturbation theory on interband transitions among three states


216

near the saddle point, we develop a semi-empirical model to take excitons in

graphene into consideration. And the model is in agreement with the

photon-energy dependence of the observed 2PA spectrum with a scaling factor of

B = (1~5) × 102 cm/MW/eV5. Our results verify, for the first time, that excitonic

Fano resonance plays an important role for the 2PA of graphene in the visible

spectrum, both experimentally and theoretically. The resultant 2PA coefficients of

graphene in the visible spectral range no longer follow the -4 scaling law ( is

the photon frequency) as predicted before and are comparable to that in the NIR

spectral region, making graphene a broadband two-photon absorber.

Besides, a quadratic photon energy dependence of the measured saturation

intensities/fluences has been observed over the investigated spectral range

(435-1100 nm). This is in agreement with the previous reports obtained in the

mid-infrared (MIR) and NIR spectral range. The revealed quadratic photon energy

dependence of the 1PA saturation in graphene can be understood by a qualitative

explanation, where the linear dependence of density of state on energy in

graphene combined with its linear increase of carrier scattering rate out of the

excited state with increasing energy is believed to lead to the quadratic

dependence.

Organic molecules with large nonlinear optical properties are in great demand

for a variety of applications in nonlinear optics, photonics and bio-photonics.

However, frequency up-converted photoluminescence (PL) or lasing exhibited by

the organic molecules in the solution is usually quenched in the solid-state form


217

due to aggregation. Efficient frequency up-converted luminescent materials in the

solid-state form are highly preferable in real applications due to a higher

resistance to photobleaching. In recent times, metal-organic frameworks (MOFs)

consisting of metal ions coordinated to organic molecules with one-, two-, or

three-dimensional crystal structures have been extensively investigated. By taking

advantage of the combined properties of the metal ions and the organic ligands,

they hold the key for promising hybrid materials with unique properties.

Furthermore, such MOFs can be porous. And it is possible to immobilize

nonlinear optically active chromophores or even lasing dyes into the pore spaces

of MOFs to minimize the aggregation-caused quenching. By encapsulating

suitable dyes into MOFs, two-photon imaging and lasing were documented one

and two years ago. The immobilization of nonlinear optically active

chromophores as ligands of MOFs should also be able to minimize

aggregation-caused quenching. Moreover, this strategy can largely enhance the

amenability as the ability of encapsulating molecules is restricted by the pore size

of MOFs. However, up to date, only one investigation has been carried out in this

field which is in parallel with our work, where a zwitterionic ligand is

incorporated into a MOF which displayed two-photon excited PL.

In Chapters 5 and 6, we have selected a nonlinear optically active ligand trans,

trans-9, 10-bis (4-pyridylethenyl) anthracene (An2Py) based on well-established

guiding principles in the architecting of chromophores with relatively large

nonlinear optical properties to synthesize [Zn2(trans,trans-4,4


218

stilbenedicarboxylic acid (SDC))2(An2Py)] (MOF 1a) with Zinc cations and

co-ligand H2SDC. Subsequently, two high quantum yielding chromophores are

encapsulated into the pore spaces of MOF 1a to obtain

[Zn2(SDC)2(An2Py)]∙perylene (MOF 2) and [Zn2(SDC)2(An2Py)]∙anthracene

(MOF 3). Multiphoton excited PL (MEPL) measurements show the crucial role of

two-, three- and four-photon absorption in the excited PL from both the ligand

An2Py and the MOFs in the solid-state form. Our experimental results reveal that

MOF 1a exhibits largely enhanced MEPL compared to that of its ligand. This is

induced by the rigidifying of the chromophore in the MOF framework which

minimizes the aggregation-caused quenching. Further enhancement on the MEPL

is achieved in MOFs 2 and 3. The Förster resonance energy transfer (FRET)

between the host MOF and the guest molecules leads to such an enhancement.

Our initial study suggest that MOF can be made to be a promising frequency

up-converted efficiently fluorescent material in the solid-state form by utilizing

the above two strategies. Out experimental finding provides possible solutions to

aggregation-caused quenching in the MEPL of organic molecules in the

solid-state form and discloses a fresh route for the future production of photonic

materials and devices in the solid-state form.

7.2 Suggestions for the future research work

For the future research on the nonlinear optical absorption properties of

graphene, several interesting directions are suggested as follows. Firstly, a

quantitative theoretical study on the spectral dependence of 1PA saturation in


219

graphene is essential and can help to provide guidance for applying graphene as

saturable absorber over a wide spectral range. Secondly, studying the excitonic

Fano resonance effect on the 2PA in physically or chemically doped graphene is

another interesting topic, in which more rich physics and desirable materials

properties can be found. Thirdly, investigating the nonlinear optical absorption

properties of graphene quantum dots and graphene nanoribbons is an intriguing

research direction, since the electronic band structure of graphene can be

modulated by the quantum confinement effect and can be tuned by controlling the

size, shape and distribution of the graphene quantum dots and nanoribbons.

Moreover, several promising and important avenues for the future

investigations on the nonlinear optical properties of MOFs are suggested as

follows. Firstly, a direct extension of the work presented in this dissertation is

incorporating chromophores with larger nonlinear optical absorption and higher

PL quantum yield as ligands of MOFs to achieve even brighter multiphoton

excited frequency-upconverted PL in the solid-state form. Secondly, another

extension of the work is to achieve multiphoton excited frequency-upconverted

lasing originating from the ligands of MOFs, which needs both incorporating

lasing materials as ligands of MOFs and the synthesizing single crystal MOFs

with planar and high quality surface serving as lasing cavity. Thirdly, since MOFs

contain metal ions or metal ion clusters in their structure, investigating the

magnetic effect on the nonlinear optical properties of MOFs by applying strong

magnetic field on the MOFs should be an enticing research topic.

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