METAL INSULATOR MULTI-LAYER SURFACE PLASMON …tc335tx2847/final... · METAL INSULATOR MULTI-LAYER...

METAL INSULATOR MULTI-LAYER SURFACE PLASMON

DEVICES

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MATERIALS

SCIENCE AND ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Anu Chandran

August 2014

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/tc335tx2847

© 2014 by Anu Chandran. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/tc335tx2847

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Mark Brongersma, Primary Adviser


Jennifer Dionne


Shanhui Fan

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Preface

Surface plasmon based devices have attracted significant of attention over the last

decade with exciting applications like negative refraction, optical cloaking, perfect

lenses, and meta-surfaces. They have also enabled highly efficient and compact

electro-optical devices bridging the gap between optical (micron) and the electronics

(nano) scale devices. At the heart of many of these devices and applications are

multi-layer metal insulator structures, where the interaction of surface plasmons at

various interfaces unlock these surprising properties. This thesis focuses on the scat-

tering and transmission properties of plasmon modes in metal insulator multilayer

structures.

In the first part of the thesis, we will describe a theoretical model for standing wave

resonances in Metal-Insulator-Metal surface plasmon cavities. These calculations,

which are in excellent agreement with full field finite difference simulations, aid in

furthering our understanding of plasmon phase pickup on reflection from the cavity

terminations. This phase pickup is associated with the near-field energy storage at

those terminations, and the imaginary part of the reflection coefficient is shown to be

approximately proportional to the stored energy.

We then focus on a different, yet related geometry for a surface plasmon antenna, a

metal stripe wave guide above a metallic ground plane. Staggered confocal microscopy

is used to study the scattering properties of the stripe antenna. CdSe/ZnS quantum

dots are sandwiched between the stripe and ground plane. Dual purposing of the

stripes as electrical lead and an optical element is illustrated through low temperature

quantum confined stark effect measurements. Finite difference calculations of the

surface plasmon transmission spectra through the truncated stripe waveguide cavity

iv

is shown to be well modeled by a two-path-two-mode coupled cavity model.

v

Acknowledgements

I would like to thank Mark, my thesis advisor, for his support and guidance. He was

very patient with me, giving enough latitude to pursue different lines of investigations.

He was always accommodating, even when some of those investigations bore no fruit.

But above all I would like to thank him for his kindness and sensitivity during my

late wife’s unsuccessful battle with cancer.

There are quite a few people in Stanford that I would like to thank, and it is only

at the interest of brevity that I don’t mention all by name. Prof. Shanhui Fan, for

introducing me to fundamentals of optics and waveguide theory, Prof. Nick Melosh

and his students for extreme generosity with chemicals and lab equipments during

fabrication runs and Dr James Conway for always being there for help with e-beam

lithography.

I consider my interaction with Rashid Zia a highlight of my Stanford experience.

Rashid, introduced a much needed dose of heavy skepticism into me, which ultimately

made me, in my opinion, a better scientist. I would like to thank Edward Barnard

for all the fun times exploring slashdot, hacker news, and experiments with arduino.

Ed has the habit of always showing up just at the right place at the right time to

help. I should also definitely mention David Barsic for showing me the delicate art

of nano-optics with toothpicks and Jon Schuller, random-T-shirt-baggy-jeans-rap-

star, for helping me realize that science does not always have to be straight laced.

I would like to thank Patrick Landreman, and Xinpeng Huang for their help with

administrative issues while I was working remotely from Houston. I would like to

thank all the group members (past and present) for an extremely enjoyable experience:

Alex, Alok, (F)anu, Justin, Linyou, Mark Selker, Ragip, Rohan, Ken, Mike, Pengyou

vi

and Young-Chul.

I would also like to express my gratitude to the whole Bechtel International center

staff, who work very hard to help foreign students jump through the visa hurdles.

I would like to thank my parents, for their love and support without which I would

not have reached this far. I would also thank my dear wife Ammu for her support

and my daughter, little Tenaya, just for being there in my life.

vii

Contents

Preface iv

Acknowledgements vi

1 Sub-wavelength optical cavities 1

1.1 Metal-Dielectric-Metal Plasmon Devices . . . . . . . . . . . . . . . . 5

1.1.1 Surface plasmon dispersion in MDM structures . . . . . . . . 5

1.1.2 Emitter plasmon interaction in metal-dielectric structures . . . 7

1.2 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 MIM plasmon cavities 11

2.1 SPP Modes of MDM structures . . . . . . . . . . . . . . . . . . . . . 12

2.1.1 Transmission into the cavity . . . . . . . . . . . . . . . . . . . 13

2.1.2 Calculation of the SPP reflection coefficient . . . . . . . . . . 15

2.1.3 Cavity Properties . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.4 Origin of the reflection phase . . . . . . . . . . . . . . . . . . 16

2.1.5 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Surface Plasmon Patch Antenna 27

3.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Scattering under normal illumination . . . . . . . . . . . . . . . . . . 32

3.3 Plasmon interference in patch antenna structures . . . . . . . . . . . 36

viii

3.4 Coupled cavity model for plasmon scattering . . . . . . . . . . . . . . 41

4 Electrical modulation 46

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Sample fabrication and experiment details . . . . . . . . . . . . . . . 47

4.3 Quantum Confined Stark Effect . . . . . . . . . . . . . . . . . . . . . 50

5 Conclusion 53

A Plasmon reflection and excitation 56

A.1 Plasmon reflection at cavity termination . . . . . . . . . . . . . . . . 56

A.2 Cavity plasmon excitation from free space . . . . . . . . . . . . . . . 59

B Energy stored in the near-field 62

C Two mode cavity resonance 66

Bibliography 70

ix

List of Figures

1.1 Schematic and field profile for a single interface surface plasmon . . . 3

1.2 Methods of surface plasmon excitation . . . . . . . . . . . . . . . . . 4

1.3 Schematic of MDM structure, field profile and dispersion . . . . . . . 6

1.4 Some optical antenna examples . . . . . . . . . . . . . . . . . . . . . 8

2.1 Schematic of a finite length MDM cavity. Hy-field profile of the sym-

metric SPP mode is shown. . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 |r| and φ (phase) for different values of εm as a function of scaled

dielectric thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Reflection amplitude |r| and φ (phase) for an Ag-Air-Ag MDM struc-

ture as a function of wavelength for different dins values. Solid lines:

Without loss. Dotted lines: With loss. . . . . . . . . . . . . . . . . . 22

2.4 rimλ for Ag-Air-Ag cavity for different dins . . . . . . . . . . . . . . 23

2.5 Transmission efficiency (Teff ) through a Ag-Air-Ag cavity for different

cavity lengths (L) as a function of wavelength. . . . . . . . . . . . . . 24

2.6 Cavity resonance length as a function of dielectric thickness for different

orders. Free space wavelength λ=900nm. (Ag-Air-Ag cavity with loss.) 25

2.7 Q-factor of the cavity vs cavity length for different dielectric thick-

nesses. Free space wavelength λ=800nm. Ag-Air-Ag cavity with loss 25

3.1 Schematic and SEM of patch antenna structure . . . . . . . . . . . . 29

3.2 Photograph of the Witec Alpha SNOM system . . . . . . . . . . . . 30

3.3 Schematic of the confocal scan configuration . . . . . . . . . . . . . . 31

3.4 Schematic of fabrication process . . . . . . . . . . . . . . . . . . . . 32

x

3.5 Confocal scan of patch antenna emission . . . . . . . . . . . . . . . . 33

3.6 Normalized confocal scan of patch antenna emission . . . . . . . . . . 34

3.7 Plasmon mode index and propagation length for patch antenna geometry 36

3.8 Schematic of plasmon scattering experiment and FDFD simulations . 37

3.9 Confocal scan of surface plasmon scattering . . . . . . . . . . . . . . 39

3.10 Normalized confocal scan of surface plasmon scattering . . . . . . . . 40

3.11 Coupled cavity model . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.12 Patch antenna transmission . . . . . . . . . . . . . . . . . . . . . . . 43

3.13 Coupled cavity interference . . . . . . . . . . . . . . . . . . . . . . . 45

4.1 Schematic of the stark shift measurement setup . . . . . . . . . . . . 48

4.2 QD temperature stability under ALD . . . . . . . . . . . . . . . . . 49

4.3 Photograph of the thermal stage mounted on the Witec SNOM . . . 49

4.4 Voltage dependent PL from quantum dots . . . . . . . . . . . . . . . 51

4.5 Wavelength shift as a function of electric field . . . . . . . . . . . . . 52

xi

Chapter 1

Sub-wavelength optical cavities

Deep sub wavelength cavities which allow mode confinement with high field concen-

tration are very attractive for small footprint active nanophotonic devices. The possi-

bility of concentrating light into a nanoscale volume has a profound effect on the effi-

ciency of linear and nonlinear optical processes, which often scale with the ratio of the

optical quality factor (Q) to the mode volume Vm. Traditional dielectric optical micro

cavities have very low losses and high quality factors, but suffer from mode volume lim-

itations. The optical modes in these structures cannot be confined to dimensions much

smaller than the wavelength in the dielectric. Metallic optical cavities, where energy

is stored in the Surface Plasmon Polariton (SPP) fields, can support modes confined

to volumes much smaller than the wavelength[1, 2, 3]. Despite their modest quality

factors (typically between 10-100), metallic cavities can have such small mode volumes

that they can outperform much higher Q dielectric microcavities (Q ∼ 106)[4, 5, 6].

As such, they have been proven useful for a variety of applications[1], including sin-

gle molecule sensing [7], spectroscopy [8, 9], optical trapping [10], surface enhanced

reactions[11, 12], spontaneous emission modification[13, 14, 15, 16], Surface Plasmon

Polariton (SPP) modulators[17, 18, 19, 20] and SPP sources [21, 22].

Surface plasmons are coherent collective electron oscillations that propagate along

a metal surface. They couple very strongly to electromagnetic waves, and as such

are better described as surface plasmon polaritons. For surface plasmons on a metal

surface with permittivity εm bounded by a dielectric material of permittivity εd we

1

CHAPTER 1. SUB-WAVELENGTH OPTICAL CAVITIES 2

can write the dispersion relationship as[23],

kx =ω

c

(εmεdεm + εd

)1/2

(1.1)

Here, kx is the wave vector along the metal-dielectric interface, ω the angular fre-

quency of the plasmon and c the velocity light in vacuum. At optical frequencies,

typical metals have Re[εm] < 0 and hence k > ωc. Maxwell’s equation constrains the

wave vectors such that (k2x + k2y + k2z)(1/2) = ω

c. So, the wave-vectors out of the plane

of propagation will be imaginary (with a small real component in the case of metals

with losses). This implies that the surface plasmon is confined to the metal dielec-

tric interface, propagates along the interface, but evanescently decays away from it.

A schematic of a surface plasmon field profile and dispersion relationship is shown

in Fig. (1.1). This is the most critical point of difference between surface plasmon

modes and optical modes in dielectric cavities. Metal-dielectric interface is capable of

supporting modes with higher momentum than what is allowed for electromagnetic

waves propagating in the dielectric material. Consequently, the usual limits of mode

confinement applicable to dielectric devices no longer apply for surface plasmon cav-

ities. The increase in field confinement is associated with increased resistive losses in

the metal, but with suitable low loss metal choice a wide variety of confinement and

propagation regimes unavailable to dielectric optical devices can be accessed in plas-

monic waveguides and cavities[24, 25] A useful simplified model for metal dispersion

in optical frequencies is the drude model in which the metal permittivity at frequency

ω is given by,

εm =

(1−

ω2p

ω2

)(1.2)

For low frequencies the εm is a large negative number and for ω = ωp/√

1 + εd, the

surface plasmon resonance frequency, we have, εm = −εd. From equation(1.1) we

now have kx → ∞. This of course is an idealization and in real metals with losses,

the wave vector only approaches a large finite value. The larger the propagation

wave vector faster the evanescent decay away from the interface, implying a strong


+ + + - - - - + + + + - - - - + H ¤

E

X

Z Dielectric

Metal

Surface Plasmon a) b)

c)

Figure 1.1: a) Schematic of surface plasmon fields on a metal dielectric interface.Plasmon propagates in the X-direction. This is a TM wave with H field directed outof the plane. b) The H field intensity near the interface. The field is strongly localizedto the surface, decaying evanescently to either side. c) The dispersion relation forsingle interface surface plasmon

confinement of energy to the interface. This dispersion related field confinement to

the interface is exploited in a wide variety of surface plasmon applications and devices.

Typically wave vector of a surface plasmon at a metal dielectric interface lies outside

the light line for the dielectric. This makes it difficult to efficiently couple free space

light to surface plasmon modes. There are many possible ways to provide extra

momentum to the incident radiation to facilitate coupling to the plasmon modes[29].

Fig. (1.2) shows some of the techniques traditionally employed in surface plasmon

excitation. A high index prism near a metal-dielectric surface, a grating with suitable

periodicity, a localized source of excitation like a probe tip with a broad spread

of available momentum states can all excite surface plasmons. In addition, other

methods like electrical excitation through hot electron tunneling, and coupling of


(g)

(d) (e) (f)

(a) (b) (c)

(h) (i)

(d)

Figure 1.2: Many methods for plasmon excitation. a) Kretchmann configurationb) Two layer Kretchmann configuration c) Otto configuration d) Excitation witha SNOM probe e) diffraction from a grating f) Scattering from surface features g)Excitation by a high energy electron beam h) Evanescent coupling from a tapered fiberi) Tunnel junction plasmon excitation. Figures taken from the following references.(a-f) [26], (g)[27], (h)[2] i)[28]

photoluminescence to surface plasmon modes are also employed in compact SPP

sources.


1.1 Metal-Dielectric-Metal Plasmon Devices

The geometry of the plasmon device can also determine the characteristics of the

surface plasmon excitations supported by it. When two metal-dielectric interfaces are

brought close to each other, the surface plasmons on the interfaces can interact and

split into degenerate modes with different wave vectors. This provides an additional

level of control over the plasmon resonance and confinement in devices. One very

simple and versatile class of such a surface plasmon device is the Metal-Dielectric-

Metal (MDM) surface plasmon geometry.

1.1.1 Surface plasmon dispersion in MDM structures

Surface plasmon modes in metal-dielectric-metal multilayer structures have been ex-

tensively studied in the past[3, 30]. They are most easily analyzed and understood

in a planar two-dimensional device geometry where the metal on either side of the

dielectric are assumed to be the same and infinitely thick. The proximity of the

two metal dielectric interfaces causes the splitting of the degenerate modes at those

interfaces. Due to the symmetry of the structure these modes have symmetric and

anti-symmetric field profile as shown in Fig. (1.3 a). A schematic of the resulting

dispersion relationship for the modes is shown in Fig. (1.3 b). As the dielectric layer

thickness ‘d’ is decreased the symmetric mode dispersion shifts to the right, giving the

mode lower wavelength and group velocity. As a consequence, a larger fraction of the

mode energy is stored in the metal, resulting in increased losses and consequently,

a lower propagation length. This high index mode is strongly confined with large

electric fields in the dielectric. Also, its high optical density of states makes it an

attractive mode to target for enhanced light matter interaction. The anti-symmetric

mode dispersion on the other hand, shifts towards the light line and has a larger

fraction of its energy guided through the dielectric. The complementary structure

to the MDM geometry is the DMD geometry, a thin metallic plate surrounded by di-

electric on either side. They can serve as nano-scale optical waveguides, guiding light

below the diffraction limit. A schematic of the structure and a plot of the plasmon

dispersion relation is shown in Fig. (1.3). For small metal thickness, the modes in


Symmetric Anti Symmetric

d

H-field profile Metal

Metal

ω

k =2π

λsp

Decreasing d

Single interface a) b)

Figure 1.3: a) Schematic of the MDM structure, and the magnetic field profile for thesymmetric and anti-symmetric modes. (b) A schematic of the dispersion relationshipfor the two modes. Single interface surface plasmon dispersion relationship is alsoincluded for highlighting the dispersion change with the dielectric thickness ‘d’

the structure split just like modes in the MDM geometry. Symmetric modes in the

plate geometry guide most of their energy through the dielectric and hence have very

long propagation length [31]. Metallic stripe waveguides and other similar structures

have found wide applicability in a variety of plasmon assisted optical devices [32, 33].

By truncating the multilayer metal dielectric structures to wavelength scale di-

mensions one can construct retardation based plasmon resonators[34, 35]. Of these,

finite-length metal dielectric metal cavities have attracted particular attention for

their ability to concentrate light to nanoscale dimensions[36] through the excitation

of wavelength-tunable cavity resonances[37]. The high field intensity in the dielec-

tric region make these structures well-suited for active plasmonic structures. MDM

plasmonic slits have also been shown to enhance optical absorption within materials

adjacent to the MDM end-face[38, 39]. The relative ease of fabricating the MDM

structures together with the possibility of using the metal layers as electrical contacts

also make this geometry well-suited for optoelectronic applications[17, 22, 40, 41].

Plasmonic cavities are most readily studied with full field simulations, which al-

though exact, do not lend themselves to a clear physical interpretation. Time or

frequency domain full field simulations correctly predict the resonance phenomena

in these cavities, but does not immediately make apparent the interaction of the


modes that resulted in the resonance. The resonant optical properties of wavelength-

scale plasmonic antennas and cavities are most easily understood if seen as trun-

cated waveguides supporting surface plasmon-polaritons (SPPs) with a well defined

λspp[42, 34, 43]. In such finite-sized structures, the SPPs undergo reflections from

the end faces and the constructive interference of multiply reflected SPPs can give

rise to Fabry-Perot resonances[44, 34]. The optical quality factor associated with

the resonances is determined by the SPP reflection amplitude as well as propagation

losses. On the other hand, λspp and the phase acquired upon reflection from the end

faces, determine the resonant length, Lres, of the cavity. This point directly follows

from the resonance condition that the round trip phase for SPPs must be an integer

multiple of 2π. For the case of the MDM cavity this means that the resonant width

depends on the order of the resonance. It has been shown that plasmonic resonators

can exhibit large reflection phases and in these cases our microwave intuition that

suggests a resonance length of mλ2

is insufficient [45, 46, 34, 42].

1.1.2 Emitter plasmon interaction in metal-dielectric struc-

tures

The presence of a metal surface near an optical emitter can dramatically affect its

emission rates. The high field intensities that can be generated near a metallic nanos-

tructure increases the optical density of states and thereby increases the excitation

and decay rates of the emitters[47, 48]. This can be effectively leveraged to increase

the decay rates through preferred radiative pathways over that through non radiative

decay channels. Typically this is done by designing the metallic nano-structure to be

resonant at the emission frequency of the optical emitter. Thus, the nano-structure

acts as an optical antenna and can also be used to shape the directionality of the

the emitted radiation. But unlike a traditional antenna, which is fed by transmission

line like current sources, optical antennas are sourced by placing a nano-scale emitter

very near the antenna. Some typical optical antenna designs are shown in Fig. (1.4).


a) b)

c) d)

Figure 1.4: Some optical antenna examples : a) Yagi Uda antenna in optical regimeand b)Split ring resonator antenna [49], c) Bow tie antenna[50] and d) TruncatedMDM cavity [37]

Optical emitters like excited molecules are inherently quantum mechanical in na-

ture. But they are very well approximated by a semi-classical formalism treating

them as oscillating dipoles. Their localized nature implies a wide uncertainty in its

momentum and hence it can couple to surface plasmon modes outside the light line,

through near field coupling. In this context it should be noted that depending on the

application, emission into a plasmon mode may be considered as non radiative if a

mechanism for coupling the plasmon mode to the free space radiation modes do not

exist. So a typical antenna has three major design parts,

1. Close spatial coupling of the emitter to the antenna, enabling near field transfer

of energy to the available surface plasmon modes.

2. A high density of plasmon mode states across the frequency band of the emitter,

usually achieved through a resonance.

3. A low loss mechanism to couple the plasmon modes to available free space

radiation or cavity modes of interest.


The presence of overlapping plasmon resonance frequency and emission frequency

is not a necessary condition for radiation rate enhancement. It has been shown that

there can be radiation rate enhancement in 2-D MDM structures by excitation of non-

resonant plasmon modes, far away from the surface plasmon resonant frequency[51].

It is also, not necessary to have distinct components perform the three basic functions

in an optical antenna. For many antennas in the optical regime, like the bow-tie or

split ring antenna, a single element performs many, if not all, of the functions for the

proper operation of the antenna. Surface plasmon cavities, due to the lossy nature

accompanying energy storage in the metal, have typically low quality factors of the

order of 10, but can outperform the high Q dielectric cavities because of their high

Q/V . These high fields can also be used to generate non-linear interactions in metallic

structures, including second[52, 53] , third harmonic generation [54], and two photon

excitation[55]. The above discussion focused on antenna operation as a transmitter.

Design rules for antenna operation in the complementary role, where antenna collects

free space radiation to generate high intensity fields and currents follow very similar

set of constraints.

1.2 Outline of this thesis

In this thesis work, we focused on the study of multi-layer metal dielectric surface

plasmon devices, looking at planar MDM devices and truncated MDM cavities. This

geometry is clearly important from a theoretical and practical device perspective. The

high mode density that can be achieved in these structures enables fundamental inves-

tigations into optical emission process tailoring. The possibility of dual-purposing the

optical antennas also as electrical leads make it extremely attractive for low footprint

optoelectronic devices.

From the earlier discussions, it is clear that a quantitative prediction of MDM cav-

ity resonances requires knowledge of the reflection phase and amplitude. The problem

of SPP reflection has been extensively studied in the past for single interface surface

plasmons with various dielectric[56] and metallic[57] discontinuities, and thin dielec-

tric overlayers [58]. An exact analytical treatment of SPP reflection in multi-layer


structures is complicated by the presence of multiple SPP modes in addition to the

bulk propagating and evanescent modes. Calculation of SPP waveguide modes along

finite width metallic stripe waveguides by using an effective index model has been done

before[59], but this framework is not ideally suited to situations where SPPs run into

an abrupt termination of a waveguide. It has been shown that for a metallic rod an-

tenna an approximation for this phase pickup with a factor for the finite reactance of

the rod end faces correctly predicts the resonance wavelengths[34]. Recently, numer-

ical calculations of the reflection amplitude and phase for a terminated metal sheet

have been made using full field simulations and these were used successfully to predict

the resonant properties of stripe antennas (Truncated DMD waveguides)[46]. These

calculations are in reasonable agreement with recent experiments[45]. For MDM cav-

ities analytical calculations of reflection phase exist for lossless and dispersion free

metals[60], but an extension to real metals would be of value.

We start with theoretical calculations of plasmon reflection coefficients in chapter-

2. We then extend the calculation to resonances in finite length truncated MDM

cavities and also look at the near field energy storage near the cavity terminations.

Next we look at a surface plasmon optical patch antenna device in chapter-3. We ex-

perimentally study the coupling between the patch antenna and CdSe/ZnS quantum

dots placed in the dielectric region between the antenna and the ground plane. Con-

focal emission scans show the evolving emission mode profile with increasing antenna

length. The scattering of single interface surface plasmon by the patch antenna is

studied with the help of a confocal scan. We also show, theoretically, the interfero-

metric nature of the antenna response due to the interaction between the different

possible modes in the structure. In chapter-4 we look at electrical modulation of quan-

tum dot emission. By applying a DC voltage bias between the patch antenna and

the ground plane we show the modulation in emission efficiency and stark effect shift

of the emission frequency. We finish this thesis with conclusions and future outlook.

Appendices at the end give more details on the different theoretical developments and

simulations in the thesis.

Chapter 2

MIM plasmon cavities

In this chapter we study the plasmon resonances in finite length Metal-Insulator-Metal

cavities by treating them analogous to Fabry Perot cavities. We start by calculating

analytically the reflection coefficient and phase acquired by SPPs upon reflection from

the cavity end face using a simple mode matching model for real metals exhibiting

both dispersion and loss. Our approach is similar to that in Ref ([60],[61]), but

employs an intuitive energy conservation boundary condition in addition to the field

matching at the cavity termination. The model clearly demonstrates the origin of the

reflection phase as arising from coupling to the evanescent, near field modes in the

free space region. We also show that the imaginary part of the reflection coefficient

is approximately proportional to the energy stored in the near field of the MDM

cavity end face. The calculations demonstrate that by choosing the right dielectric

thickness it is possible to maximize this near field energy stored, resulting in a high

electric field intensity in that region. With knowledge of the excitation and reflection

coefficients, we finally also calculate analytically the transmission cross section and

the quality factor (Q) of finite length MDM cavities with real material properties

including losses. Comparison with full-field finite difference simulations show that the

model can very accurately predict the resonance behavior of MDM cavity structures

for a wide range of dielectric thicknesses and cavity lengths. Design of a plasmonic

device for operation at a particular wavelength, accounting for the SPP dispersion

and scattering will require the use of full-field simulations. However, an analytical

11

CHAPTER 2. MIM PLASMON CAVITIES 12

model that captures the essential details of surface plasmon resonance conditions in

these devices, can serve as a good design rule and further our understanding of the

physics of SPP reflections in MDM devices. This would enable leveraging of familiar

concepts and designs from other areas, like microwave and radio frequency circuits.

2.1 SPP Modes of MDM structures

Figure(2.1) shows a schematic of the truncated MDM waveguide resonator that we

investigate. It consists of two infinitely thick metallic layers separated by a thin

dielectric region, through which power is guided in an MDM or gap SPP mode.

The thickness of the dielectric is denoted by dins and the SPPs propagates in the

x-direction. The dielectric and the metal dielectric constants are denoted by εd and

εm respectively.

It is important to understand the dependence of the wavelength and propagation

loss of the allowed SPPs in the MDM cavity as they determine the resonant cavity

lengths and the associated quality factors. SPP modes in planar MDM structures have

been extensively studied in the past [25, 30, 3, 62, 63]. In general, these waveguides

support SPP modes with both symmetric and anti-symmetric field profiles (Hy-field),

but for sufficiently thin dielectrics only the mode with a symmetric field profile is

allowed; such structures are considered here. Also, the symmetry of the structure

prevents mixing between the modes at the reflective cavity termination. For this

reason, only the symmetric mode is included in this study. The validity of using only

this mode will be verified by full-field simulations. As the dielectric thickness, dins,

is reduced the mode index as well as the propagation loss for the symmetric mode

increases. It is clear that the increased lateral mode confinement comes at the cost

of lowered SPP propagation length. This in turn could affect the Q in the regime

where the losses are dominated by propagation losses rather than reflection losses.

A detailed analysis of the variation in SPP dispersion with the structure dimensions

can be found in Ref.([62]).

In the following section we look at resonances in finite length MDM cavities as-

cribing them to constructive interference of field symmetric modes reflected from the


cavity end faces. We assume that the field inside the MDM cavity can be described

only using forward propagating and reflected SPPs. In addition to the propagating

modes, the structure also supports a continuum of evanescent (in the propagation

direction) modes, which are required for a complete description of the fields inside

the cavity[64]. Such local modes are important near terminations of waveguides and

compact cavities. We assume that the contribution of these modes on the SPP reflec-

tion coefficient can be ignored. No assumption is made regarding the nature of the

fields outside the cavity. We look at resonance properties in the visible to near infra

red frequency range for very thin dielectric MDM cavities. The theory is developed

assuming infinite metal outer layer thickness and a small dielectric thickness.

Figure 2.1: Schematic of a finite length MDM cavity. Hy-field profile of the symmetricSPP mode is shown.

2.1.1 Transmission into the cavity

In this section we explore the coupling of a normally incident, transverse magnetic

(TM) plane wave, H = (0, Hy, 0), with a free space wavelength λ, into an MDM cavity

Fig.(2.1). The wave that is transmitted into the cavity is assumed to be a symmetric

gap SPP. The reflected light is described by a continuum of waves moving back away

from the cavity. From continuity of the Ez field we then find:

Epwz + Eref

z = tEspz (2.1)


Here, ‘t’ is the amplitude of the forward propagating symmetric SPP electric field Espz

and can be viewed as an SPP excitation coefficient. By assuming unity amplitude

for the incoming plane wave field, Epwz , and expanding the reflected field, Eref

z , into

a continuum of plane wave modes with amplitude g(k), Eqn.(2.1) can be re-written

as:

1 +

∫ ∞−∞

g(k)eikzdk = tEspz (2.2)

By taking the fourier transform of Eqn.(2.2) we get

g(u) =t

2π

∫ ∞−∞

Espz e−ik0uzdz − δ(u) (2.3)

where, k is written as k0u with k0 = 2πλ

and δ is the Dirac impulse.

In addition to the field continuity equation we need another boundary condition

to calculate, t, the SPP excitation coefficient. One physically meaningful boundary

condition is the continuity of the total integrated x-directed poynting flux passing

through the y-z plane at the cavity termination. As the system is translationally

invariant along the y-direction, this boundary condition can be expressed in terms of

integrals along the z-direction. With this we get:∫ ∞−∞

dz(Epwz + Eref

z )× (Hpwy +Href

y )∗ =

tt∗∫ ∞−∞

dzEspz ×Hsp ∗

y (2.4)

Here ‘∗’ denotes the complex conjugate of the quantity. Simplifying Eqn.(2.4) with

Eqn.(2.2) and solving for ‘t’, we arrive at the following expression,

t =

2I1(0)√

ε0µ0

1λ

√ε0µ0

∫∞−∞ du

|I1(u))2|√1−u2 −

∫∞−∞ dzE

spz H

sp∗y

∗ (2.5)

where

I1(u) =

∫ ∞−∞

Espz e−ik0uzdz (2.6)


2.1.2 Calculation of the SPP reflection coefficient

Figure(2.1) also schematically indicates the SPP reflection process, which is con-

sidered next. It shows how a symmetric SPP mode is incident from the left and

propagates towards the cavity termination on the right. Upon reflection from the end

face, a backward propagating SPP is generated together with a continuum of forward

propagating plane waves, Efs, outside of the cavity. Again, we can write a continuity

equation for the electric field, which looks as follows,

(1 + r)Espz = Efs

z (2.7)

By balancing the total Poynting flux through the yz plane at the cavity termination

we obtain:

(1 + r)(1− r∗)∫ ∞−∞

dzEspz

(Hspy

)∗=∫ ∞

−∞dzEfs

z

(Hfsy

)∗(2.8)

Using the same simplifications as in the calculation of the excitation coefficient, and

expanding the free space transmitted electric field into a continuum of plane waves,

we arrive at the following expression for the reflection coefficient:

1− r∗

1 + r∗=

1

λ√

µ0ε0

∫∞−∞ dzE

spz H

sp∗y

×

∫ ∞−∞

du−|I1(u)2|√

1− u2(2.9)

2.1.3 Cavity Properties

In this section we discuss cavity properties of interest and how they can be determined

from the SPP behavior described in the previous sections. One of the key properties

of a cavity that can be verified experimentally is the total transmitted power through

the cavity, Pout. This quantity can be derived analogous to that of a conventional


Fabry-Perot cavity as[65]:

Pout =

∣∣∣∣ teiβL

1− r2e2iβL

∣∣∣∣2 ∫ ∞−∞

dzEspz H

sp∗y

(1− |r|2

)(2.10)

The spectral behavior of Pout near a resonance can be approximated by a Lorentzian

line shape centered at an angular frequency ω0 and whose full width at half maximum,

∆ω, is determined by the optical quality factor for the cavity.

Q =ω0

∆ω(2.11)

We can also define a transmission efficiency for a finite length cavity by normalizing

Pout to the power coupled into a cavity as,

Teff =

∣∣∣∣ eiβL

1− r2e2iβL

∣∣∣∣2 (1− |r|2) (2.12)

From Eqn.(2.12) it can be seen that the cavity transmission efficiency has a maximum

when reiβL is purely real. This resonance condition provides an expression for the

resonance length of the cavity:

Lres,m =mπ − φ

π

λSP2

(2.13)

where m=1,2,3 ... is the order of the resonance and φ is the phase of the reflection

coefficient such that r = |r|eiφ

2.1.4 Origin of the reflection phase

The phase pickup on reflection is critically important when determining the resonant

wavelengths of the MDM cavity. The origin of this phase pickup, which is present

even in a perfect electrical conductor (PEC)[66], is related to the small metal-to-metal

spacing. When the size of the aperture is small compared to the wavelength of light,

there is a substantial transmission to evanescent diffraction orders. This can be seen

clearly if we simplify Eqn.(2.8). By substituting the expressions for the free space


fields and normalizing the field profiles such that the incident time-averaged SPP

Poynting flux is unity, we find:

(1 + r)(1− r∗) =|(1 + r)|2

2λ√

µ0ε0

∫ ∞−∞

du|I1(u)|2√

1− u2(2.14)

Splitting the reflection coefficient ‘r’ into its real and imaginary parts gives:

r = rr + irim (2.15)

Substituting for r in the left hand side of Eqn.(2.14) and simplifying, we obtain:

1− |r|2 + 2irim =|(1 + r)|2

2λ√

µ0ε0

∫ ∞−∞

du|I1(u)|2√

1− u2(2.16)

As expected, the real part of the integrated time averaged power flow through the

interface, (1− |r|2), corresponds to the propagating (|u| ≤ 1) field components. Also

the contribution to the imaginary part of the reflection coefficient comes entirely from

the arm of the integral with |u| > 1, the evanescent components. From the definition

of time averaged Poynting flux[67], this is proportional to the difference between the

stored magnetic and electric energies in the near field. We have for harmonic time

varying fields:

We =1

4

∫V

E ·D∗dV (2.17)

Wm =1

4

∫V

B ·H∗dV (2.18)∮C

S · ndA+ 2iω(We −Wm) = 0 (2.19)

Where, We,Wm are the energies stored in the electric and magnetic fields respectively.

‘S’ is the time averaged Poynting flux. Here ‘V’ is the volume under consideration

and ’C’ is the area of the closed surface enclosing it with an outward normal ‘n’. If

the volume ‘V’ is chosen as the semi-infinite half-space ahead of the MDM structure,


the imaginary part of the Poynting flux has contributions only from the input face

(yz-plane) near the cavity termination. With this we get:

−2irim + 2iω(We −Wm) = 0 (2.20)

rimλ

2πc= We −Wm =

|1 + r|2ε04π∫ ∞

u=1

|I1(u)|2√u2 − 1

du (2.21)

Even though the imaginary part of the reflection coefficient is directly related to

the difference in the electric and magnetic energy, the quantity of interest in most

situations is the total near-field energy stored. High energy storage in the electric

near field could lead to a higher electric field intensity in the near field region of the

cavity. Energy stored in the electromagnetic field is not usually an easy quantity to

calculate, but in this case we can easily decompose the total electromagnetic field in

front of the cavity into normal modes and sum up the energy in each mode. The total

energy including that of the propagating modes is obviously infinite, but if we only

consider the near field contribution we get after a straight forward calculation:

We +Wm =|1 + r|2ε0

4π

∫ ∞u>1

|I1(u)|2√u2 − 1(

1 +1

u2 − 1

)du (2.22)

The integral blows up at u=1 due to the second term in the bracket. This term

decays very fast for larger u, contributing to the integral only very near u=1 and

hence these corresponds to waves with very slow spatial decay away from the cavity.

This energy contribution though substantial is of limited interest, as the fields are

not localized near the cavity. If we are only interested in the rapidly decaying high

intensity near fields in front of the cavity we can neglect that term and write an

approximate expression for the energy stored in the near field of the cavity as:

WNF ≈|1 + r|2ε0

4π

∫ ∞u=1

|I1(u)|2√u2 − 1

du (2.23)


This is equal to the difference in the stored electric and magnetic energy. From

Eqn.(2.21) we can thus obtain a very simple expression of the energy stored in the

near field in terms of the imaginary part of the reflection coefficient:

WNF =rimλ

2πc(2.24)

We find that the imaginary part of the reflection coefficient is directly proportional

to the near-field energy stored at the cavity termination.

2.1.5 Model Validation

The above described intuitive model for MDM cavity resonances involve several sim-

plifications in terms of the exact field distributions throughout the structure. In order

to have complete field matching at all points along the cavity edges we need in addi-

tion to the propagating modes in the cavity, a continuum of evanescent modes which

exist in the cavity as well as laterally propagating (along the z-direction) SPP modes

at the cavity edge surface[64]. The simplification ignoring the evanescent modes in-

side the cavity will lead to some error in the field calculations, but since these modes

are not expected to transmit energy in the direction of propagation for sufficiently

long cavities we expect that the energy matching method will lead to a reasonably

accurate calculation of the relevant quantities. Also the generation of laterally prop-

agating SPPs are expected to be most efficient at higher dielectric thicknesses than

what is mostly considered in this study[68]. It is expected that the approximations

made are more valid in cases where the metal properties and the structure dimensions

favor the simplifications involved. For example, ignoring the finite penetration of the

plane wave at the in-coupling face in the transmission coefficient calculation will be

a good approximation at longer wavelengths where the metal has a large negative

dielectric constant. In order to check the validity of the assumptions, for our cavity

geometries and our choice of metal (Ag), we compared the results with those obtained

from full-field finite-difference frequency domain (FDFD) simulations[69]. In all cases

analyzed in section(2.2), we see excellent agreement between the two, confirming the

validity of the assumptions.


2.2 Numerical Results

In this section, we explore the dependence of the cavity properties on the different

cavity parameters like dins, εm, L, λ etc. This dependence is somewhat complicated by

the frequency dependence of the materials response. In order to understand the effects

of each of these variables separately, we first look at the variation in the magnitude

and phase of the reflection coefficient with the normalized insulator thickness dins

λfor

various wavelength-independent values of the metal dielectric constant.

As shown in Fig.(2.2a), the reflection coefficient magnitude (|r|) increases as the

cavity dielectric thickness is reduced and metal dielectric constant moves towards

resonance (εm → −1). This can be attributed to mainly two factors, a higher effec-

tive index contrast, due to increasing gap SPP mode index and an increased mode

mismatch due to tighter vertical confinement of the mode. The phase pickup on re-

flection, shown in Fig.(2.2b) on the other hand increases as the metal properties move

towards resonance and it decreases on reducing the cavity dielectric thickness.

The electric energy stored is greater than the magnetic energy as seen from the

positive sign of rim (0 ≤ φ ≤ π). Thus the cavity end faces have associated with them

a finite capacitance, which originates from excitation of the evanescent modes in the

free space region.

When the cavity thickness, dins decreases, the near-field energy stored is lower and

the reflection phase decreases. For real metals supporting SPPs there is, in addition

to the aperture effect, a contribution from the evanescent nature of the SPP mode

profile into the metal. When |εm| decreases the SPP extends further into the metal,

resulting in a higher coupling to the free space evanescent modes and we get high

near-field energy ahead of the cavity which increases the reflection phase.

Next, we explore the reflection properties for a cavity metal with wavelength-

dependent material properties. The calculations are done for silver (Ag) and its

material properties for the metal are taken from Rakic et. al.[70] In our study we

consider Ag with and without loss. Lossless material properties are obtained by con-

sidering only the real part of the dielectric constant. Figure(2.3) shows the variation

of reflection coefficient magnitude and phase as a function of wavelength for different


Figure 2.2: |r| and φ (phase) for different values of εm as a function of scaled dielectricthickness

cavity dielectric thicknesses. The lossless case is plotted with solid lines and the case

with loss is shown with dashed lines. Clearly evident is the presence of two regimes

in the variation of the reflection coefficient magnitude as a function of wavelength.

As seen in Fig(2.3a) the cavity truncation becomes a better reflector near the surface

plasmon resonance frequency (short wavelength). On increasing wavelength |r| goes

through a minimum, which is the result of two competing factors that contribute to

the reflection. At short wavelengths, the rapid variation in mode index with wave-

length due to a change in εm determines the behavior of r. So |r| decreases with

increasing wavelength. But for larger wavelengths, the cavity termination, which acts

as a radiating antenna, becomes less effective due to the size mismatch between the

free space wavelength and the SPP mode, increasing the reflection coefficient. To-

gether, these two competing factors result in a minimum in the magnitude of the

reflection coefficient. The introduction of losses (dotted line in Fig.(2.3a)) changes


the short wavelength characteristics of the cavity. In a lossy MDM structure the mode

index does not rise as high as in the lossless case at short wavelengths. Consequently

the low index and the decreased vertical confinement leads to a decrease in the re-

flection coefficient magnitude. At longer wavelengths losses are negligible as the SPP

mode is pushed out of the metal and the reflection characteristics are similar to the

lossless case. The reflection phase on the other hand (Fig. (2.3b)), monotonically

decreases with increasing wavelength, and is larger for a thicker insulating spacer in

the cavity. The phase pickup is almost unaffected by the introduction of losses in the

metal, even very close to the surface plasmon resonance frequency. This fact is inter-

esting from a device design perspective as it facilitates easy design rules for resonant

cavity devices without introducing the complexity of loss at a given wavelength.

Figure 2.3: Reflection amplitude |r| and φ (phase) for an Ag-Air-Ag MDM structureas a function of wavelength for different dins values. Solid lines: Without loss. Dottedlines: With loss.

The near-field energy stored in front of the cavity, WNF is proportional to λrim.

Figure(2.4) shows a plot of λrim as a function of dins for different free space wave-

lengths. We see that for longer wavelengths there exists a maximum in the near-field


energy. The near-field energy storage in front of the cavity is the result of mode

mismatch and coupling to the evanescent modes. For a low reflection coefficient ,

with little mode mismatch there is very little energy stored in the near-field. Hence

for large dielectric thickness, with low |r|, near-field energy storage decreases with

increasing dielectric thickness. The increase in near-field energy storage with wave-

length in the large insulator thickness regime is also the result of increasing |r|. But

for small dielectric thickness, the contribution from the evanescent mode profile is

larger for smaller λ, giving higher energy storage . The existence of the maximum

for a given wavelength allows us to tune the cavity to have larger near-fields at a

wavelength of choice. This can be of importance for applications where high local

fields are desired, such as surface plasmon Raman spectroscopy. This maximum arises

from a single reflection event at the cavity termination and is different from the cavity

resonance of the finite length cavity.

Figure 2.4: rimλ for Ag-Air-Ag cavity for different dins

The transmission efficiency of the cavity, as defined in Eqn.(2.12), will be con-

sidered next. This quantity can be obtained from experiments and is most directly

linked to the fundamental optical processes associated with the cavity. Shown in Fig.

(2.5) is the transmission efficiency of a lossy Ag cavity as a function of wavelength for

a dielectric thickness dins = 20 nm and for different cavity lengths. The plot shows

the cavity resonances, which move to longer wavelengths as the cavity length is in-

creased. The results from full-field FDFD calculations are also plotted in the figure,

showing excellent agreement with the analytical calculations.


Figure 2.5: Transmission efficiency (Teff ) through a Ag-Air-Ag cavity for differentcavity lengths (L) as a function of wavelength.

The cavity resonance length (Lres) for different resonance orders, as a function of

dielectric thickness is plotted in Fig. (2.6). The good correspondence between the

analytical calculation and the full-field simulations confirm the validity of our model

for the considered parameters. From the figure it can be seen that the resonant

length calculations made by ignoring the phase pickup on reflection (dotted lines)

would result in substantial error, especially at higher dielectric thicknesses. Another

interesting feature in the plots is the relatively weak dependence of the resonance

length on the dielectric layer thickness for sufficiently large thicknesses (> 50 nm).

This can be understood from in Eqn.(2.13), which shows that the resonance length

is dependent on two factors: 1) the gap SPP wavelength and 2) the phase pickup

on reflection. As the dielectric layer thickness is increased, the gap SPP wavelength

increases and approaches that of the single interface mode. As the same time, the

reflection phase also increases. As the effects of an increased wavelength and phase

work in opposite directions, the resonant length stays more-or-less the same.

As the dielectric thickness is reduced in an MDM cavity, the symmetric SPP mode

is more confined resulting in a very small mode volume. This is very advantageous

for active plasmonic devices allowing for example, efficient coupling of quantum emit-

ters to SPP gap modes in MDM cavities [13]. Strong emission rate enhancement

is also predicted even for non-resonant conditions in an infinite length MDM slab


Figure 2.6: Cavity resonance length as a function of dielectric thickness for differentorders. Free space wavelength λ=900nm. (Ag-Air-Ag cavity with loss.)

Figure 2.7: Q-factor of the cavity vs cavity length for different dielectric thicknesses.Free space wavelength λ=800nm. Ag-Air-Ag cavity with loss

geometry[51]. The transmission cross section can be used to calculate the quality fac-

tor (Q) of the finite length MDM cavities. Shown in Fig.(2.7) is a plot of Q vs cavity

length for different dielectric thicknesses at λ = 800nm for Ag-Air-Ag MDM cavity

with metal losses included. The cavity Q increases with length, showing evidence of

being reflection loss limited. This is true even for dielectric thickness as low as 10 nm

with cavity lengths as large as 1500 nm, demonstrating that propagation loss is not

the dominating loss mechanism in these cavities. This suggests the possibility of in-

creasing the quality factor of these cavities further by end face shaping thus realizing

very low reflection losses. Such a device will exhibit larger Q/V values and enable


very effective coupling of optical emitters to a well-defined SPP mode.

2.3 Conclusion

In conclusion we have developed a fully analytical theory for SPP resonances in finite-

length MDM cavities. It builds on previous results that indicate that a variety of

wavelength scale plasmonic systems can be viewed as resonators for SPPs[34, 46, 42].

Such a model requires knowledge of the basic optical properties of SPP modes sup-

ported by an extended MDM waveguide and the SPP reflection and transmission

properties at the termination of such a waveguide. We have presented an analyt-

ical framework to determine these properties for cavities consisting of real metals

exhibiting loss and dispersion. Similar to what was found for other wavelength-scale

plasmonic cavities, these calculations predict a substantial phase pick up by the SPP

upon reflection from the cavity end faces. We showed that the origin of this phase

pick up lies in the excitation of evanescent modes in free space region just outside the

cavity. Furthermore, we found that the imaginary part of the reflection coefficient is

proportional to the energy storage in the near-field of the cavity termination. From

the calculation of this phase pick up one can correctly predict both the position and

shape of the MDM cavity transmission resonances over a wide range of wavelength

and geometric parameters. The results agree very well with full-field FDFD simula-

tions. The dependence of the quality factor on the length of the cavity shows that

these resonances are reflection loss limited even at very small dielectric thickness and

suggests the possibility of further improving the quality factor of these resonances by

end face shaping.

Chapter 3

Surface Plasmon Patch Antenna

In the previous chapter, we looked at plasmon resonances and energy storage in a

truncated MDM cavity with infinitely thick metals separated by a dielectric. Optical

devices based on this geometry have finite metal thickness, and the additional metal

surface opens up the possibility of further tailoring the optical properties through

mode interaction. In this chapter we explore a novel dual purpose patch antenna in the

optical regime. Metal patch antennas have been studied in the past as good candidates

for single photon emission sources [71], and have also attracted a lot of attention lately

for their applicability in meta surface structures[72, 73]. However, traditionally metal

antennas in optical frequencies have exploited a single mode plasmon resonance for

its action[34]. We demonstrate an optically excited plasmon source which exploits

the interference action of a two-path two-mode resonance to function as an effective

radiative antenna. The interference action of the two modes provides for an additional

level of control over the antenna emission characteristic. This allows us to efficiently

change the resonance characteristics of the cavity to use it either as an efficient single

lobed radiator, a directional emitter or an excellent plasmon coupler. A large fraction

of the cavity round trip phase pickup needed for resonance is accommodated by the

reflection phase, resulting in an extremely compact device much smaller than the

effective plasmon wavelength in the structure.

27

CHAPTER 3. SURFACE PLASMON PATCH ANTENNA 28

Fulfilling the promise of a complete surface plasmon based optical circuit re-

quires compact devices that can excite as well as route surface plasmons and me-

diate energy transfer between near and far fields. Recent efforts in the field have

resulted in plasmonic antennas based on meta-material structures[74], and Yagi-Uda

like designs[75, 76, 77] for for a variety of applications. Various configurations of

plasmon waveguides, that have effectively optimized the tradeoff between mode con-

finement and propagation loss, have been explored in the past. [78, 79, 80, 81, 82, 83].

Many different optical and electrical plasmonic sources have also been demonstrated

including those with silicon[22] and organic semiconductors[84]. An optical antenna

is another necessary component needed for the concentration of light to enhance

the interaction between propagating wavelength dimensions and device scale. They

have found extensive use in scattering[85], redirecting[86], and enhancement of op-

tical fields[87] for a variety of applications[88]. For a complete plasmonic circuit,

however, one needs a device geometry that not only can be tailored to fit many of

these different roles but also is amenable to easy fabrication. Here, we demonstrate a

metal insulator multilayer device with a geometry which can be very easily tailored

to function in all these roles very effectively.

Resonances in truncated metal stripe waveguides in a dielectric background have

been studied extensively in the past[89, 42]. The plasmon mode resonance occurs in

these structures when the round trip phase pick up, due to propagation and end face

reflections, add up to an integral multiple of 2π. The thickness and length of the stripe

is chosen to allow resonance of a single mode at the desired wavelength. This mode

is excited through a variety of optical and electrical methods. However, the closely

spaced metal surfaces in a metal stripe antenna or a stripe patch antenna above a

metal ground plane allow for multiple modes with different field symmetries. All these

modes can be simultaneously excited and though they propagate independently, they

can interact through reflection at the antenna terminations. These interactions can

be constructive or destructive and lead to preferential transmission or reflection into

some modes while inhibiting power coupled into the others.


3.1 Sample fabrication and experiment details

An SEM image and a schematic showing the basic device design is shown in Fig.

(3.1a,b). It consists of a silver stripe patch antenna over a silver ground plane sep-

arated by a spacer layer of alumina. Quantum dots (CdSe-ZnS core-shell) dispersed

in the alumina layer illuminated by an excitation laser emit into the plasmon modes.

These type-1 quantum dots were chosen for their good photo-stability and high emis-

sion quantum efficiency. The quantum dots below the stripe antenna, are sandwiched

between the stripe and the ground plane. This enhances its emission rate into the

gap plasmon mode that has high intensity fields in the alumina region.

L

H

D

Detector

Pinhole

Ar ion Laser

(a)

(b)

(c)

Figure 3.1: (a) SEM of the stripe antenna structure. White bar is 5µm (b) Aschematic of the device geometry. Thickness D = 40 nm, H = 50 nm, L = 140nm - 340 nm. A rendering of illuminating Ar-ion beam and the two lobed antennaemission is shown (c) Confocal measurement set up. The illuminating laser and thecollected PL is polarized perpendicular to the stripe. Dichroic filter removes theillumination beam from the collected signal.

Silver ground plane film layer (150nm) is deposited with e-beam evaporation on

polished Si wafer substrate immediately followed by a 10nm coating of alumina by

atomic layer deposition with trimethyl aluminum hydroxide and water. Quantum


Figure 3.2: Photograph of the Witec Alpha SNOM system

dots (Ocean Nano CdSe-ZnS core-shell) are put down by spin coating from a toluene

solution followed by another 10 nm layer of alumina deposition (Low temperature

ALD at 80◦C.) The metallic antenna structures are fabricated by standard e-beam

lithography lift-off with a protective layer of 10nm AlOx covering the whole structure.

The emission characteristics of the quantum dots were confirmed to be unchanged

by PL measurements before and after the fabrication process. A Witec alpha 300s

SNOM system, shown in Fig. (3.2) was used for the confocal scans with a 100X

mitutoyo (0.9 NA) objective to illuminate and collect during the scans. The scattered

PL was collected in a confocal scan mode as shown in Fig. (3.3a) . We employ a

slight modification on this standard confocal scan configuration to also study surface

plasmon scattering from the antenna as described in section[3.3]. In a normal confocal

scan geometry the illumination and collection is from the same spot on the sample. In

contrast to this, for surface plasmon scattering we excite the plasmons at a distance,

s = 7.5µm away from the antenna, but collection of the scattered radiation is focused


on a spot above the antenna. A schematic of this configuration is shown in Fig.

(3.3b).

s

a) b) In focus fluorescent emission Out of focus fluorescent emission

In focus fluorescent emission Out of focus fluorescent emission

Objective lens Objective lens

Out of focus focal plane Out of focus focal plane

In-focus focal plane

Confocal Pin hole

Staggered Confocal Pin hole

Figure 3.3: Schematic of the confocal scan configuration a) Standard confocal b)Staggered confocal. Illumination at a distance s = 7.5µm away from the collectionspot on the sample.


150 nm Ag E-beam evaporation. Si substrate

10 nm AlOx ALD Protect Ag from oxidation

Spin on Q dots CdSe/ZnS core-shell Approx 10nm diameter

20 nm AlOx ALD Total insulator thickness =40nm

Antenna: Ag :40nm thick 140-340nm width E-beam litho, lift-off

ALD AlOx 10nm Protective coating

Figure 3.4: Schematic of fabrication process

3.2 Scattering under normal illumination

First, we take a look at the device’s antenna characteristics, and we employ a confocal

scan to study the beam shape of the emission. The stripe region is illuminated by

the defocused excitation laser (Ar-ion 514nm) polarized perpendicular to the stripe

length and an X-Z confocal scan of the emitted photoluminescence (PL) is performed.

Figure (3.5) shows the radiation pattern from the antenna for stripe widths from 140

nm - 340 nm. The antenna emission pattern evolves from a single lobe emission in

smaller width stripes, with the excitation of lowest order resonance, to a two lobed

emission in larger stripes, exciting higher order modes. It should be noted that the

scan images are normalized to the maximum intensity for each stripe. Figure[ 3.6]

shows the normalized scans for the stripes normalized to the maximum intensity from

the 140 nm stripe. The absolute intensity at 340 nm antenna length is about 25 %

of the intensity at 140 nm.

In order to understand the radiation properties, we need to study the plasmon

modes in the structure. Like all metallic antennas in the optical regime, the transfer of


0 1 2 3 4 5x µm

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140nm

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0 1 2 3 4 5x µm

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0 1 2 3 4 5x µm

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Min

0.25

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0.75

Max

Figure 3.5: Confocal scans of stripe antennas under de-focused normal illumination.Length of the stripes is shown for each scan image

energy between the near and far field is mediated by surface plasmons. A schematic

of the magnetic field for various plasmon modes in the structure is given in Fig.

(3.7a). The presence of the ground plane breaks the symmetry of the modes that

would have existed in an isolated metallic stripe. We do not have purely symmetric

and anti-symmetric modes in the patch antenna. The two modes of relevance for the


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Min

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Max

Figure 3.6: Confocal scan of the stripe antenna with the maximum intensity normal-ized to the emission intensity from the 140 nm stripe.

device dimensions of interest have predominantly MIM mode shape (field maxima in

the insulator region between the stripe and the ground plane) and IMI mode shape

(field maxima at the top of the metallic stripe). In this context the metallic antenna

can be thought of as a plasmonic cavity with the cavity reflection coefficient and

resistive losses determining the antenna efficiency. Here the vertical confinement of


the plasmon mode is determined by the insulator and metal thickness, which also

controls the plasmon reflection coefficient from the cavity end faces. Shown in Fig.

(3.7 b) is the calculated mode index of the MIM mode, where as, Fig. (3.7 c-d) show

the propagation length of the MIM and IMI modes respectively as function of alumina

thickness (D) and antenna thickness (H). The mode indices and propagation lengths

are calculated using the reflection pole method[90]. For simulations εAg = −13.73 −1.15i at 620 nm is taken from Rakic et al [91] and εAlumina = 2.72. For efficient coupling

of quantum dot emission to the plasmon modes and to increase the cavity reflection

coefficient it is attractive to increase the mode index by decreasing the insulator

thickness. But this increase in confinement comes at the cost of decreased propagation

length of the plasmon modes. To obtain a balance of high mode confinement and low

propagation loss, values for D and H were both chosen to be 40 nm for the experiments.


(a)

(b)

(c)(d)

0

1

Ground Plane

Antenna

2

D

H

Figure 3.7: (a) Schematic of Hy field profile for the various plasmon modes in thestructure: 0 - Ground plane mode, 1- MIM mode and 2- IMI mode. (b) Mode index(λ0/λ for the MIM mode as a function of the antenna thickness (H) and spacerthickness (D) at 620 nm. (c,d) Propagation length in nm for the MIM mode and IMImode respectively.

3.3 Plasmon interference in patch antenna struc-

tures

To exploit the interference aspect of the antennas optical response we illuminate the

antenna with a ground plane plasmon mode and study its response with confocal

microscopy. Figure (3.8a) shows the schematic of the surface plasmon scattering

experiment configuration. A plasmon mode is excited at a distance of around 7.5µm

from the stripe by illuminating the quantum dots with a focused beam. The excitons


in the quantum dots relax to the plasmon mode on the antenna ground plane. This

plasmon mode propagates to the antenna structure and is scattered to free space

radiation modes. A fraction of the incident plasmon energy is reflected back and

transmitted through the antenna into the ground plane plasmon modes as well. This

however is not picked up in the scans as confocal scans can only measure the fraction

of energy that is scattered into radiation modes within the numerical aperture of the

collection objective.

x nm

y n

my n

m

x nm

y n

m

x nm

a) b)

c) d)

Figure 3.8: (a) Schematic of the plasmon scattering experiment setup. (b-d)|H| fromFDFD simulation of plasmon scattering for different stripe widths (b) L = 160 nm(c) L = 280 nm (d) L=320nm

Full field FDFD simulations, Fig. (3.8 b-d), where surface plasmon polariton is

incident from the left on to a patch antenna show the scattering field pattern of the

antenna for various antenna lengths. Majority coupling to the forward lobe and weak

emission through the backward lobe can be observed in the simulations for longer

stripes. Confocal scans (shown in Fig. (3.9) ) show the directional scattering of

the plasmon modes for various antenna stripe lengths. The radiation mode pattern


is mostly unperturbed for smaller stripe widths, compared to the scattering under

normal illumination. Under asymmetric illumination with a surface plasmon mode,

the two lobed pattern observed for longer antennas is no longer observed, and is

replaced by a forward scattering single lobe. This is a clear evidence of the antenna

being reflection loss limited as opposed to being limited by resistive losses in the

cavity. Similar to the observation in the normal illumination confocal scans, the

stripes at longer widths scatter weakly and the maximum intensity at stripe length of

340nm is approximately 25% of that at 140nm. In order to understand the amplitude

behavior of the scattering spectra we need to understand the scattering process in

these antennas. This is most accurately achieved through FDFD and a near to far

field transform to see the radiation pattern, but this does not provide intuition into

the physical mechanism of scattering. So in the next section, we derive a multi-

path interference model for the scattering amplitudes for a patch antenna through a

semi-analytical mode matching technique.


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Min

0.25

0.5

0.75

Max

Figure 3.9: Confocal scans for the stripe antenna of different lengths illuminated witha focused spot at a distance of 7.5µm to the left of the antenna. The intensity ineach image is normalized to the maximum intensity in the scan. The plasmon isincident on the stripe from the left and the resulting radiation from the antenna isasymmetric.


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Min

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Max

Figure 3.10: Confocal scans for the stripe antenna of different lengths illuminatedwith a focused spot at a distance of 7.5µm to the left of the antenna. The intensity ineach image is normalized to the maximum intensity for 140nm stripe. The plasmonis incident on the stripe from the left and the resulting radiation from the antenna isasymmetric.


3.4 Coupled cavity model for plasmon scattering

The scattering property of the antenna and its interference action can be best un-

derstood by studying the interaction between antenna plasmon modes in the cavity.

A complete description of the stripe ground plane system will involve the excita-

tion and interaction between all the possible discrete and continuum surface plasmon

modes. But a basic understanding of the antenna characteristics can be achieved

by modeling the antenna as a surface plasmon cavity with discrete modes. The two

distinct degenerate plasmon modes possible in this structure at dimensions of inter-

est (MIM and IMI) have energy concentrated at different interfaces and have very

different wave numbers. These modes interact through scattering at the cavity end

faces. In addition, they couple to both the radiation channel (free space modes) and

the ground plane plasmon mode (GP). The strength of coupling to the radiation

channel competes with the coupling to the bound plasmon modes. When the ground

plane plasmon mode is incident on the antenna, the two antenna modes are excited

(MIM and IMI). These modes couple to each other through reflection at the end faces,

and propagate independently with energy concentrated at different interfaces . We

can model this as coupled Fabry-Perot cavities, where the difference in the reflection

phase pick up and the mode index of the two modes, lead to constructive or destruc-

tive transmission to the ground plane plasmon mode out of the cavity for different

antenna lengths. Such Fabry-Perot models have been shown to be very effective in

modeling plasmonic cavity and antenna structures[92, 93].

The patch antenna can be decomposed into two Fabry Perot cavities as shown in

Fig. (3.11). We consider the ground plane plasmon incidence on the patch antenna

and derive the transmission and reflection coefficients for the GP mode. When the GP

mode transmits through the patch antenna stack, it goes through two parallel paths,

each with differing strengths and acquired phase. The resultant interference can be

predicted by the model provided all the coupling coefficients can be calculated. For

the three modes of interest there are 6 coupling coefficients that we need to calculate.

The coupling coefficient between two modes i and j is denoted by rij for reflection

and tij for transmission, as shown in the Fig. (3.11). They can be calculated from a


r11

r12

r21

r22 t20

t10

r00

mode 1: MIM

mode 2 : ASYM mode 0

mode 0 E1

E2

t01

t02

Stripe

Ground plane Cavity 1

Cavity 2

Figure 3.11: Two cavity model.

field decomposition at appropriate truncations of a one dimensional geometry. When

a plasmon mode (GP, MIM, IMI) is incident on a structure discontinuity, it reflects

and transmits into all the possible modes on either side of the interface. The total

electric field on either side of the interface can be written as a sum over all the possible

orthogonal modes,

Etotal =∑modes

cmodeEmode (3.1)

FDFD simulation of this scenario can generate the total field profile, and we can then

use orthogonality relations of the modes on either side of the interface to determine

the coefficient cmode. We can now ignore the scattering into the radiation modes and

only look at coupling between the 3 modes of interest. From the numerically calcu-

lated coupling coefficients between the modes at the patch antenna truncation, we

can derive a coupled cavity model for transmission through the patch antenna as a


0 100 200 300 400 500 600L antenna

0.0

0.2

0.4

0.6

0.8

1.0

R,T

Ta

R a

T f

R f

S f

I r

Figure 3.12: Transmission and reflection spectra for ground plane surface plasmonincident on stripe antenna. Tf , Rf from full field simulations and Ta, Ra from theanalytical model (Details in appendix). Scattered intensity assuming no loss in thecavity, Sf = (1−Tf−Rf ), is also plotted. The measured maximum radiated intensityin the staggered confocal scan is normalized and overlaid on this plot (Ir). Thescattered intensity calculation can be seen to be correctly predicting the measuredintensity for a range of stripe lengths.

function of cavity length. Transmission and reflection coefficients out of the cavity

are derived in appendix C. The validity of this simple model for antenna scattering

is proven through full field simulations. In Fig. (3.12i) we have plotted transmission

and reflection from a patch antenna as function of antenna length, calculated with

FDFD simulations. Also, plotted are the transmission and reflection results from the

coupled cavity model. The semi-analytical model calculations reproduce all the es-

sential features of the full field simulations. There is a small difference in magnitude

of the calculated transmission and reflection, especially at low cavity lengths. This

is to be expected as we ignored the coupling between the free space modes (propa-

gating and evanescent) and the cavity modes. The resulting error will be larger for

smaller cavities and can be expected to reduce with increasing cavity lengths, due to

evanescent and spherical divergence decay of the ignored field amplitudes.

We can also compare the results directly with the experimental results if we ignore


losses in the cavity. In the absence of resistive losses in the cavity the difference

between the incident power (normalized to unity) and the total coupled power into the

ground plane plasmon mode (Rf +Tf ) is the scattering into the radiation modes. The

calculated scattered energy assuming no loss in the cavity (1− (Tf +Rf )) agrees very

well with the measured normalized scattered intensity. For ease of comparison the

scattered intensity plot is overlaid on the analytical calculations so that the maxima

of the two coincide. The experimental results closely follow the analytical calculations

for small stripe lengths. For larger stripe lengths the experimental results drop below

the analytical calculations. This is to be expected as in longer antennas the cavity

losses can no longer be neglected and the analytically calculated scattering energy that

assumes zero loss will over estimate the scattering strength. The mode propagation

losses can be estimated and subtracted from the total loss to get a better estimate

of the scattering strength of the cavity. There are several other interesting features

in this transmission spectra. At an antenna length of around 160 nm, as shown

in Fig. (3.13a,b) both transmission and reflection simultaneously decrease, due to

destructive interference of the two antenna modes. This increase in the coupling to

the radiative channel makes this an ideal length for a radiating antenna. At around

L = 280 nm, as shown in Fig. (3.13c,d) the constructive interference of the antenna

modes, leads to near zero reflection and enhanced transmission. This is a good length

for a plasmon source that efficiently excites the ground plane plasmon mode. The

peak of the advancing wavefronts also show the shallower angle of emission in the 280

nm long stripe compared to the 160 nm stripe as is confirmed by the experiments. It

should be noted that in addition to the difference in the reflection phase pick up of

the two plasmon modes, the coupling between the modes at the cavity termination

is necessary to account for the interference effects. Moreover, for good modulation of

the reflection and transmission coefficients we need the total power in the two cavity

modes to be approximately the same, through near equal excitation from the ground

plane mode or through good coupling between the modes due to reflections at the

cavity terminations.

In this chapter we have shown that a metallic patch antenna in the optical regime

is a versatile design which can be easily tailored to function as a plasmon source,


X nm

X nm

Z n

mZ n

m

X nm

X nm

Z n

mZ n

m

c)

g)

a)

c)

b)

d)

Figure 3.13: (a) Re[Hy] for 160nm antenna length. The decreased transmission can beclearly seen. (b) Simulated |Hy| for plasmon scattering from a 160 nm long antenna.The fields are normalized for unit amplitude of incident mode field maxima. Thecolormap scale is clipped to clearly show the antenna radiation mode profile. (c)Re[Hy] for 280 nm antenna length. The enhanced transmission due to the constructiveinterference from the two arms can be clearly observed (d) Simulated |Hy| for 280 nmantenna.

radiator or a directional antenna. Here, multiple plasmon modes in the structure

interact to facilitate enhanced optical response under various illumination conditions.

The design can be optimized for energy transfer from localized wavelength or device

dimensions to propagating far field wavelength scale while reducing intrinsic losses.

The same structure can also be used for in-plane surface plasmon interferometric

sensing applications as the resonance conditions are very sensitive to the refractive

index changes near the metal stripe antenna. A very simple analytical scattering

model that explains all the essential features of this plasmon antenna structure is

derived and validated with full field simulations and experimental results.

Chapter 4

Electrical Modulation of Surface

Plasmon Coupled Emission

4.1 Introduction

In the previous chapter we looked at scattering of plasmons by metallic antennas,

thereby probing the optical functionality of these devices. In this chapter we look

at dual-purposing the same metallic antennas as electrical leads, and demonstrate an

active plasmonic device based on MDM geometry. The patterned metallic electrodes

in an MDM cavity can serve as the contact pads as well as the optical element

in a device that is electrically pumped for light emission. The proximity of the

metallic surfaces to the active regions of the device, enhances the electron-hole pair

recombination rate by coupling the energy to plasmon modes, greatly increasing the

internal quantum efficiencies. This has been exploited in a number of plasmon assisted

light emitting devices like Quantum Well light emitting diodes (LED)[94] and Organic

LEDs. [95, 84].

Here, we look at a quantum dot light emitting device based on the patch antenna

geometry discussed in chapter [3] and demonstrate active electrical control over its

emission intensity and wavelength. We apply a voltage across the patch antenna -

quantum dot structure, and utilize Quantum Confined Stark Effect (QCSE)[96] to

shift its emission wavelength. The small foot print and ease of fabrication of such a

46

CHAPTER 4. ELECTRICAL MODULATION 47

device makes it a prime candidate for a nanoscale surface plasmon source.

4.2 Sample fabrication and experiment details

In this section we will outline the fabrication and experimental details for the surface

plasmon QCSE modulator. The fabrication of the device parallels that of the patch

antenna structure with some minor differences. Silver ground plane film layer (150

nm) is deposited with e-beam evaporation on polished Si wafer substrate immediately

followed by a 10 nm coating of alumina by atomic layer deposition with trimethyl

aluminum hydroxide and water. Quantum dots (Ocean Nano CdSe-ZnS core-shell)

are put down by spin coating from a toluene solution followed by another 10 nm layer

of alumina deposition by ALD. The metallic antenna structures are fabricated by

standard e-beam lithography lift-off with a protective layer of 10 nm AlOx covering

the whole structure. An SEM image of the antenna structure and a schematic of the

measuring setup is shown in Fig. (4.1) Here, unlike in the normal patch antenna

structure, we require a high quality ALD oxide to enable application of electrical bias

without breakdown. For a good electrical insulator AlOx, with low defect density, the

ALD growth must be performed at high temperatures[97]. However, the quantum dots

which will need to be sandwiched between the oxide layers have a polymer coating that

may degrade these temperatures. These organic coatings are proprietary and exact

details of the thermal stability characteristics could not be determined. The vendor

supplied tolerable highest temperature (<70◦C) seemed to be overly conservative, as

these quantum dots were unaffected by the ALD deposition at 80◦C. The quantum

dots deposited by spin coating from a toluene solution on to silicon substrates and

were annealed at temperatures from 130◦C to 300◦C. As can be seen from Fig. [4.2],

for temperatures less than 200◦C the changes in the PL spectra of the quantum dots

were insignificant. However, since the annealing was only done for 10 minutes for each

sample, in order to avoid any effect from longer time exposure to high temperatures

we decided to perform the ALD at 100◦C. The PL spectra taken after the fabrication

of the stack show no change in width or emission center wavelength compared to

emission from an initial sample of quantum dots. For Stark shift measurements, the


L

H

D

Laser

Spectrometer

V

(b)

(c)

a)

Figure 4.1: (a) SEM image of the stark shift measurement antenna structure. Theantenna fingers shown are 20 µm long. (b) Schematic of the antenna (c) Schematic ofthe measurement set up. The thermal stage to hold the sample at low temperatureis not shown in the schematic.

quantum dots from a 4 µ × 2 µ area on either side of a stripe towards the middle

of the stripe were removed with focused ion beam milling. Following this the sample

was cleaned with acetone and iso-propyl alcohol and additional 10nm of alumina was

deposited with ALD. This was done so as to remove as much as possible emission

from quantum dots outside the antenna stack during spectra collection under voltage

bias. During QCSE measurement, the sample was held at -150◦C in a Linkham

THMS thermal control stage. The thermal stage was first heated to 40◦C and purged

with nitrogen to reduce the amount of residual water vapor before cooling down to

low temperatures with liquid nitrogen. The sample was cooled at a rate of 5◦C per

minute so as to minimize the possibility of a severed electrical contact. A Witec alpha

SNOM system was used with a mitutoyo 50X long working distance objective (0.55

NA) to collect the low temperature PL. A photograph of the Witec and thermal stage

measurement setup is shown in Fig. (4.3). A Keithley 6430 SMU was used as the


560 580 600 620 640 660 680Wavelength (nm)

0

5000

10000

15000

20000

25000

30000

35000

Inte

nsi

ty (

AU

)

No Anneal130 C200 C250 C300 C

Figure 4.2: The PL spectra from quantum dots after annealing at various tempera-tures.

voltage source for the measurements. The sample was illuminated by a 514nm Ar-Ion

laser with the beam polarized perpendicular to the stripe width.

Figure 4.3: Photograph of the thermal stage mounted on the Witec SNOM


4.3 Quantum Confined Stark Effect

Figure[4.4] shows the voltage bias dependent PL emission spectra from the quantum

dots in the patch antenna. The emission broadens and the peak of the emission is

red shifted. This can be explained as arising from the quantum confined stark effect.

The shifting of the energy levels in the quantum dots due to the applied electric

field lowers the electron hole recombination energy, and the resulting emission is

at a longer wavelength. The application of voltage bias also causes a reduced PL

efficiency in the quantum dots. The electrons and holes are physically separated in

the quantum dot, reducing the wave function overlap and the recombination cross-

section. Also, the large fields could dissociate the electron-hole pairs and the free

carriers can facilitate non radiative recombination, further increasing the luminescence

quenching. It should be noted that consistent with Stark effect, the reduced emission

at the center wavelength is accompanied by a slight increase in emission intensity at

longer wavelength. This is consistent with other observations of Stark effect in CdSe

quantum dots [98]. The Stark shift in emission energy ∆E is given by perturbation

theory to be

∆E = −µF − αF 2 + · · · (4.1)

Here µ is the built in polarization of the quantum dot, α is the polarizability of the

quantum dots and F is the internal electric field in the quantum dot. Even though

the Cd-Se quantum dots have a Wurtzite crystal structure and an associated built in

dipole moment, we do not expect to see the linear contribution of the Stark effect.

This is because the measured PL is an ensemble average of the quantum dots with all

possible orientations in the patch antenna structure. We can hence fit the emission

shift to a quadratic function to determine the polarizability of the quantum dots. The

electric field inside the quantum dot was calculated as,

F =3

εQD

εd+ 2

F0 =3

εQD

εd+ 2

V

d(4.2)


560 580 600 620 640 660 680Wavelength (nm)

0.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed P

L0V3V6V9V

Figure 4.4: PL spectra of the quantum dots in the patch antenna structure for variousbias voltages.

Here, εQD and εd are the dielectric constants and V is the applied voltage across the

dielectric of thickness d = 40 nm. The values of the dielectric constants chosen were

εQD = 9.2 and εd = 2.25. A plot of emission peak energy shift as a function of the

internal electric field is given in Fig. (4.5). The peak shift shows a quadratic increase

at low electric fields, 10 meV at around 600 kV/cm, with sub-quadratic increase

at higher electric fields. Fit to the peak energy shift data gives a polarizability of

α ≈ 3.2× 10−5.

In this chapter we have demonstrated experimentally a simple active plasmonic

antenna, based on the MDM geometry. The high field enhancement in the dielectric

region due to the plasmon modes, enhances the quantum dot emission. The ease


0 200 400 600 800 1000 1200 1400F (Electric Field kV/cm)

0

5

10

15

20

25

30

35

40

45

∆ E

(m

eV

)

α=3.2×10−5meV ·cm2

(kV)2

Energy Shift

∆E=αF 2

Figure 4.5: The emission center wavelength as a function of the quantum dot internalfield. The red line is the quadratic fit to the wavelength shift data. Calculatedpolarizability is given in the inset.

of fabrication, low foot print and the ability to dual task the electrical leads as the

metallic antenna structure makes this an ideal candidate design for optoelectronic

applications.

Chapter 5

Conclusion

Over the last two decades we have made tremendous advances in the field of in-

formation processing. Computer cores have become faster, smaller and more power

efficient at an increasingly rapid pace. All this is driven by the need to generate,

consume and analyze data at a rate which would have been unthinkable just a few

years ago. While the bulk of information transfer is handled by fiber optic cables,

arguably optics has not really broken into the field of traditional computing. The

advantages of all optical computing are many; from the possibility of higher clock

cycles to avoiding the unnecessary conversion back and forth between optical and

electrical signals. Yet, a fundamental limitation holds back the promise of all opti-

cal compute : The diffraction limit. Light cannot be confined to dimensions much

smaller than its wavelength in a medium. Hence for practical applications traditional

optical devices are limited to dimensions of the order of microns. Surface plasmons

provide an exciting and practical work around this limit. Surface plasmon modes can

be evanescent in one or more dimensions orthogonal to the direction of propagation,

and thereby can be confined to the nanoscale dimensions comparable to electronic

devices. More over, this confinement is accompanied by very large field enhancements

facilitating applications like surface enhanced Raman spectroscopy while holding out

tantalizing possibilities like single photon non-linear optics. However, any device de-

sign that hopes to supplant traditional electronics, should be amenable to the large

53

CHAPTER 5. CONCLUSION 54

scale fabrication and integration that has spurred the advances in the field of nano-

electronics. This points to device designs that are simple, amenable to traditional

lithographic route of fabrication, and compatible with addressing schemes similar to

the cross-wire memory architecture. One very good candidate design that satisfies all

the above criteria is a multilayer planar metal dielectric metal structure

We have conducted an extensive study of surface plasmon modes in Metal Dielec-

tric Metal geometry. This seemingly simple structure is one of the earliest geometries

to be exploited for plasmonics. Yet, we see that a surprising array of applications

are still being envisioned based on this topology. We have looked at two distinct but

related device structures based on MDM geometry. We first studied surface plasmon

resonances in finite length truncated MDM cavities with a simple analytical method.

The derivation of the surface plasmon reflection coefficient at the cavity truncation,

highlighted the origin of reflection phase from the excitation of evanescent modes.

We looked at the energy storage in the near field of the cavity and showed that the

cavity can be designed to optimally store energy in the near field. From the numerical

results it was clear that for most wavelengths of interest, imaginary part of the metal

dielectric constant critical to plasmon propagation length , has a very small part to

play in determining the resonance conditions. Next we studied experimentally and

analytically the surface plasmon modes in a patch antenna structure also based on

the MDM geometry. The interaction of quantum dots with the plasmon modes was

probed with a Stark shift measurement in the patch antenna structure. We showed

that all essential features of plasmon and light scattering from a patch antenna can

be explained by treating it as a coupled cavity.

Through this thesis, we have attempted to simplify surface plasmon mode be-

havior to provide an intuitive understanding of the physical picture behind it. All

the structures we have studied in this thesis can be easily simulated accurately with

full field simulations. This however does not provide us the benefit of intuition to

guide further device design. For example, understanding the interference process in

the patch antenna structure allows one to immediately intuit that designs which op-

timize transmission of surface plasmons or ones that optimally couples to radiation

are definitely possible. Similar intuitive arguments have been used to great effect

CHAPTER 5. CONCLUSION 55

in understanding energy storage in nano-scale surface plasmon optical elements by

borrowing ideas from circuit theory. A combination of such “lumped element” ap-

proach and Fourier optics based propagating field approaches can dramatically aid

in our understanding of the behavior of nano-optical systems. This would, we hope,

ultimately usher an exciting era of plasmonic computing.

Appendix A

Plasmon reflection and excitation

A.1 Plasmon reflection at cavity termination

Here we will outline the steps in the derivation of plasmon reflection and excitation

coefficients for an MDM cavity. This is the derivation of results from chapter [2] and

the terms have the same meaning as in the chapter.

For an MDM plasmon mode propagating in the ‘x′ direction incident on a cavity

termination at x=0, we have from continuity of the electric field in ‘z′-direction,

(1 + r)Espz = Efs

z (A.1)

Similarly from the ‘y’-direction magnetic field continuity,

(1− r)Hspy = Efs

z (A.2)

Here, the superscripts fs and sp stand for free-space and surface plasmon respectively.

We now employ a power conservation argument, and balance the x-directed inte-

grated poynting flux on either side of the cavity. For the poynting flux balance we

56

APPENDIX A. PLASMON REFLECTION AND EXCITATION 57

have from either side,∫ ∞−∞

Sspx dz =

∫ ∞−∞

Hsp∗y Esp∗

z dz =

∫ ∞−∞

(1 + r)(1− r∗)Espz H

sp∗y dz (A.3)∫ ∞

−∞Sfsx dz =

∫ ∞−∞

Hfs∗y Efs∗

z dz (A.4)

Writing both sides of equation [A.1] in terms of Fourier transformed quantities we

have,

(1 + r)

2π

∫ ∞−∞

I1eikzzdkz =

∫ ∞−∞

g(kz)eikzzdkz (A.5)

I1 =

∫ ∞−∞

Espz e−ikzzdz (A.6)

So we have,

g(kz) =(1 + r)

2πI1 (A.7)

Also, from

∇ · E = 0 (A.8)

we have, ∫ ∞−∞

Efsx e−ikzzdz = f(kz) =

−kzg(kz)√k20 − k2z

(A.9)

Efsx =

−kzg(kz)√k20 − k2z

(A.10)

Efsx = −

∫ ∞−∞

1 + r

2π

I1kz√k20 − k2z

eikzzei√k20−k2zxdkz (A.11)

Now we derive the Hfsy from the continuity relations. From Maxwell’s equations we


have,

∇× E = −∂B∂t

(A.12)

−∂Efsz

∂x+∂Efs

x

∂z= iωHfs

y (A.13)

Substituting from above and simplifying we get,

Hfsy =

∫ ∞−∞

−1

ωµ0

k20g(kz)√k20 − k2z

eikzzdkz (A.14)

Hfsy =

∫ ∞−∞

−1

ωµ0

(1 + r)

2π

k20I1√k20 − k2z

eikzzdkz (A.15)

(A.16)

Now we can write the expression for Poynting flux in the free space as,∫ ∞−∞

Sfsx dz =

∫ ∞−∞

Efsz H

fs∗y dz = (1 + r)

∫ ∞−∞

Espz H

fs∗y dz (A.17)

= (1 + r)(1 + r∗)−1

2πωµ0

∫ ∞−∞

k20I∗1I1√

k20 − k2zdkz (A.18)

Equating to the flux from the surface plasmon side we get,∫ ∞−∞

Sspx dz = (1 + r)(1− r∗)∫ ∞−∞

Espz H

sp∗y dz

= (1 + r)(1 + r∗)−1

2πωµ0

∫ ∞−∞

k20I∗1I1√

k20 − k2zdkz (A.19)

So we have the result,

1− r∗

1 + r∗=

1∫∞−∞E

spz H

sp∗y dz

−1

2πωµ0

∫ ∞−∞

k20I∗1I1√

k20 − k2zdkz (A.20)


Which simplifies the equation [2.9] from chapter[2], with u = kzk0

= λkz2π

1− r∗

1 + r∗=

1

λ√

µ0ε0

∫∞−∞ dzE

spz H

sp∗y

×

∫ ∞−∞

du−|I1(u)2|√

1− u2(A.21)

A.2 Cavity plasmon excitation from free space

We consider the excitation of the MDM plasmon mode by a normally incident TM

wave from free space. We can write the z-directed electric field continuity at the

cavity termination in terms of the excitation plane wave, reflected wave and the

surface plasmon MDM mode field as,

Epwz + Eref

z = tEspz (A.22)

Now assuming the incident field amplitude to be unity and expanding the reflected

wave on the free space side and the plasmon field into a continuum of modes we have,

1 +

∫ ∞−∞

g(k)eikzdk = tEspz =

t

2π

∫ ∞−∞

I(kz)eikzzdz (A.23)

Taking Fourier transform of both sides of equation[A.23] we get,

g(kz) =t

2πI(kz)− δ(kz) (A.24)

g(u) =t

2πI(u)− δ(u) (A.25)

Where, u = kz/k0 with k0 = 2πλ

is the normalized wave vector in the z-direction.

Now, we need another boundary condition, and we choose the time averaged poynt-

ing flux balance across the cavity interface. This is a physically meaningful energy


conservation condition. We can write the poynting flux balance as,∫ ∞−∞

dz(Epwz + Eref

z )× (Hpwy +Href

y )∗ =

tt∗∫ ∞−∞

dzEspz ×Hsp ∗

y (A.26)

Here the ∗ represents the complex conjugate. Again, as in the previous section we

can derive the magnetic field from the electric fields in the free space side as,

Hpwref =

1

ωµ0

∫ ∞−∞

k20√k20 − k2z

g(kz)eikzzdkz (A.27)

Hpwinc =

−1

ωµ0

k20√k20 − k2z

eikzz (A.28)

Now, we can simplify the poynting flux from the free space side. We have,∫Spwx dz =

∫ ∞−∞

dz(Epwz + Eref

z )× (Hpwy +Href

y )∗ (A.29)

=

∫ ∞−∞

dz tEspz × (Hpw

y +Hrefy )∗ (A.30)

Substituting for the H we get,∫Spwx dz =

−tωµ0

k0

∫ ∞−∞

Espz dz +

t

ωµ0

∫ ∞−∞

∫ ∞−∞

dkzdzk20g

∗(kz)√k20 − k2z

Espz e−ikzz (A.31)

Substituting from g∗(kz) from equation[A.25] we get,

∫Spwx dz =

t k20ωµ0

[−I(kz = 0)

k0+

∫ ∞−∞

t∗|I(kz)|2

(√k20 − k2z)∗

dkz −I(kz = 0)

k0

](A.32)

For the cavity (plasmon) side we have,∫Sspx dz = tt∗

∫ ∞−∞

Espz H

sp∗y dz (A.33)


Equating both sides we get,

tt∗∫ ∞−∞

Espz H

sp∗y dz =

t k20ωµ0

[−2

I(kz = 0)

k0+

∫ ∞−∞

t∗|I(kz)|2

(√k20 − k2z)∗

dkz

](A.34)

Simplifying we get,

t∗

(∫ ∞−∞

Espz H

sp∗y dz − k20

ωµ0

∫ ∞−∞

|I(kz)|2

(√k20 − k2z)∗

dkz

)=−2 k0ωµ0

I(kz = 0) (A.35)

Finally

t∗ =

−2 k0ωµ0

I(kz = 0)(∫∞−∞E

spz H

sp∗y dz − k20

ωµ0

∫∞−∞

|I(kz)|2

(√k20−k2z)∗

dkz

) (A.36)

(A.37)

This can be written in terms of the normalized wave number as before to get

equation[2.5]

t =

2I1(0)√

ε0µ0

1λ

√ε0µ0

∫∞−∞ du

|I1(u))2|√1−u2 −

∫∞−∞ dzE

spz H

sp∗y

∗ (A.38)

Appendix B

Energy stored in the near-field

Here we will outline the basic steps in the derivation of the near field energy storage

ahead of the cavity termination for a single plasmon reflection event. The derivation

parallels the reflection coefficient calculation in chapter[]. The various terms have

their usual meaning from the same calculation. The energy stored in the near field

has contributions from the electric and magnetic fields. For the energy stored in the

electric field we can write,

WE =

∫1

4ε0|E|2dV (B.1)

=

∫1

4ε0(|Ez|2 + |Ex|2)dV (B.2)

From the derivation of the reflection coefficient we have,

Ez =

∫ ∞−∞

1 + r

2πI1e

ikzzei√k20−k2zxdkz (B.3)

For the near field we have,

EzNF =

∫k2z>k

20

1 + r

2πI1e

ikzzei√k20−k2zxdkz (B.4)

62

APPENDIX B. ENERGY STORED IN THE NEAR-FIELD 63

also, from ∇ · E = 0

Ex = −∫ ∞−∞

1 + r

2π

I1√k20 − k2z

eikzzei√k20−k2zxdkz (B.5)

ExNF = −∫k2z>k

20

1 + r

2π

I1√k20 − k2z

eikzzei√k20−k2zxdkz (B.6)

We can rewrite the expression for the nearfield energy using fourier transformed

quantities.

Energy =

∫1

4ε0|ENF |2dV =

∫1

4ε0|ENF |2dxdz (B.7)

=1

4π2

∫1

4ε0|F (ENF )|2dkxdkz (B.8)

For the Fourier transforms of the near fields we have,

F (EzNF ) =

∫ ∞−∞

EzNF eikxxeikzzdzdx (B.9)

Substituting from B.3 and writing ei√k20−k2z as e−

√k2z−k20 we get after simplification,

F (EzNF ) =(1 + r)I1(kz)√k2z − k20 + ikx

|kz| > k0 (B.10)

= 0 |kz| < k0


We can now calculate the energy stored in the nearfield in Ez as

WNF,Ez =ε0

16π2

∫|F (EzNF )|2dkzdkx =

ε0|1 + r|2

16π2

∫ ∞|kz |=k0

dkz

∫ ∞kx=−∞

dkx|I1(kz)|2

k2z − k20 + k2x(B.11)

= 2ε0|1 + r|2

16π2

∫ ∞kz=k0

dkz

∫ ∞kx=−∞

dkx|I1(kz)|2

k2z − k20 + k2x(B.12)

=ε0|1 + r|2

8π2

∫ ∞kz=k0

dkz|I1(kz)|2π√

(k2z − k20)(B.13)

=ε0|1 + r|2

8π

∫ ∞kz=k0

dkz|I1(kz)|2√(k2z − k20)

(B.14)

Similarly for the Ex field we get,

WNF,Ex =ε0|1 + r|2

8π

∫ ∞kz=k0

dkz|I1(kz)|2k2z

(k2z − k20)3/2(B.15)

The calculation for the energy in the magnetic field can be performed similarly

and we get,

WNF,Hy =ε0|1 + r|2

8π

∫ ∞kz=k0

dkz|I1(kz)|2k20

(k2z − k20)3/2(B.16)

Now we can write the total energy in the near field as,

WNF = WNF,Hy +WNF,Ex +WNF,Ez

=ε0|1 + r|2

8π

∫ ∞kz=k0

dkz|I1(kz)|2√k2z − k20

(1 +

k2z + k20k2z − k20

)(B.17)

=ε0|1 + r|2

8π

∫ ∞kz=k0

dkz|I1(kz)|2√k2z − k20

(2 +

2k20k2z − k20

)(B.18)

=ε0|1 + r|2

4π

∫ ∞u=1

du|I1(u)|2√u2 − 1

(1 +

1

u2 − 1

)(B.19)

Where u = kzk0

.


Also from above we can verify that,

We −Wm =ε0|1 + r|2

4π

∫ ∞u=1

du|I1(u)|2√u2 − 1

(B.20)

Appendix C

Two mode cavity resonance

For deriving the transmission spectra for the structure, we denote the 3 relevant

plasmon modes in the structure using indices 0 (Ground plane mode), 1(MIM mode)

and 2 (IMI mode). Development a cavity model for the plasmon cavity requires

the coupling coefficients between the different modes in the cavity. In the following

equations tij and rij corresponds to coupling between modes i and j. The letter ‘t’

is used to denote coupling from mode 0 to the other modes. The coupling between

the two antenna modes (mode 1 and 2) is denoted by ‘r’. These reflection and

transmission coefficients between the modes can be calculated from the mode overlap

integrals with full field simulations of half space junctions of suitable geometry. When

a plasmon mode is incident on a truncation of a semi-infinite metal antenna, it scatters

into all possible modes allowed on either side of the junction. The total electric field

can then be written as

Etotal =∑modes

cmodeEmode (C.1)

Where the sum is over all possible modes in each half space and Emode is the electric

field mode profile. The strength of excitation for each of the modes can be calculated

from orthogonality relations as,

cmode =1

2

∫(Emode ×Htotal + Etotal ×Hmode) · dA∫

Emode ×Hmode · dA(C.2)

66

APPENDIX C. TWO MODE CAVITY RESONANCE 67

The integral in the above expressions is over a plane normal to the propagation

direction of the incident plasmon mode. More details on the method used to evaluate

these coefficients can be found in the references.[99, 100] From full field simulations,

we get the following values for the coupling coefficients between the three modes:r00 t01 t02

t10 r11 r12

t20 r21 r22

=

−0.124− 0.148i 0.698− 0.184i 0.324− 0.009i

0.684− 0.186i −0.228− 0.438i 0.078 + 0.104i

1.165 + 0.004i 0.290 + 0.390i −0.006− 0.215i

(C.3)

Also, the mode index for the two cavity modes at λ = 620 nm are calculated to be,

k1 = k0(2.78− 0.066i) (C.4)

k2 = k0(1.070− 0.006i) (C.5)

k0 =2π

λ(C.6)

Once the relevant coupling coefficients between the modes are calculated one can

develop a coupled Fabry-Perot cavity model for the stripe patch antenna. For unit

amplitude incident ground plane plasmon mode field, we can write from the continuity

of the electric fields in the z-direction just inside the cavity,

t01 + AE1 +BE2 = E1 (C.7)

t02 + CE1 +DE2 = E2 (C.8)

(C.9)


where,

A =2∑j=1

r1jrj1e−i(k1+kj)L (C.10)

B =2∑j=1


C =2∑j=1


D =2∑j=1


and E1 and E2 are the forward propagating field amplitudes at the cavity entrance

for modes 1 and 2. In all these expressions the variation of the fields along z axis is

implicit and L is the cavity length. Now, we can solve for E1 and E2 as,

E1 =(D − 1)t01 −Bt02

BC − (D − 1)(A− 1)(C.14)

E2 =(A− 1)t02 − Ct01

BC − (D − 1)(A− 1)(C.15)

Similarly we can write the back propagating fields as,

E1b =(D − 1)t01b −Bt02bBC − (D − 1)(A− 1)

(C.16)

E2b =(A− 1)t02b − Ct01b

BC − (D − 1)(A− 1)(C.17)

where,

t01b =2∑j=1

rj1t0je−i(k1+kj)L (C.18)

t02b =2∑j=1

rj2t0je−i(k2+kj)L (C.19)


and Finally the reflection and transmission coefficients can be derived to be ,

t = E1t10e−ik1L + E2t20e

−ik2L (C.20)

r = r00 + E1bt10 + E2bt20 (C.21)

The calculated values for the reflection (R = |r|2) and transmission (T = |t|2)for different cavity lengths and the same quantities derived from full field FDFD

simulations is given in 3.12i. The excellent agreement between the two, even for very

small stripe widths, validate the coupled cavity model.

Bibliography

[1] Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface plasmon subwavelength

optics. Nature 2003, 424, 824–830.

[2] Maier, S. Plasmonics: Fundamentals and Applications; Springer: 2007.

[3] Economou, E. Surface plasmons in thin films. Physical Review 1969, 182, 539.

[4] Maier, S. Effective Mode Volume of Nanoscale Plasmon Cavities. 2006, 38,

257-267.

[5] Min, B.; Ostby, E.; Sorger, V.; Ulin-Avila, E.; Yang, L.; Zhang, X.; Va-

hala, K. High-Q surface-plasmon-polariton whispering-gallery microcavity. Na-

ture 2009, 457, 455–458.

[6] Gong, Y.; Vuckovic, J. Design of plasmon cavities for solid-state cavity quantum

electrodynamics applications. Applied Physics Letters 2007, 90, 033113-1-3.

[7] Yokota, H.; Saito, K.; Yanagida, T. Single molecule imaging of fluorescently

labeled proteins on metal by surface plasmons in aqueous solution. Physical

Review Letters 1998, 80, 4606-9.

[8] Pettinger, B.; Ren, B.; Picardi, G.; Schuster, R.; Ertl, G. Nanoscale probing of

adsorbed species by tip-enhanced Raman spectroscopy. Physical Review Letters

2004, 92, 096101.

[9] Pettinger, B.; Tadjeddine, A.; Kolb, D. Enhancement in raman intensity by

use of surface-plasmons. Chem. Phys. Lett. 1979, 66, 544-548.

70

BIBLIOGRAPHY 71

[10] Righini, M.; Volpe, G.; Girard, C.; Petrov, D.; Quidant, R. Surface plas-

mon optical tweezers: Tunable optical manipulation in the femtonewton range.

Physical Review Letters 2008, 100, 186804.

[11] Chen, C.; Osgood, R. Direct observation of the local-field-enhanced surface

photochemical-reactions. Physical Review Letters 1983, 50, 1705-1708.

[12] Cao, L.; Barsic, D. N.; Guichard, A. R.; Brongersma, M. L. Plasmon-Assisted

Local Temperature Control to Pattern Individual Semiconductor Nanowires and

Carbon Nanotubes. Nano Letters 2007, 7, 3523-3527.

[13] Jun, Y. C.; Pala, R.; Brongersma, M. L. Strong Modification of Quantum

Dot Spontaneous Emission via Gap Plasmon Coupling in Metal Nanoslits. The

Journal of Physical Chemistry C 2009, 7269-7273.

[14] Bakker, R. M.; Yuan, H.-K.; Liu, Z.; Drachev, V. P.; Kildishev, A. V.;

Shalaev, V. M.; Pedersen, R. H.; Gresillon, S.; Boltasseva, A. Enhanced lo-

calized fluorescence in plasmonic nanoantennae. Applied Physics Letters 2008,

92, 043101.

[15] Farahani, J. N.; Pohl, D. W.; Eisler, H.-J.; Hecht, B. Single Quantum Dot

Coupled to a Scanning Optical Antenna: A Tunable Superemitter. Phys. Rev.

Lett. 2005, 95, 017402.

[16] Taminiau, T. H.; Moerland, R. J.; Segerink, F. B.; Kuipers, L.; van

Hulst, N. F. Œ/4 Resonance of an Optical Monopole Antenna Probed by Single

Molecule Fluorescence. Nano Letters 2007, 7, 28-33.

[17] Cai, W.; White, J. S.; Brongersma, M. L. Compact, High-Speed and Power-

Efficient Electrooptic Plasmonic Modulators. Nano Letters 2009, 4403-4411.

[18] Nikolajsen, T.; Leosson, K.; Bozhevolnyi, S. I. Surface plasmon polariton based

modulators and switches operating at telecom wavelengths. Applied Physics

Letters 2004, 85, 5833-5835.

BIBLIOGRAPHY 72

[19] Krasavin, A. V.; Zheludev, N. I. Active plasmonics: Controlling signals in

Au/Ga waveguide using nanoscale structural transformations. Applied Physics

Letters 2004, 84, 1416-1418.

[20] Domenico Pacifici, Henri J. Lezec, H. A. A. All-optical modulation by plasmonic

excitation of CdSe quantum dots. Nature Photonics 2007, 1, 402-406.

[21] Hryciw, A.; Jun, Y. C.; Brongersma, M. L. Plasmonics: Electrifying plasmonics

on silicon. Nat Mater 2010, 9, 3–4.

[22] Walters, R. J.; van Loon, R. V. A.; Brunets, I.; Schmitz, J.; Polman, A. A

silicon-based electrical source of surface plasmon polaritons. Nat Mater 2010,

9, 21–25.

[23] Raether, H. Surface Plasmons; Springer Tracts in Modern Physics Springer:

1988.

[24] Weeber, J.-C.; Bouhelier, A.; Colas des Francs, G.; Markey, L.; Dereux, A.

Submicrometer In-Plane Integrated Surface Plasmon Cavities. Nano Letters

2007, 7, 1352-1359.

[25] Zia, R.; Selker, M. D.; Catrysse, P. B.; Brongersma, M. L. Geometries and

materials for subwavelength surface plasmon modes. Journal of the Optical So-

ciety of America A: Optics and Image Science, and Vision 2004, 21, 2442 –

2446.

[26] Zayats, A. V.; Smolyaninov, I. I.; Maradudin, A. A. Nano-optics of surface

plasmon polaritons.. Physics Reports 2005, 408, 131 – 314.

[27] Hofmann, C. E.; Vesseur, E. J. R.; Sweatlock, L. A.; Lezec, H. J.; Garcıa de

Abajo, F. J.; Polman, A.; Atwater, H. A. Plasmonic Modes of Annular Nanores-

onators Imaged by Spectrally Resolved Cathodoluminescence. Nano Letters

2007, 7, 3612-3617.

[28] Bharadwaj, P.; Bouhelier, A.; Novotny, L. Electrical Excitation of Surface

Plasmons. Phys. Rev. Lett. 2011, 106, 226802.

BIBLIOGRAPHY 73

[29] Sambles, J. R.; Bradbery, G. W.; Yang, F. Optical excitation of surface plas-

mons: An introduction. Contemporary Physics 1991, 32, 173-183.

[30] Dionne, J.; Sweatlock, L.; Atwater, H.; Polman, A. Planar metal plasmon

waveguides: frequency-dependent dispersion, propagation, localization, and loss

beyond the free electron model. Physical Review B 2005, 72, 075405.

[31] Berini, P. Long-range surface plasmon polaritons. Adv. Opt. Photon. 2009, 1,

484–588.

[32] Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.;

Aussenegg, F. R.; Krenn, J. R. Silver Nanowires as Surface Plasmon Res-

onators. Phys. Rev. Lett. 2005, 95, 257403.

[33] Takahara, J.; Yamagishi, S.; Taki, H.; Morimoto, A.; Kobayashi, T. Guiding

of a one-dimensional optical beam with nanometer diameter. Opt. Lett. 1997,

22, 475–477.

[34] Novotny, L. Effective wavelength scaling for optical antennas. Physical Review

Letters 2007, 98, 1 – 4.

[35] Søndergaard, T.; Bozhevolnyi, S. I. Strip and gap plasmon polariton optical

resonators. physica status solidi (b) 2008, 245, 9–19.

[36] Miyazaki, H. T.; Kurokawa, Y. Controlled plasmon resonance in closed

metal/insulator/metal nanocavities. Appl. Phys. Lett. 2006, 89, 211126.

[37] Miyazaki, H.; Kurokawa, Y. Squeezing visible light waves into a 3-nm-thick

and 55-nm-long plasmon cavity. Physical Review Letters 2006, 96, 097401.

[38] White, J. S.; Veronis, G.; Yu, Z.; Barnard, E. S.; Chandran, A.; Fan, S.;

Brongersma, M. L. Extraordinary optical absorption through subwavelength

slits. Opt. Lett. 2009, 34, 686-688.

[39] Ishi, T.; Fujikata, J.; Marita, K.; Baba, T.; Ohashi, K. Si nano-photodiode

with a surface plasmon antenna. Jpn. J. Appl. Phys. 2005, 44, L364-L366.

BIBLIOGRAPHY 74

[40] Jun, Y. C.; Huang, K. C. Y.; Brongersma, M. L. Plasmonic beaming and

active control over fluorescent emission. Nat Commun 2011, 2, 1-4.

[41] Neutens, P.; Van Dorpe, P.; De Vlaminck, I.; Lagae, L.; Borghs, G. Electrical

detection of confined gap plasmons in metal-insulator-metal waveguides. Nat

Photon 2009, 3, 283–286.

[42] Bozhevolnyi, S. I.; Søndergaard, T. General properties of slow-plasmon resonant

nanostructures: nano-antennas and resonators. Opt. Express 2007, 15, 10869–

10877.

[43] Søndergaard, T.; Bozhevolnyi, S. Slow-plasmon resonant nanostructures: Scat-

tering and field enhancements. Phys. Rev. B 2007, 75, 073402.

[44] Bryant, G. W.; Garcia de Abajo, F. J.; Aizpurua, J. Mapping the Plasmon

Resonances of Metallic Nanoantennas. Nano Letters 2008, 8, 631–636.

[45] Sondergaard, T.; Beermann, J.; Boltasseva, A.; Bozhevolnyi, S. I. Slow-

plasmon resonant-nanostrip antennas: Analysis and demonstration. Physical

Review B 2008, 77, 115420.

[46] Barnard, E. S.; White, J. S.; Chandran, A.; Brongersma, M. L. Spectral

properties of plasmonic resonator antennas. Opt. Express 2008, 16, 16529–

16537.

[47] Ford, G. W.; Weber, W. H. Electromagnetic interactions of molecules with

metal surfaces. Phys. Rep. 1984, 113, 195–287.

[48] Barnes, W. L. Fluorescence near interfaces: The role of photonic mode density.

Journal of Modern Optics 1998, 45, 661-699.

[49] Novotny, L.; van Hulst, N. Antennas for light. Nat Photon 2011, 5, 83–90.

[50] Fromm, D. P.; Sundaramurthy, A.; Schuck, P. J.; Kino, G.; Moerner, W. E.

Gap-Dependent Optical Coupling of Single “Bowtie” Nanoantennas Resonant

in the Visible. Nano Letters 2004, 4, 957-961.

BIBLIOGRAPHY 75

[51] Jun, Y. C.; Kekatpure, R. D.; White, J. S.; Brongersma, M. L. Nonreso-

nant enhancement of spontaneous emission in metal-dielectric-metal plasmon

waveguide structures. Phys. Rev. B 2008, 78, 153111.

[52] Cai, W.; Vasudev, A. P.; Brongersma, M. L. Electrically Controlled Nonlinear

Generation of Light with Plasmonics. Science 2011, 333, 1720-1723.

[53] Bouhelier, A.; Beversluis, M.; Hartschuh, A.; Novotny, L. Near-Field Second-

Harmonic Generation Induced by Local Field Enhancement. Phys. Rev. Lett.

2003, 90, 013903.

[54] Lippitz, M.; van Dijk, M. A.; Orrit, M. Third-Harmonic Generation from

Single Gold Nanoparticles. Nano Letters 2005, 5, 799-802.

[55] Beversluis, M. R.; Bouhelier, A.; Novotny, L. Continuum generation from

single gold nanostructures through near-field mediated intraband transitions.

Phys. Rev. B 2003, 68, 115433.

[56] Jamid, H. A.; AlBader, S. J. Diffraction of surface plasmon-polaritons in an

abruptly terminated dielectric-metal interface. IEEE Photonics Technology Let-

ters 1995, 7, 321 – 3.

[57] Leskova, T.; Gapotchenko, N. Fabry-Perot type interferometer for surface-

polaritons - resonance effects. Solid State Comm. 1985, 53, 351-357.

[58] Leskova, T.; Maradudin, A.; Zierau, W. Surface plasmon polariton propagation

near an index step. Opt. Comm. 2005, 249, 23-35.

[59] Zia, R.; Chandran, A.; Brongersma, M. L. Dielectric waveguide model for

guided surface polaritons. Opt. Lett. 2005, 30, 1473 – 1475.

[60] Gordon, R. Light in a subwavelength slit in a metal: Propagation and reflec-

tion. Physical Review B (Condensed Matter and Materials Physics) 2006, 73,

153405.

BIBLIOGRAPHY 76

[61] Porto, J.; Garcia-Vidal, F.; Pendry, J. Transmission resonances on metallic

gratings with very narrow slits. Physical Review Letters 1999, 83, 2845-2848.

[62] Szentirmay, Z. Slow-mode surface plasma oscillations in layered structures.

Physical Review B 1987, 36, 2607–13.

[63] Bozhevolnyi, S. I., Ed.; Plasmonic Nanoguides and Circuits; Pan Stanford:

2009.

[64] Sukru Ekin Kocabas,; Veronis, G.; Miller, D. A. B.; Fan, S. Modal analysis

and coupling in metal-insulator-metal waveguides. Physical Review B 2009, 79,

035120.

[65] Hernandez, G. Fabry-Perot Interferometers; Oxford Oxfordshire: Oxford Uni-

versity Press: 1986.

[66] Takakura, Y. Optical Resonance in a Narrow Slit in a Thick Metallic Screen.

Physical Review Letters 2001, 86, 5601–5603.

[67] Jackson, J. D. Classical electrodynamics; 3rd ed.; Wiley: New York, NY, 1999.

[68] Lalanne, P.; Hugonin, J.; Rodier, J. Theory of surface plasmon generation at

nanoslit apertures. Physical Review Letters 2005, 95, 263902.

[69] Fan, S. Surface Plasmon Nanophotonics. In ; Mark L. Brongersma,; Kik, P. G.,

Eds.; Springer Series in Optical Sciences Springer: 2007; Chapter 12, pages

169–182.

[70] Rakic, A.; Djurisic, A.; Elazar, J.; Majewski, M. Optical properties of metallic

films for vertical-cavity optoelectronic devices. Appl. Opt. 1998, 37,.

[71] Esteban, R.; Teperik, T. V.; Greffet, J. J. Optical Patch Antennas for Single

Photon Emission Using Surface Plasmon Resonances. Phys. Rev. Lett. 2010,

104, 026802.

BIBLIOGRAPHY 77

[72] Sun, S.; Yang, K.-Y.; Wang, C.-M.; Juan, T.-K.; Chen, W. T.; Liao, C. Y.;

He, Q.; Xiao, S.; Kung, W.-T.; Guo, G.-Y.; Zhou, L.; Tsai, D. P. High-

Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces. Nano

Letters 2012, 12, 6223-6229.

[73] Pors, A.; Albrektsen, O.; Radko, I. P.; Bozhevolnyi, S. I. Gap plasmon-based

metasurfaces for total control of reflected light. Sci. Rep. 2013, 3, 1-6.

[74] Liu, Y.; Palomba, S.; Park, Y.; Zentgraf, T.; Yin, X.; Zhang, X. Com-

pact Magnetic Antennas for Directional Excitation of Surface Plasmons. Nano

Letters 2012, 12, 4853-4858.

[75] Kriesch, A.; Burgos, S. P.; Ploss, D.; Pfeifer, H.; Atwater, H. A.; Peschel, U.

Functional Plasmonic Nanocircuits with Low Insertion and Propagation Losses.

Nano Letters 2013, 13, 4539-4545.

[76] Kosako, T.; Kadoya, Y.; Hofmann, H. F. Directional control of light by a

nano-optical Yagi-Uda antenna. Nat Photon 2010, 4, 312–315.

[77] Pakizeh, T.; Kall, M. Unidirectional Ultracompact Optical Nanoantennas.

Nano Letters 2009, 9, 2343-2349.

[78] Weeber, J. C. Near-field observation of surface plasmon polariton propagation

on thin metal stripes. Phys. Rev. B 2001, 64, 045411.

[79] Zia, R.; Selker, M. D.; Brongersma, M. L. Leaky and bound modes of surface

plasmon waveguides.. Physical Review B 2005, 71, 165431 – 1.

[80] Berini, P.; Charbonneau, R.; Lahoud, N. Long-Range Surface Plasmons on

Ultrathin Membranes. Nano Letters 2007, 7, 1376-1380.

[81] Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Laluet, J.-Y.; Ebbesen, T. W.

Channel plasmon subwavelength waveguide components including interferome-

ters and ring resonators. Nature 2006, 440, 508–511.

BIBLIOGRAPHY 78

[82] Dionne, J. A.; Sweatlock, L. A.; Atwater, H. A.; Polman, A. Plasmon slot

waveguides: Towards chip-scale propagation with subwavelength-scale localiza-

tion. Phys. Rev. B 2006, 73, 035407.

[83] Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Ebbesen, T. W. Channel

plasmon-polariton guiding by subwavelength metal grooves. Phys. Rev. Lett.

2005, 95, 046802.

[84] Koller, D. M. Organic plasmon-emitting diode. Nature Photon. 2008, 2, 684–

687.

[85] Nie, S.; Emory, S. R. Probing Single Molecules and Single Nanoparticles by

Surface-Enhanced Raman Scattering. Science 1997, 275, 1102-1106.

[86] Lezec, H. J.; Degiron, A.; Devaux, E.; Linke, R. A.; Martin-Moreno, L.;

Garcia-Vidal, F. J.; Ebbesen, T. W. Beaming Light from a Subwavelength

Aperture. Science 2002, 297, 820-822.

[87] Schuck, P. J.; Fromm, D. P.; Sundaramurthy, A.; Kino, G. S.; Moerner, W. E.

Improving the Mismatch between Light and Nanoscale Objects with Gold

Bowtie Nanoantennas. Phys. Rev. Lett. 2005, 94, 017402.

[88] Bharadwaj, P.; Deutsch, B.; Novotny, L. Optical Antennas. Adv. Opt. Photon.

2009, 1, 438–483.

[89] Barnard, E. S.; White, J. S.; Chandran, A.; Brongersma, M. L. Spectral

properties of plasmonic resonator antennas. Opt. Express 2008, 16, 16529–

16537.

[90] Anemogiannis, E.; Glytsis, E. N.; Gaylord, T. Determination of guided and

leaky modes in lossless and lossy planar multilayer optical waveguides: reflection

pole method and wavevector density method. Lightwave Technology, Journal of

1999, 17, 929-941.

BIBLIOGRAPHY 79

[91] Rakic, A. D.; Djurisic, A. B.; Elazar, J. M.; Majewski, M. L. Optical Properties

of Metallic Films for Vertical-Cavity Optoelectronic Devices. Appl. Opt. 1998,

37, 5271–5283.

[92] Barnard, E. S.; Pala, R. A.; Brongersma, M. L. Photocurrent mapping of

near-field optical antenna resonances. Nat Nano 2011, 6, 588–593.

[93] Chandran, A.; Barnard, E. S.; White, J. S.; Brongersma, M. L. Metal-

dielectric-metal surface plasmon-polariton resonators. Phys. Rev. B 2012, 85,

085416.

[94] Okamoto, K.; Niki, I.; Scherer, A.; Narukawa, Y.; Mukai, T.; Kawakami, Y.

Surface plasmon enhanced spontaneous emission rate of InGaNGaN quantum

wells probed by time-resolved photoluminescence spectroscopy. Applied Physics

Letters 2005, 87, 71102-1-3.

[95] Wedge, S.; Wasey, J. A. E.; Barnes, W. L.; Sage, I. Coupled surface

plasmon-polariton mediated photoluminescencefrom a top-emitting organic

light-emitting structure. Applied Physics Letters 2004, 85, 182-184.

[96] Miller, D. A. B.; Chemla, D. S.; Damen, T. C.; Gossard, A. C.; Wiegmann, W.;

Wood, T. H.; Burrus, C. A. Band-Edge Electroabsorption in Quantum Well

Structures: The Quantum-Confined Stark Effect. Phys. Rev. Lett. 1984, 53,

2173–2176.

[97] Drozd, V.; Baraban, A.; Nikiforova, I. Electrical properties of Si—Al2O3

structures grown by ML-ALE. Applied Surface Science 1994, 82–83, 583 - 586.

[98] Empedocles, S. A.; Bawendi, M. G. Quantum-Confined Stark Effect in Single

CdSe Nanocrystallite Quantum Dots. Science 1997, 278, 2114-2117.

[99] Liu, J. S. Q.; White, J. S.; Fan, S.; Brongersma, M. L. Side-coupled cavity

model for surface plasmon-polariton transmission across a groove. Opt. Express

2009, 17, 17837–17848.

BIBLIOGRAPHY 80

[100] Lalanne, P.; Hugonin, J. P.; Rodier, J. C. Approximate model for surface-

plasmon generation at slit apertures. J. Opt. Soc. Am. A 2006, 23, 1608–1615.

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