IPT 544000: Selected Topics in Ultrafast Optics

Third-Order Ultrafast Nonlinear Optics

Chen-Bin (Robin) Huang

Institute of Photonics Technologies

National Tsing Hua University, Taiwan

Nonlinear propagation equations

Basic formulation

2 j 2

022

22

22

1

aaaj

taj

ta

za

effAcnn

20

2020

NLSE Waveguidesg Lossless

02'

22

2

20

2

aaja

Tj

za

Dimensionless NLSE Dimensionless NLSE

aaaaj 22

22

2)sgn(

2

2

Split-step Fourier method

Input pulse envelope 222

22ja a j a a

z t

0( , )a t

F T

Spectral envelope

F.T.

0( )A Spectral envelope

Dispersed spectral envelope

0( , )A 2

202

( , ) ( , )exp[ ]DzA z A j

2

I.F.T.

Dispersed pulse envelope ( , )Da z t

2( ) ( ) ( ) Dispersed, SPM pulse envelope

Now do iterations all the way to the output

2, ( , ) ( , )exp[ ( , ) ]D SPM D Da z t a z t j a z t z

Now do iterations all the way to the output

3

Dispersionless SPM

Spectral broadening

Experimental data Asymmetry?

A. M. Weiner, Ultrafast Optics (Wiley, 2009)

4Stolen, Lin, Phys. Rev. A 17, 1448 (1978)

SPM + Normal dispersion

Normal dispersion: 2 > 0 Blue-shifted waves travel slower

Power spectrum Less oscillation

Time-domain envelope Time-domain envelope Square pulse

5A. M. Weiner, Ultrafast Optics (Wiley, 2009)

Wave breaking Homework: triangular pulse

SPM + Normal dispersion Fast oscillations in pulse edges FWM spectral side lobes

Avoid wave breaking:monotonic chirp similaritons

FWM spectral side-lobes

6W. J. Tomlinson, Opt. Lett. 10, 457 (1985)

Modulational instability

MI gain spectrum

2

022 42

PK

22

0Pg max

2c

max

7G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995)

Higher-order solitons

N=2L=z0/2 L=z0

ensi

tyIn

te

peakj PN

jNP 2

2)122(

T

spec

trum 122

0

jNT

Tj

Pow

er s

8

Higher-order solitons

N=3 L=z0/4 L=z0/2

ensi

tyIn

tesp

ectru

m

Large spectral broadening

Pow

er s Large spectral broadening

9

Soliton behaviors First experimental evidence of soliton orders

700m SMF with 7-ps FWHM durationz =1 26 km P =1W L~z /2 z0=1.26 km, Pc=1W, L~z0/2,

pect

raS

trac

esIA

t

dispersive N 3 N 4

10L. F. Mollenauer, Stolen, Gordon, Phys. Rev. Lett. 45, 1095 (1980)

dispersivebroadening

N=2 N=3 N=4N=1

Soliton collision

Center frequency group velocity During collision

St li i t ti)1ˆ(

ˆ2 j

Strong nonlinear interaction Complicated pulse envelope

After collision

2ˆ)ˆsech(),( j eea

Pulses are restored, with initial duration, amplitude Phase and timing location changed

Bad for coherent communications

11A. M. Weiner, Ultrafast Optics (Wiley, 2009)

Adiabatic soliton temporal compression

Dispersion control Energy conservation

0

22T

U

)()0(

)()0(

2

2

0

0

zzTT

B/D

IV

Dispersion-decreasing fiberPMCW

20 d

seed pulses

D(0) D(L)-10

0

dB) 298 fs

-30

-20

SHG

(d

12

-60 0 60-40(ps)

Pedestal removal

Nonlinear optical loop mirror (NOLM) Nonlinear differential phasep

Cancellation of counter-propagating pulses

400/(200) fs@10 GHz

-20Smooth comb

>30dB-40

-30

0

um (d

Bm

)

-60

-50

40

Spec

tru

13

1525 155560

Wavelength (nm)

Huang, Park, Leaird, Weiner, Opt. Express 16, 2520 (2008)

Nonlinearly broadened combs Dispersion-Decreasing Fiber (anomalous: soliton)

L= 2 km; D(z): 10 to 1.5 ps/nm/km

Highly Non-Linear Fiber (normal: SPM) L= 247 m;

= 10 5 (W km)-1; = 10.5 (W km) 1; D= -1.88 ps/nm/km; D’=0.016 ps/nm2/km Commercially available fibers

0 dB

/DIV

10

14

Adiabatic soliton spectral compression

Dispersion-increasing fiber Simple idea, never realized

Id l i ti D /D 22 5 Ideal compression ratio = Dout/Din=22.5

1 km in lengthDin=0.60 ps/nm/km

205 fs input pulseBW: 13 nm

10x 10

4

in pDout= 13.5 ps/nm/km

Loss: 0.4 dB/km= 3.5 (W km)-1

T =3 fs

BW: 13 nm

5

10 TR=3 fsCompression ratio=4.5

15400

0 2

0

1550

15601570

0.20.4

0.60 8NLSE 1570

1580

0.81 Wavelength (nm)z (km)

NLSEby SSF

H.-P. Chuang and C.-B. Huang, Opt. Lett. 36, 2848 (2011)

Large spectral compression ratio

Positively chirped 305 fs input pulse Explanation

St bilit Stability

Time domainSpectral domain Compression

20

Time-domain

4x 10

5

Spectral-domain Compressionratio= 12.5

0

10

0

2

-50

0

00.2

0.40 6

0

15401550

1560

00.2

0.40 6

0

0

50

0.60.8

1 Time (ps)z (km)

15601570

1580

0.60.8

1 Wavelength (nm)z (km)

Experiment: setup

1 km in lengthDin=0.60 ps/nm/km

Dout= 13.5 ps/nm/kmout 3 5 ps/ /Loss: 0.4 dB/km= 3.5 (W km)-1

TR=3 fs

10%95%

90%5%

1

350 fs

1

13 nm

0

350 fs

0

13 nm

0Delay (ps)

-0.8 -0.4 0 0.4 0.8Wavelength (nm)

1540 1560 15800

Experiment: results

Spectral compressionratio=15.5

Intensitycross-correlation

H.-P. Chuang and C.-B. Huang, Opt. Lett. 36, 2848 (2011)

Raman response

Delayed nonlinear phase delayed instantaneous frequency Red-shift of the pulse power spectrum

Time-domain view We will perform freq-domain derivations

19A. M. Weiner, Ultrafast Optics (Wiley, 2009)

Fourier-transform properties Raman response real F(-)=F*() A single-sided function

Im{F( )} < 0 for > 0

Frequency-domain results

Im{F()} < 0 for > 0 Im{F()} > 0 for < 0 Derivative of Re{F()} is zero at =0

)}~~(Im{ psF

Re

Derivative of Im{F()} is negative at =0

200

300ReIm

1

F()

0

1000.6

0.8

f(t)

-100

0

0.2

0.4

20-0.5 0 0.5 1

-2000 10 20 30 40 50

0

Raman gain

Raman gain spectrum for fused silica Peak 13.2 THz

Bandwidth 40 THz

222

spRamans aagz

a

Bandwidth ~ 40 THz Inhomogeneous broadening

Peak gain g= 9.9x10-16 cm2/W)}~~(Im{4 2

psRamanng

F

0

~)~sin()}~(Im{2)(

dtFtf

f(t)

Period ~ 75 fs

21A. M. Weiner, Ultrafast Optics (Wiley, 2009)www.osa.org

Raman: soliton self-frequency shift

Due to Raman response, solitons shift their center frequency to the red Log-log plot FWHM bandwidth also given

kmTHz

Tx

z 40

3105.9

22J. P. Gordon, Opt. Lett. 11, 622 (1986)

Raman: soliton fission

Breakup of higher-order solitons

Anomalous dispersionAnomalous dispersionred light slower

Shorter,red-shifted

pulse

23Dudley et.al, Nature Physics 3, 597 (2007)A. M. Weiner, Ultrafast Optics (Wiley, 2009)

pulse

Self-steepening

Shock term gives rise to intensity-dependent group velocity Dispersionless, only electronic response

M d b d i i bl More pronounced broadening in blue

0'

1 2

aajja

'0

t

jz

03 2

a

aa 0

'0

ta

z

)'( ztfa )(v

tfa

02

0

3 av

24A. M. Weiner, Ultrafast Optics (Wiley, 2009)

Class Presentation of ECE 616 Ultrafast Optics

Ultrafast Supercontinuum Generation using Microstructured Fibers

Robin C.B. HuangRobin C.B. Huang

Purdue UniversityySchool of Electrical and Computer Engineering

Dec. 07, 2004

Outline

Supercontinuum (SC) generation Definition History and progress Nonlinear processes

Photonic crystal fibers (PCF) Microstructured fibers (MF) and photonic band-gap fibers Properties

SC using MFSC us g Anomalous pumping Normal pumping

Summary

26

SC: Definition What is SC?

Coherent light source having large bandwidth Broadened input spectrum by nonlinear optical processes Broadened input spectrum by nonlinear optical processes

Applications Metrology, spectroscopy, sensing, ultrashort pulse……

27

SC: History Historical evolution

Birth of Frequency CombsBirth of Frequency Combstightly linked

28www.bath.ac.uk/physics/groups/ppmg/research_pcf_scg.html

SC: Major Nonlinear Processes

SPMAL

2||

tLinst

Elasticprocesses Inelastic

FWM4321

SRSASSp 2

processesProcess

Along withSSFS

SS4321

ISp 2

kM+kWG+kNL=0

ASSp

p S

+ SS

ASp

29

pI S

Microstructured Fibers

Photonic Crystal Fibers(PCF)(PCF)

Photonic Band-gap Fibers(PBF)

Microstructured Fibers(MF)

Guided by photonic band-gap Effective index

(PBF) (MF)

Confined within air Confined within material

30Russel, Science 299, 358 (2003)

Variable MF Properties

Small effective modal area Large nonlinearities! Lower power required

Endlessly single-mode Endlessly single mode Cladding index engineering

Lattice pitch, not core diameter!

405.22 22

clcoeff nnV

1500nm400nm 800nm

31G. Genty, Ph.D. Dissertation, (Helsinki University of Technology,2004).

Variable MF Properties

Zero-dispersion wavelength (ZD) Core size

Dispersion relation Dispersion relation Air-hole diameter Lattice

32Reeves et. al., Nature 424, 511 (2003)

G. Genty, Ph.D. Dissertation (Helsinki University of Technology,2004).

Comparison of MF Properties

Fiber\Properties SMF DSF DCF HNLF MF

Attenuation (dB/km) 0.2 0.2 0.45 0.7 80-240

Modal area (um2) 85 50 19 12 3

(1/W/km) 1.8 2.7 5 15 50

Ability to tune L and NL properties

Much lower power is required to generate SC

33

to generate SC

First SC Generated using MF Ranka, Windeler and Stentz (2000)

PM

MF

SMF

p = 790 nmZD = 767 nmt = 100 fsPp = 8 kWPav = 64 mWL = 75 cm

34Ranka et. al., Opt. Lett. 25, 25 (2000)

ZD=767nm

SC Generation in MF

Defining pumping modes Anomalous

N l Normal Normal pumping

/nm

/km

)

0

Anomalous pumping

rsio

n (p

s/ 0

-100

p p g

Higher-order

Dis

per

-200

-300

Solitons

ZD

35

Wavelength

ZD

Anomalous Pumping-1

SC generation flow Higher-ordered soliton formation

S lit fi i

peakj PN

jNP 2

2)122( 122

0

jNT

Tj

Soliton fission Higher-order dispersion, Raman scattering, self steepening

Linear radiation wave (RW) Akhmediev et. al., Phys. Rev. A 51, 2602 (1995).

Stimulated Raman scattering (SRS) Soliton Self-Frequency Shift (SSFS)

Later broadening FWM + SRS for anomalous dispersion regime SPM for normal dispersion regime

p

p g

36wavelengthZDHusakou and Hermann, PRL. 87, 203901 (2001)

Anomalous Pumping-2

Effect of pump power Wider, flatter

1.5kW

6651tP

N peak

N=4N 3122

0jN

TTj

p = 850 nm

665.12

N 2

N=3122 jNj

pZD = 806 nmt = 200 fs

L = 6 m

N=2

RW

SSFS

37Ortigosa-Blanch et. al., JOSA-B 19, 2567 (2002)

Anomalous Pumping-3

Effect of t (fixed energy) Longer pulse, SC flatter, but not wider

ttt

UN

665.12

N larger, but pulsed wider, decreased SSFS4)( tSSFS

t=300fs N=15ZD = 635 nmp = 790 nmP = 35 mW

t 300fs, N 15

Pav 35 mWL = 14 mt=100fs, N=9

t=70fs, N=7

38M. Lehtonen et. al., Appl. Phys. Lett. 82, 2197 (2003)

Anomalous Pumping-4 Effect of p

More into anomalous region Temporal broadening reduced 1.4 m OH absorptionp g Enhanced SSFS

728nm

ZD = 635 nm771nm

Pav = 35 mWt = 250 fsL = 14 m810nm

39M. Lehtonen et. al., Appl. Phys. Lett. 82, 2197 (2003)

Normal Pumping: Case 1

Pumping far from ZD SPM dominate

Stronger power desirable ps/n

m/k

m)

0

Stronger power desirable Dispersion sets limitation

Dis

pers

ion

(p

WavelengthD ZDp = 756 nmZD = 950 nmt = 200 fsL = 14 m

40mW 100mW

40G. Genty, Ph.D. Dissertation, (Helsinki University of Technology,2004).

Normal Pumping: Case 2 Pumping near ZD

SPM FWM (p

s/nm

/km

)

0

FWM SSFS

Dis

pers

ion

ZD

Wavelength

p= 753 nmZD= 806 nmt= 200 fs

41

t 200 fs.

Ortigosa-Blanch et. al., JOSA-B 19, 2567 (2002)

Summary

SC using MF expands over two octavesReali ation of optical freq enc comb! Realization of optical frequency comb!

Different pumping yields different nonlinear processes Anomalous pumping: higher-order soliton formationp p g g

Power Pulse width Wavelengthg

Normal pumping SPM dominates (far from ZD)

FWM creates soliton (near ZD with high power) FWM creates soliton (near ZD with high power)

42