nonlinear optics and gap solitons in periodic photonic...

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Nonlinear Optics and Gap Solitons Nonlinear Optics and Gap Solitons in Periodic Photonic Structuresin Periodic Photonic Structures

Yuri KivsharYuri Kivshar

Nonlinear Physics CentreNonlinear Physics CentreResearch School of Physical Sciences and EngineeringResearch School of Physical Sciences and Engineering

Australian National UniversityAustralian National University

Perspectives of Soliton Physics University of Tokyo, 17 Feb. 2007


Wadati-sensei and gap solitons

A rigorous approach for analysing gap solitons for deep gratings


OutlineOutline of my talk today

Our team in CanberraOur team in CanberraExamples of nonlinear periodic systemsExamples of nonlinear periodic systems(waveguide arrays, Bose(waveguide arrays, Bose--Einstein condensates, Einstein condensates,

photonic crystals, opticallyphotonic crystals, optically--induced lattices)induced lattices)

Discrete vs. gap solitons Discrete vs. gap solitons 2D gap solitons2D gap solitonsSurface solitons (nonlinear Tamm states)Surface solitons (nonlinear Tamm states)““RainbowRainbow”” gap solitonsgap solitons


Our Team in CanberraOur Team in Canberra

1993

2004 Nonlinear Physics Centre

Nonlinear Optics

Atom-optics(NLPC)


NLPC: Research directionsNLPC: Research directions

Nonlinear photonics: experiment(Dr. D. Neshev)

Nonlinear atom optics & BEC(Dr. E. Ostrovskaya)

Left-handed metamaterials: theory & experiments(Dr. I Shadrivov)Singular light &

optical vortices(Dr. A. Desyatnikov)

Nonlinear photonics and solitons: theory

(Dr. A. Sukhorukov)


Nonlinear periodic structuresNonlinear periodic structures


Waveguide Arrays: Discrete solitonsWaveguide Arrays: Discrete solitons

4um4μm4 μ

mAl0.24

Ga0.76

As

Al0.24

Ga0.76

AsAl0.18

Ga0.82

A s

1.5 μ

m

1.5 μ

m

4.0 μ

m

1 μ

m

Odd mode - stable Even mode -unstable

Broken translational symmetry:• Peierls-Nabarro potential

• Beam trapping at higher powersTheory: Christodoulides & Joseph (1988), Kivshar (1993)

Experiment: Silberberg’s and Aitchison’ groups (1999-2003)


Photonic CrystalsPhotonic Crystals

2 PRLs 58 (1987):

Sajeev John; Eli Yablonovitch

Earlier suggested by V.P. Bykov (Minsk) and Ph. Russell (UK)


BEC in Optical LatticesBEC in Optical Lattices

JILA BEC: 1995Nobel Prize: 2001 VLatt =V0 sin2(kL x + δt)VLatt =V0 sin2(kL x + δt)VLatt =V0 sin2(kL x + δt)


Optically induced photonic latticesOptically induced photonic lattices

Interference patternInterference pattern

0),(

02 =−∇+∂∂

⊥ yxIEVE

zEi

t

nlγ

z

e

o

Theory & ExperimentsEfremidis et al. PRE (2002) Fleischer et al. PRL (2003) Neshev et al. OL (2003)Fleischer et al. Nature (2003)Martin et al. PRL (2004)

Biased photorefractive crystal

e

)(cos)(cos 220 d

ydxIII bt

ππ+=

V0

o

SBN

co

o

o

Strong nonlinearity at low powersStrong nonlinearity at low powersλ=532nm


Optical solitonsOptical solitons


What is What is ““solitonsoliton”” ??


SolitonsSolitons

Intrinsic localized modes


SelfSelf--focusing and focusing and spatialspatial optical solitonsoptical solitons


How does periodicity How does periodicity affect solitons ?affect solitons ?


Dispersion relations and solitonsDispersion relations and solitonsBulk media

Waveguide array

TIR GAPSPATIAL SOLITON

LATTICE SOLITON

Theory: Christodoulides & Joseph (1988), Kivshar (1993) Experiments: Eisenberg (1998), Fleischer (2003), Neshev (2003), Martin (2004)

TIR GAP

BR GAP


Effective discrete systemsEffective discrete systems

Self-focusing nonlinearity

Defocusing nonlinearity

Christodoulides and Joseph (1988) Eisenberg et al. (1998)

Kivshar (1993) Chen et al. (2005) Matuszewski et al. (2006)

DISCRETE SOLITONS

GAP SOLITONS

Bandgaps, modification and control of wave diffractionBandgaps, modification and control of wave diffraction

zβ

Kx


-100 -50 0 50 100x, μm

Inte

nsit

y, arb

. unit

s

Selective excitation of Bloch wavesSelective excitation of Bloch waves

x, μm

input output

-100 -50 0 50 100x, μm

Inte

nsit

y, arb

. unit

s

-100 -50 0 50 100x, μm

Inte

nsit

y, arb

. unit

s


Gap SolitonsGap Solitons –– focusing casefocusing case

d=22.4 μm

Inpu

t pro

file

Output profilesOutput profiles

PRL 93, 083905 (2004);

TIR GAP

BR GAP


Gap Solitons Gap Solitons -- defocusing casedefocusing case

low power 10nW high power 100μWLiNbO3 waveguide array

TIR GAP

BR GAP

Opt. Exp. 14, 254 (2006)


TwoTwo--dimensional dimensional gap solitonsgap solitons


TwoTwo--dimensional gap solitonsdimensional gap solitons

experiment

theo

ry

Fischer et al. PRL 96, 023905 (2006)


Nonlinear guiding & confinementNonlinear guiding & confinement


Enhanced beam steeringEnhanced beam steering

Theory vs. experiment

Fischer et al. PRL 96, 023905 (2006)


Surface solitonsSurface solitons


MultiMulti--solitons near surfacesolitons near surface

Power diagramPower diagram

M. Molina M. Molina et al,et al, Opt. Opt. LettLett. . 3131, 1693 (2006), 1693 (2006)


DISCRETE SURFACE SOLITONS

SURFACE GAP SOLITONS

THEORY AND EXPERIMENT Makris et al. OL (2005) Suntsov et al. PRL (2006)

THEORY Kartashov et al. PRL (2006)

Self-focusing nonlinearity

x

z

NONLINEAR TAMM STATE

Defocusing nonlinearity

Nonlinear optical surface wavesNonlinear optical surface waves


LiNbO3 waveguide arrayX-cut

LiNbOLiNbO33 waveguide arraywaveguide array

Input beam

w = 2.7μm

Single-site excitation

LiNbO3 sample

defocusing nonlinearity

Optics Express 14, 254 (2006)


Nonlinear optical Tamm statesNonlinear optical Tamm states

Theory

t = 25min

PRL 97, 083901 (2006)

ExperimentInput at surface


Nonlinear discrete modelNonlinear discrete model

Effective potential

Collective coordinate

Mode power

Effective mode energy

Below threshold Above threshold

Observation of nonlinear optical Tamm states in truncated photonic lattices


Polychromatic (Polychromatic (““rainbowrainbow’’)) gap solitonsgap solitons


MotivationMotivation

Light bulbLight bulb + all colors+ all colors -- all directionsall directions

LasersLasers -- one colourone colour+ one direction+ one direction+ very bright+ very bright

WhiteWhite--light laserlight laser+ all colors+ all colors + one direction+ one direction + high brightness + high brightness

Nonlinear optics: Nonlinear optics: lightlight--matter matter interactionsinteractions

http://upload.wikimedia.org/wikipedia/commons/d/dd/Starfield_Optical_Range_-_sodium_laser.jpg


Wavelength dependent diffractionWavelength dependent diffractionz

Kβ

x

λ=580nm λ=532nm λ=490nm


Wavelength dependent diffractionWavelength dependent diffractionz

Kβ

x

Idea: Use nonlinear self-action to control broadband radiation in periodic structures


The first step: SimulationsThe first step: SimulationsNot only space has to be discretized, but also the frequency space

Motzek, Sukhorukov, Kivshar, Opt. Exp. 14, 9873 (2006)


Simulation resultsSimulation results

•We observe the expected effect that the blue light is trapped and the red light diffracts

•The white light is modeled by 9 components with wavelengths •between 443 nm and 665nm (initially flat spectrum)

Diffraction coefficient


Polychromatic gap solitonsPolychromatic gap solitons

•In polychromatic gap solitons the red part of the spectrum has a larger spatial extent than the blue one

•The solitons have a blue centre and red tails


Brighter than 10,000 sunsBrighter than 10,000 suns

High radiance: light is trapped in microHigh radiance: light is trapped in micro--corecore

1 μm

800 nm


LiNbO3 waveguide array

Fabricated structuresFabricated structures

532nmInput beam

w = 2.7μm

Single-site excitation

LiNbO3 sample

Kivshar, OL 18, 1147 (1993)


SpectrallySpectrally--resolved discrete diffractionresolved discrete diffraction

waveguide channel5 0 0 6 0 0 7 0 0 8 0 0

1 0 1

1 0 2

1 0 3

1 0 4

s u p e rc o n tin u u m in c a n d e s c e n t la m p

I(λ),

arb.

uni

ts

λ , n m


Light selects its colorsLight selects its colors

OpticallyOptically--controlled separation controlled separation and mixing of colors and mixing of colors

Power

Micro-scale prism Filtering of redWhite-light input and output


Trapped supercontinuumTrapped supercontinuum

10μW 6mW 11mW


Polychromatic surface solitonsPolychromatic surface solitons

1st 2nd 3rd 4th 5th 6th

spectrometer

10μW 1.5mW 6mW 11mW


ConclusionsConclusions•

Many interesting “discrete”

systems are being studied in

linear and nonlinear optics: links to solid state physics

•

Optically-induced photonic lattices and arrays of coupled waveguides offer a fascinating ground for the study of many nonlinear effects in periodic media, including:

lattice and gap solitonssteering and negative refraction surface solitons“rainbow”

solitons

nonlinear optics and gap solitons in periodic photonic...

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