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www.rsphysse.anu.edu.auwww.rsphysse.anu.edu.au/nonlinear/nonlinear
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
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Wadati-sensei and gap solitons
A rigorous approach for analysing gap solitons for deep gratings
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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
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Our Team in CanberraOur Team in Canberra
1993
2004 Nonlinear Physics Centre
Nonlinear Optics
Atom-optics(NLPC)
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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)
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Nonlinear periodic structuresNonlinear periodic structures
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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)
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Photonic CrystalsPhotonic Crystals
2 PRLs 58 (1987):
Sajeev John; Eli Yablonovitch
Earlier suggested by V.P. Bykov (Minsk) and Ph. Russell (UK)
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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)
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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
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Optical solitonsOptical solitons
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What is What is ““solitonsoliton”” ??
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SolitonsSolitons
Intrinsic localized modes
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SelfSelf--focusing and focusing and spatialspatial optical solitonsoptical solitons
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How does periodicity How does periodicity affect solitons ?affect solitons ?
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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
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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
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-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
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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
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Gap Solitons Gap Solitons -- defocusing casedefocusing case
low power 10nW high power 100μWLiNbO3 waveguide array
TIR GAP
BR GAP
Opt. Exp. 14, 254 (2006)
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TwoTwo--dimensional dimensional gap solitonsgap solitons
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TwoTwo--dimensional gap solitonsdimensional gap solitons
experiment
theo
ry
Fischer et al. PRL 96, 023905 (2006)
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Nonlinear guiding & confinementNonlinear guiding & confinement
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Enhanced beam steeringEnhanced beam steering
Theory vs. experiment
Fischer et al. PRL 96, 023905 (2006)
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Surface solitonsSurface solitons
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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)
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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
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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)
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Nonlinear optical Tamm statesNonlinear optical Tamm states
Theory
t = 25min
PRL 97, 083901 (2006)
ExperimentInput at surface
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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
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Polychromatic (Polychromatic (““rainbowrainbow’’)) gap solitonsgap solitons
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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
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Wavelength dependent diffractionWavelength dependent diffractionz
Kβ
x
λ=580nm λ=532nm λ=490nm
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Wavelength dependent diffractionWavelength dependent diffractionz
Kβ
x
Idea: Use nonlinear self-action to control broadband radiation in periodic structures
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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)
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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
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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
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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
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LiNbO3 waveguide array
Fabricated structuresFabricated structures
532nmInput beam
w = 2.7μm
Single-site excitation
LiNbO3 sample
Kivshar, OL 18, 1147 (1993)
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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
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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
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Trapped supercontinuumTrapped supercontinuum
10μW 6mW 11mW
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Polychromatic surface solitonsPolychromatic surface solitons
1st 2nd 3rd 4th 5th 6th
spectrometer
10μW 1.5mW 6mW 11mW
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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