Nonlinear Optics and Gap Solitons in Periodic Photonic Structures

Transcription

1 Nonlinear Optics and Gap Solitons in Periodic Photonic Structures Yuri Kivshar Nonlinear Physics Centre Research School of Physical Sciences and Engineering Australian National University Perspectives of Soliton Physics University of Tokyo, 17 Feb. 2007

2 Wadati-sensei and gap solitons A rigorous approach for analysing gap solitons for deep gratings

3 Outline of my talk today Our team in Canberra Examples of nonlinear periodic systems (waveguide arrays, Bose-Einstein condensates, photonic crystals, optically-induced induced lattices) Discrete vs. gap solitons 2D gap solitons Surface solitons (nonlinear Tamm states) Rainbow gap solitons

4 Our Team in Canberra Nonlinear Optics Nonlinear Physics Centre (NLPC) Atom-optics

5 NLPC: Research directions Nonlinear photonics and solitons: theory (Dr. A. Sukhorukov) Nonlinear atom optics & BEC (Dr. E. Ostrovskaya) Nonlinear photonics: experiment (Dr. D. Neshev) Singular light & optical vortices (Dr. A. Desyatnikov) Left-handed metamaterials: theory & experiments (Dr. I Shadrivov)

6 Nonlinear periodic structures

7 Waveguide Arrays: Discrete solitons 1.5 μ m 1.5 μ m 4.0 μ m 4um 4μm 4 μ m Al 0.24 Ga 0.76 As Al 0.18 Ga 0.82 A Al s 0.24 Ga 0.76 As 1 μ m Theory: Christodoulides & Joseph (1988), Kivshar (1993) Odd mode - stable Even mode -unstable Broken translational symmetry: Peierls-Nabarro potential Beam trapping at higher powers Experiment: Silberberg s and Aitchison groups ( )

8 Photonic Crystals 2 PRLs 58 (1987): Sajeev John; Eli Yablonovitch Earlier suggested by V.P. Bykov (Minsk) and Ph. Russell (UK)

9 BEC in Optical Lattices JILA BEC: 1995 Nobel Prize: 2001 V Latt = V 0 sin 2 (k L x + δt)

10 Optically induced photonic lattices o z SBN o Biased photorefractive crystal e o e V0 c o Theory & Experiments Efremidis et al. PRE (2002) Fleischer et al. PRL (2003) Neshev et al. OL (2003) Fleischer et al. Nature (2003) Martin et al. PRL (2004) o Interference pattern I t = I λ=532nm b + I 0 cos 2 πx ( ) cos d 2 πy ( ) d i E z + 2 E γ nl Strong nonlinearity at low powers I t V ( x, 0 E y) = 0

11 Optical solitons

12 What is soliton?

13 Solitons Intrinsic localized modes

14 Self-focusing focusing and spatial optical solitons

15 How does periodicity affect solitons?

16 Dispersion relations and solitons Bulk media SPATIAL SOLITON TIR GAP Waveguide array LATTICE SOLITON TIR GAP BR GAP Theory: Christodoulides & Joseph (1988), Kivshar (1993) Experiments: Eisenberg (1998), Fleischer (2003), Neshev (2003), Martin (2004)

17 Effective discrete systems Bandgaps, modification and control of wave diffraction Self-focusing nonlinearity Defocusing nonlinearity DISCRETE SOLITONS GAP SOLITONS Christodoulides and Joseph (1988) Eisenberg et al. (1998) Kivshar (1993) Chen et al. (2005) Matuszewski et al. (2006) β z K x

18 Selective excitation of Bloch waves input output Intensity, arb. units Intensity, arb. units Intensity, arb. units x, μm x, μm x, μm x, μm

19 Gap Solitons focusing case Output profiles TIR GAP BR GAP Input profile d=22.4 μm PRL 93, (2004);

20 Gap Solitons - defocusing case LiNbO 3 waveguide array low power 10nW high power 100μW TIR GAP BR GAP Opt. Exp. 14, 254 (2006)

21 Two-dimensional gap solitons

22 Two-dimensional gap solitons experiment theory Fischer et al. PRL 96, (2006)

23 Nonlinear guiding & confinement

24 Enhanced beam steering Theory vs. experiment Fischer et al. PRL 96, (2006)

25 Surface solitons

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27 Multi-solitons near surface Power diagram M. Molina et al, Opt. Lett. 31,, 1693 (2006)

28 Nonlinear optical surface waves x z DISCRETE SURFACE SOLITONS Self-focusing nonlinearity THEORY AND EXPERIMENT Makris et al. OL (2005) Suntsov et al. PRL (2006) Defocusing nonlinearity SURFACE GAP SOLITONS THEORY Kartashov et al. PRL (2006) NONLINEAR TAMM STATE

29 LiNbO 3 waveguide array LiNbO 3 waveguide array X-cut defocusing nonlinearity Input beam LiNbO 3 sample w = 2.7μm Single-site excitation Optics Express 14, 254 (2006)

30 Nonlinear optical Tamm states t = 25min Input at surface Experiment Theory PRL 97, (2006)

31 Observation of nonlinear optical Tamm states in truncated photonic lattices Nonlinear discrete model Effective potential Effective mode energy Below threshold Above threshold Collective coordinate Mode power

32 Polychromatic ( rainbow( rainbow ) gap solitons

33 Motivation Light bulb + all colors - all directions Lasers - one colour + one direction + very bright White-light laser + all colors + one direction + high brightness Nonlinear optics: light-matter interactions

34 Wavelength dependent diffraction z x K β λ=580nm λ=532nm λ=490nm

35 Wavelength dependent diffraction z x K β Idea: Use nonlinear self-action to control broadband radiation in periodic structures

36 The first step: Simulations Not only space has to be discretized, but also the frequency space Motzek, Sukhorukov, Kivshar, Opt. Exp. 14, 9873 (2006)

37 Simulation results The white light is modeled by 9 components with wavelengths between 443 nm and 665nm (initially flat spectrum) Diffraction coefficient We observe the expected effect that the blue light is trapped and the red light diffracts

38 Polychromatic 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

39 Brighter than 10,000 suns 800 nm 1 μm High radiance: light is trapped in micro-core core

40 Fabricated structures Kivshar, OL 18, 1147 (1993) LiNbO 3 waveguide array LiNbO 3 sample Input beam 532nm w = 2.7μm Single-site excitation

41 Spectrally-resolved resolved discrete diffraction 10 4 supercontinuum incandescent lamp I(λ), arb. units waveguide channel λ, nm

42 Light selects its colors Micro-scale prism Filtering of red White-light input and output Power Optically-controlled controlled separation and mixing of colors

43 Trapped supercontinuum 10μW 6mW 11mW

44 Polychromatic surface solitons 1st 2nd 3rd 4th 5th 6th spectrometer 10μW 1.5mW 6mW 11mW

45 Conclusions 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 solitons steering and negative refraction surface solitons rainbow solitons