Light localization and control in homogeneous and periodic media

Transcription

1 Light localization and control in homogeneous and periodic media Wieslaw Krolikowski, Laser Physics Centre, RSPhysSE Australian National University, Canberra, Australia

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3 In collaboration Dragomir Neshev, Andrey Sukhorukov, Christian Rosberg*, Robert Fischer*, Sangwoo Ha, Barry Luther Davies, Yuri Kivshar Alexander Dreischuh Sofia University, Sofia, Bulgaria Jeremy Bolger, Benjamin J. Eggleton School of Physics, University of Sydney, Sydney, Australia Arnan Mitchell, Michael W. Austin RMIT University, Melbourne, Australia

4 Outline of the talk Introduction - photorefractive materials Spatial solitons in in photorefractive crystals soliton collision anomalous interaction of soliton Light propagation in periodic optical media Bloch waves and discrete diffraction Discrete solitons Discrete localization of polychromatic light

5 Photorefractive materials and solitons

6 Nonlinear self-localization- spatial solitons Spatial soliton z Low power High power Self-focusing Optical soliton is a fundamental mode of the self-induced waveguide

7 Photorefractive materials and their applications The photorefactive effects local index of refraction modified by a spatial variation of the light intensity. Photo-excited charge carriers migrate due to drift or/and diffusion and form space-charge separation. Such a field induces a refractive index change via the Electro-Optic Effect. History In 1966 A.Ashkin from Bell Labs found that an intense optical beam experiences distortion when propagating in lithium niobate crystal. Distortion was caused by a mysterious refractive index inhomogeneities ( optical damage ) in the crystal. Damaged crystal can be cured by illuminating with broad light beam or heating. Application: dynamic holography. Materials: lithium niobate, strontium barium niobate, barium titanate

8 Photorefractive effect Illumination of the PR crystal with an optical beam Photo-excitation of charge carriers Drift and/or diffusion of charges and their subsequent trapping Formation of a space-charge electric field Refractive index modulation via Pockels effect

9 Photorefractive effect in action Beam fanning in the photorefractive crystal

10 Formation of screening soliton in a biased photorefractive crystal Light intensity Electric field R r R Refractive index profile V Equivalent electrical circuit for biased PR crystal illuminated by 1-dimensional beam illuminated

11 Experimental setup

12 Formation and self-bending of screening solitons 50μm

13 Formation and self-bending of screening solitons 50μm Time step between frames is approximately 0.8s. Electric field applied along horizontal axis. Total lateral shift Δx=50μm over 5mm distance.

14 Soliton collision in self-focusing media Elastic collision in Kerr medium Sticky collision in saturable medium X-junction Y-junction

15 Soliton collision in self-focusing media

16 Soliton collision in self-focusing media

17 Soliton collision in self-focusing media

18 Soliton collision in self-focusing media

19 Soliton collision in self-focusing media

20 Soliton collision in self-focusing media

21 The Australian National University Laser Physics Centre Experimental set-up for studies of collision of multisoliton complexes M1, M2 - mirrors BS- beam splitter, L1, L2 - lenses PZT-piezoelectric transducer PM- phase mask

22 Coherent collision: fusion and repulsion (intersection angle <1degree) In-phase collision (fusion) A B A+B A B Out-of-phase collision A B

23 Soliton collisc ollision ion - experiments Incoherent collisions coherent collisions -spiraling

24 Mutual rotation of coherent solitons A B Temporal sequence of mutual rotation of coherent solitons. Individual trajectories of these beams do not intersect. Propagation distance =5mm. Time step approx. 0.5sec. B A

25 Energy exchange due to the collision A B A B Initial phase π/2 Initial phase -π/2

26 Soliton birth upon collision C A B A B A C B Intersection angle 0.8deg. Both beams are in-phase. Propagation distance =0.5cm. Input power P 1 =P 2 =1μW

27 Multiple soliton interaction Simultaneous collision of two weak (A,B) and one strong (C) beams Intersecting angle (A,B)=0.9deg. Propagation distance =1cm (vertical geometry). Input power: A=B=0.3μW, C=1.2μW; Background power=5mw A B C B C Collision determined by the relative phases of solitons A

28 Attraction of incoherent solitons propagating in the Y-plane, ( initial separation of 15m (a) 30mm (b) and 50mm ). in In out Out Theory Experiment

29 The Australian National University Laser Physics Centre Identifying interacting solitons Due to the slow response of the photorefractive effect, the refractive index change induced by interacting solitons decays slowly after one of the beam (A or B) is blocked. This provides a way to determine identities of solitons in the collision process. lower beam (B) blocked A A A B B upper beam (A) blocked Time

30 3D trajectories of incoherent solitons (simulations) Rotating solitons Oscillating solitons Spiraling solitons

31 Light localization and control in photorefractive lattices

32 Introduction Outline Nonlinear wave transport and localisation in optically induced lattices - Rectangular lattice - Triangular lattice Polychromatic effects in fabricated planar structures - spectral-spatial control of supercontinuum Conclusions

33 Band-gap diagram and Bloch waves Bulk 1D periodic material 2D periodic z β K x x Complete analogue of 1D and 2D photonic crystal

34 Tuning of the band gap structure z β K b

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

36 Nonlinearity & periodicity Nonlinear materials High optical intensity Bulk media TIR GAP Self-focusing Defocusing Periodic media TIR GAP BR GAP

37 Nonlinearity & periodicity defocusing Periodic media: focusing TIR GAP BR GAP

38 2D reduced symmetry solitons Mobility discrete solitons do not like to move (usually) PRL 96, (2006)

39 Nonlinear guiding & confinement embedded waveguide PRL 94, (2005)

40 Optically induced triangular lattice o e z V0 o c o Biased photorefractive crystal e λ = 532nm o SBN Discrete and gap solitons in triangular photonic lattices

41 Nonlinear self-localization Photonic crystal defect waveguide or cavity Nonlinear light self-trapping in defect free triangular lattice? Lattice Brillouin zone 2D bandgap Discrete solitons y, μm Gap solitons x, μm Self-localization localization in bulk media Self-focusing Spatial soliton Low power z Square lattices Discrete Fleischer, Nature (2003) Martin, PRL (2004) Cohen, Nature (2005) Gap Fleischer, Nature (2003) Bartal, PRL (2005) Fischer, PRL (2006) High power

42 First band discrete soliton Γ point Bloch wave Input beam Fourier spectrum Low power High power Theory

43 Second band gap soliton Y point Bloch wave Phase Input beam Fourier spectrum y Output Low power High power Theory Discrete and gap solitons in triangular photonic lattices

44 Phase structure Bloch wave Phase y Intensity Phase Interferogram π phase jump Theory Experiment Discrete and gap solitons in triangular photonic lattices

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

46 Staggered solitons in LiNbO 3 LiNbO 3 waveguide array low power 10nW high power 100μW TIR GAP BR GAP Opt. Expr. 14, 254 (2006)

47 Interaction with the surface Experiment Input at surface Theory Low power diffraction no linear surface modes! x z PRL 97, (2006)

48 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

49 Nonlinear optical surface waves t = 25min Experiment Input at surface Theory x z surface PRL 97, (2006)

50 Polychromatic light Spectral-spatial control

51 Wavelength sensitivity Beam self-collimation & steering Rakich et al., Nature Materials 5, 93 (2006) How to control beams with ultra-broadband frequency spectrum?

52 Polychromatic light z x K x β Can we use nonlinear self-action to control broadband radiation? Notomi et al., NTT

53 Experimental setup 10 4 supercontinuum incandescent lam p I(λ), arb. units λ, nm

54 Spectrally-resolved discrete diffraction waveguide channel

55 Nonlinear spectral control 10μW 6mW 11mW

56 Nonlinear localisation in large diffraction array period 10μm larger Δn

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

58 Conclusions We have demonstrated some fundamental concepts of wave propagation in 2D periodic structures. Employed nonlinear effects to achieve control over propagation of beams in periodic structures. Achieved nonlinear control over a ultra-wide spectral bandwidth. Future Spatio-temporal control of optical signals.