Nonlinear spatial beam dynamics in optical NLS systems

Transcription

1 Nonlinear spatial beam dynamics in optical NLS systems Zhigang Chen San Francisco State University, USA Nankai University, China

2 Introduction: What do we do with light? Spatial solitons & dynamics Photonic structures Defect and surface states Beam engineering Trapping and manipulation NLO in soft matter

3 Introduction: A few eamples of eperimental nonlinear optical systems governed by the NLSE. Spatial solitons in optically induced photonic lattices Nonlinear control of accelerating beams Nonlinear self-induced transparency in soft-matter systems

4 Spatial beam dynamics in photonic lattices Diffraction Kerr NL Periodic inde Nonlinear Schrödinger equation 0 ) ( 1 r n n i Array Input Input ) ( 0 r V U m t i Gross-Pitaevskii equation in BEC

5 Why photonic lattices? Fundamental issues eplored in a simple optical setting have tight link to condensed matter physics, quantum mech., BEC Solitons, modulation instability Optical Bloch waves and band-gap Defect and surface states X waves and shock waves Photonic superlattices & quasicrystals Random lattices &amorphous lattices Anderson localiation & disorder phenomena Photonic graphene Topological insulator, edge states, Quantum correlation PT and SUSY Lederer et al, Phys. Rep. (008) Chen, Segev, Christodoulides, Rep. Prog. Phys. (01).

6 Spatial solitons in photonic lattices Linear discrete diffraction Nonlinear lattice solitons G b M Optically induced lattices Efremidis et al., PRE (00) -p/d p/d k Discrete solitons Christodoulides et al, OL 1988; Eisenberg et al., PRL, (1998). First Brillouin Zone Gap solitons Kivshar, Opt. Lett. (1993); Fleischer, et al., PRL, Nature (003).

7 Other eamples of lattice beam dynamics Edge states and surface solitons (with Rechtsman, Segev ) Self-imaging solitons (with Yang ) NL beam dynamics in engineered lattices (with Efremidis, Christodoulides ) NL beam dynamics in disordered lattices (with Rechtsman, Yang )

8 Self-imaging Solitons: Stable gap solitons of arbitrary shapes Photonic lattices induced under self-defocusing NL i V y U U U y U U U (, ) 0, Yang et al., OL (011). 8

9 Soliton-based Tet/Image transmission Input No lattice Linear, lattice NL, lattice Eperimental results Simulation results Gap soliton clusters of arbitrary shapes!

10 Nonlinear control of self-accelerating beams G. A. Siviloglou et al, y OL(007); PRL (007) Airy beams: Non-diffracting, Self-accelerating, Self-healing Particle manipulation Curved plasma light bullets Routing SPP

11 Self-accelerating beams: from linear to NL? Linear case Nonlinear case i i 1 D. N. Christodoulides, et al, OL 1, 1460 (1996) S. Jia, et al, PRL 104, (010) D. Abdollahpour, et al, PRL 105, (010) R. Chen, et al, PRA 8, (010) Y. Hu, et al, OL 35, 3 (010) R. Bekenstein, et al, OE 19, 3706 (011) I. Kaminer, et al, PRL 106, (011) A. Lotti, et al, PRA 84, 01807(R) (011) I. Dolev, et al, PRL. 108, (01) Self-defocusing Linear Airy Shape-preserving accelerating beams by nonlinearity!

12 Linear control of Airy beams p Wrapped cubic phase spectrum 0 Linear Paraial equation i Y. Hu, et al, OL 35, 13 (010)

13 Airy beams: Light in ballistic trajectory Eperimental results Self-accelerating Airy beams Y. Hu et al, OL (010).

14 Nonlinear control of Airy beams NLS equation under a saturable nonlinearity: i i 1 Linear ( = 0) Self-focusing ( >0) Self-defocusing ( < 0) Y. Hu, et al, OL 35, 13 (010)

15 Spectrum NL-induced self-shifting spectral defects Linear Self-focusing Self-defocusing k Uniform Negative defect Positive defect

16 I(a.u.) I(a.u.) U(a.u.) U(a.u.) Spectrum of nonlinear modes Mode (self-focusing) Mode (self-defocusing) Spectrum Spectrum along Spectrum Spectrum along Normalied k Normalied k Normalied k Normalied k

17 Eperimental setup SLM SBN BS M PC BS Laser CL CCD L L capture the spectrum CCD capture the intensity profile

18 Airy beams kicked off by nonlinearity Linear Focusing Defocusing y SBN 1cm y Output =1cm y SBN 1cm air 1cm y Output =cm Spectrum k y k Counterintuitive?

19 Numerical simulations y Z=1cm Z=cm Spectrum Energy flow Self-focusing SBN air 1cm 1cm 1cm cm Selfdefocusing Spectrum Anomalous Diffraction?

20 I (a.u.) I (a.u.) I (a.u.) Self-shifting spectral defects Beam intensity Linear Spectrum Eperimental results under a saturable nonlinearity I II Self-focusing II I Self-defocusing or t or k II I Y. Hu, et al, OL (01)

21 From spatial to temporal domain i i 1 t Saturable Kerr i i t

22 Spectral Normalied spectrum NL spectral reshaping in fibers: self-focusing Wrapped cubic phase shift 5 1 Eperimental results (nm) Simulation (self-focusing) Spectrum at output /nm Y. Hu, et al, OL 38, 380 (013)

23 Spectral Normalied spectrum NL spectral reshaping in fibers: self-defocusing 5 Wrapped cubic phase shift 1 Eperimental results (nm) Simulation (self-defocusing) Spectrum at output Y. Hu, et al, OL 38, 380 (013) (nm)

24 From paraial to nonparaial?! Helmholt equation (No paraial approimation ) k 0 (Cylindrical coordinate system) (, ) J n( k 4 )ep( inarctan( )) (mm) Large curvatures for micronano-scale applications I. Kaminer, et al, PRL (01); P. Zhang, et al, Opt. Lett (01)

25 From circular NABs to other trajectories? E+k E=0 Circular NABs Cylindrical coordinates Mathieu NABs Elliptic coordinates a=b a<b Weber accelerating beams parabolic coordinates P. Zhang, et al., PRL (01); P. Aleahmad et al., PRL (01) WAB paraial Airy

26 Eperimental demonstrations MAB a<b a=b a>b WAB WAB Airy WAB Airy = 1 = y = 1 =

27 Nonlinear beam dynamics in soft-matter systems Develop stable colloidal nanosuspensions (negative, mied polariibility, tunable NL) Stable self-trapping against scattering loss, self-induced transparency, non-destructive particle manipulation and distribution Brownian motion Optical forces Nonlinear scattering Soliton effects

28 Optical nonlinearities of colloidal systems: An interdisciplinary field Colloidal Physics Soft-matter Statistical Mechanics Nonlinear Optics Fluid mechanics Chemistry/ electrochemistry Life sciences

29 Historical overview Arthur Ashkin A. Ashkin, Acceleration and trapping of particles by radiation pressure, Phys. Rev. Lett. 4, (1970). Four-wave miing in artificial Kerr Media P.W. Smith, A.Ashkin, and W.J. Tomlinson, Opt. Lett., 6, 84 (1981) Self focusing in artificial Kerr media A.Ashkin, J.M. Diedic, and P.W. Smith, Opt. Lett., 7, 76 (198) Soliton-like beams in aqueous suspensions V.E. Yashin et al, Optics and spectroscopy, 98, 466 (005)

30 Optical Forces In the Rayleigh regime (dipole appro.) 1 m 1 p 3V p n E m p E 0 where m 3Vp n m m n n p b n n 0 p b Positive polariability (PP) n n 0 p b Negative polariability (NP)

31 Optical gradient force: Optical Forces F I 4 m 3Vp n m n p >n b S. Stenholm, Rev. Mod. Phys. (1986) J.P. Gordon, Phys. Rev. A (1973) Optical Radiation Pressure: F rad S c s 5 a 4 4 n1 a m 18 p 1 3 m

32 Optical Tweeers Single-beam optical trap E. coli bacterium Ashkin et al., Opt. Lett (1986) Science (1987) Polystyrene beads Zhang et al., BioMed. Opt. Ep (01) Opt. & Photon News (01)

33 Nonlinearity in Colloidal Suspension Nernst-Planck Eq: (diluted sample) (neglecting thermal effects) Drift due to gradient force Fgrad I 4 Diffusion due to Brownian motion At steady state condition: I kt ( I) 0 ep 4 B Mawell-Garnett formula: f ( I) V ( I) p R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, OE 007

34 Particle manipulation in tunable nanosuspensions n p n p b b n n Positive polariability Mied polariability Negative polariability The optical forces result in higher local refractive inde along optical path which leads to self-trapping with Tunable Nonlinearity

35 Why focus on Negative Polariability suspensions? Both positive and negative suspensions have higher refractive inde along optical path. Positive Polariability (PP) Large scattering loss Super-Kerr => unstable Negative Polariability (NP) Self-cleaned channel (Enhanced transparency) Saturable => stable

36 Beam propagation in tunable nanosuspensions Eperimental side-view catastrophic self-focusing collapse severe scattering losses n p > n b PP Beam Collapse n p < n b NP Enhanced transmission n p = n b ZP Linear diffraction

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38 NLS like Equation - beam propagation in tunable nanosuspensions Helmholt eq: SVEA: E k0 neff E 0 n (1 f ) n fn eff b p E(, y, ) (, y, )ep( ik n ) 0 b 1 i i k0 np nb f f k0nb V p 0 Eponential nonlinearity Tunable NL scattering losses αi 4k B T ln f + B f 0 f 0 V f 1 + 3B 3f 0 f f 0 V f 0 1 f = f 0 ep α I 4k B T non-ideal gas model Saturable for NP

39 Summary We presented a few eamples of spatial beam dynamics in nonlinear optical systems governed by the NLSE. Spatial solitons in photonic lattices Linear and nonlinear self-accelerating beams Nonlinear self-induced transparency in soft-matter systems

40 Thank you for your attention! Website: Collaborator: Efremidis, Christodoulides, Yang, Morandotti, Rechtsman, Segev El-Ganainy, Makris, Chremmos, Zhang, Hu, Fardad, Man Funding: NSF, AFOSR

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