Spatially Dispersive Shock Waves in Nonlinear Optics

We discuss recent experimental work demonstrating spatial dispersive shock waves (DSWs). These structures occur whenever nonlinearity enhances diffraction so that wave spreading becomes intensity-dependent. The mechanism of this spreading follows naturally from a hydrodynamic description of light flow, in which wave steepening from phase gradients allows faster parts of a beam to overtake slower parts. Scaling relationships are developed for this spreading and experimentally observed, in both local and nonlocal media.

[1]  P. Yeh,et al.  Photorefractive conical diffraction in BaTiO3 , 1986 .

[2]  Gennady El,et al.  General solution of the Cauchy problem for the defocusing NLS equation in the Whitham limit , 1995 .

[3]  D. Z. Anderson,et al.  Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[4]  Claudio Palma,et al.  Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Optical shock waves in nonlinear dispersive amplifying media. , 1994, Optics letters.

[6]  Michael Albiez,et al.  Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. , 2005, Physical review letters.

[7]  J. Burgers.  The Nonlinear Diffusion Equation , 2013 .

[8]  M. Segev,et al.  Light-induced self-synchronizing flow patterns , 2011 .

[9]  Jason W. Fleischer,et al.  Dispersive, superfluid-like shock waves in nonlinear optics: Properties & interactions , 2007, 2007 Quantum Electronics and Laser Science Conference.

[10]  Y. Kivshar,et al.  Experimental reconstruction of nonlocal response of thermal nonlinear optical media. , 2007, Optics letters.

[11]  J. A. Hermann,et al.  Analysis of spatial scanning with thick optically nonlinear media , 1993 .

[12]  Optical bistability in the frustrated-total-reflection optical cavity. , 1983, Optics letters.

[13]  Romano A. Rupp,et al.  Anisotropic selfdiffraction in BaTiO3 , 1984 .

[14]  Agrawal,et al.  Kink solitons and optical shocks in dispersive nonlinear media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[15]  E. Mclean,et al.  INTERFEROMETRIC OBSERVATION OF ABSORPTION INDUCED INDEX CHANGE ASSOCIATED WITH THERMAL BLOOMING , 1968 .

[16]  Fleischer,et al.  Burgers' turbulence with self-consistently evolved pressure , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Vincent Hakim,et al.  Nonlinear Schrödinger flow past an obstacle in one dimension , 1997 .

[18]  Gennady El,et al.  Decay of an initial discontinuity in the defocusing NLS hydrodynamics , 1995 .

[19]  J. S. Aitchison,et al.  Discrete Spatial Optical Solitons in Waveguide Arrays , 1998 .

[20]  C. Warde,et al.  High-order anisotropic diffraction in photorefractive crystals , 1988 .

[21]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[22]  Lene Vestergaard Hau,et al.  Observation of hybrid soliton vortex-ring structures in Bose-Einstein condensates. , 2005, Physical review letters.

[23]  R. Morandotti,et al.  Nonlinear scattering and trapping by local photonic potentials , 2007, 2007 Quantum Electronics and Laser Science Conference.

[24]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[25]  A. M. Kamchatnov,et al.  Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms , 2004 .

[26]  Bogdan Damski.  Formation of shock waves in a Bose-Einstein condensate (8 pages) , 2004 .

[27]  Blasberg,et al.  Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[28]  M. G. Forest,et al.  Onset of Oscillations in Nonsoliton Pulses in Nonlinear Dispersive Bers , 1997 .

[29]  W. Tomlinson,et al.  Femtosecond white-light continuum pulses. , 1983, Optics letters.

[30]  M. Saffman,et al.  Circular solitons do not exist in photorefractive media. , 1998, Optics letters.

[31]  Marc Haelterman,et al.  Vector soliton associated with polarization modulational instability in the normal-dispersion regime. , 1994 .

[32]  Kivshar,et al.  Dark-soliton dynamics and shock waves induced by the stimulated Raman effect in optical fibers. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[33]  Y. Shen,et al.  Spectral broadening of ultrashort pulses in a nonlinear medium. , 1984, Optics letters.

[34]  Temporal dynamics of tunneling : Hydrodynamic approach , 2006, cond-mat/0608452.

[35]  Reverse propagation of femtosecond pulses in optical fibers. , 2003, Optics letters.

[36]  Tal Carmon,et al.  Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons. , 2005 .

[37]  F Agulló-López,et al.  Isotropic versus anisotropic modeling of photorefractive solitons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  P Leach,et al.  Two-dimensional steady-state photorefractive screening solitons. , 1996, Optics letters.

[39]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[40]  V. M. Petnikova,et al.  Formation of spatial solitons and spatial shock waves in photorefractive crystals , 1997 .

[41]  C. Barsi,et al.  Imaging through nonlinear media using digital holography , 2009 .

[42]  F. Devaux,et al.  Polarization and configuration dependence of beam self-focusing in photorefractive LiNbO 3 , 2009 .

[43]  Jack Feinberg,et al.  Asymmetric self-defocusing of an optical beam from the photorefractive effect , 1982 .

[44]  G P Agrawal,et al.  Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium. , 1992, Optics letters.

[45]  Collisionless shock resolution in nematic liquid crystals , 2008 .

[46]  Mark J. Ablowitz,et al.  Interactions of dispersive shock waves , 2007 .

[47]  Livingston Pm.  Thermally Induced Modifications of a High Power cw Laser Beam. , 1971 .

[48]  Mansoor Sheik-Bahae,et al.  Nonlinear Refraction and Optical Limiting in Thick Media , 2022 .

[49]  J. P. Gordon,et al.  Long‐Transient Effects in Lasers with Inserted Liquid Samples , 1965 .

[50]  D. Christodoulides.  Fast and slow Raman shock-wave domains in nonlinear media , 1991 .

[51]  Wave Tunneling and Hysteresis in Nonlinear Junctions , 2010 .

[52]  Dan Anderson,et al.  Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides , 1983 .

[53]  Demetrios N. Christodoulides,et al.  Bright, dark, and gray spatial soliton states in photorefractive media , 1995 .

[54]  Y. Kivshar,et al.  Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media , 2009 .

[55]  Carlo F. Barenghi,et al.  Quantized vortex dynamics and superfluid turbulence , 2001 .

[56]  G Korn,et al.  Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers. , 2002, Physical review letters.

[57]  Jason W Fleischer,et al.  Diffraction from an edge in a self-focusing medium. , 2010, Optics letters.

[58]  Paul H. Roberts,et al.  The Nonlinear Schrödinger Equation as a Model of Superfluidity , 2001 .

[59]  D. P. Krindach,et al.  Thermal self-actions of laser beams , 1968 .

[60]  I. Coddington,et al.  Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics , 2006 .

[61]  F. Omenetto,et al.  Interaction of an optical soliton with a dispersive wave. , 2005, Physical review letters.

[62]  V. V. Khodorovskii,et al.  Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  C. Barsi,et al.  Peakon profiles and collapse-bounce cycles in self-focusing spatial beams. , 2008, Optics express.

[64]  Zachary Dutton,et al.  Observation of Quantum Shock Waves Created with Ultra- Compressed Slow Light Pulses in a Bose-Einstein Condensate , 2001, Science.

[65]  A. Fratalocchi,et al.  Suppression of transverse instabilities of dark solitons and their dispersive shock waves , 2009, 1201.6617.

[66]  M. Segev,et al.  Observation of locked optical kink-antikink spatial shock waves. , 2003, Physical review letters.

[67]  M. Soskin,et al.  Holographic storage in electrooptic crystals. i. steady state , 1978 .

[68]  E. Madelung,et al.  Quantentheorie in hydrodynamischer Form , 1927 .

[69]  T. Müller,et al.  Direct observation of second-order atom tunnelling , 2007, Nature.

[70]  R. Morandotti,et al.  Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons. , 2003, Physical review letters.

[71]  M. Peccianti,et al.  Tunable refraction and reflection of self-confined light beams , 2006 .

[72]  E. Gross.  Structure of a quantized vortex in boson systems , 1961 .

[73]  M. Peccianti,et al.  Escaping solitons from a trapping potential. , 2008, Physical review letters.

[74]  B. Malomed,et al.  Raman-induced optical shocks in nonlinear fibers. , 1993, Optics letters.

[75]  S. Wabnitz,et al.  Analytical theory of guiding-center nonreturn-to-zero and return-to-zero signal transmission in normally dispersive nonlinear optical fibers. , 1995, Optics letters.

[76]  E. W. Stryland,et al.  Sensitive Measurement of Optical Nonlinearities Using a Single Beam Special 30th Anniversary Feature , 1990 .

[77]  Falk Lederer,et al.  Investigation of optical tunneling through nonlinear films , 1988 .

[78]  M. Hoefer,et al.  Theory of two-dimensional oblique dispersive shock waves in supersonic flow of a superfluid , 2009 .

[79]  Guy Millot,et al.  Polarization Domain Wall Solitons with Counterpropagating Laser Beams , 1998 .

[80]  Jason W Fleischer,et al.  Dispersive shock waves with nonlocal nonlinearity. , 2007, Optics letters.

[81]  G. Masi,et al.  Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons , 2004 .

[82]  Ichirou Yamaguchi,et al.  Phase-shifting digital holography , 1997 .

[83]  M. Segev,et al.  Observation of soliton tunneling phenomena and soliton ejection. , 2008, Physical review letters.

[84]  Carmel Rotschild,et al.  Long-range interactions between optical solitons , 2006 .

[85]  O. Bang,et al.  INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS , 2004 .

[86]  P. Engels,et al.  Stationary and nonstationary fluid flow of a bose-einstein condensate through a penetrable barrier. , 2007, Physical review letters.

[87]  J. Fleischer,et al.  Rayleigh-Taylor instability in nonlinear optics , 2008, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[88]  Giancarlo Ruocco,et al.  Shocks in nonlocal media. , 2007, Physical review letters.

[89]  Marco Peccianti,et al.  Observation of a gradient catastrophe generating solitons. , 2008, Physical review letters.

[90]  A. M. Kamchatnov,et al.  Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire , 2008, 0802.0345.

[91]  W. Tomlinson,et al.  Nonlinear optical interfaces: Switching behavior , 1984 .

[92]  Agrawal.  Induced focusing of optical beams in self-defocusing nonlinear media. , 1990, Physical review letters.

[93]  George I. Stegeman,et al.  Third order nonlinear integrated optics , 1988 .

[94]  Mordechai Segev,et al.  Spatial photonics in nonlinear waveguide arrays. , 2005, Optics express.

[95]  Tal Carmon,et al.  Observation of discrete solitons in optically induced real time waveguide arrays. , 2003, Physical review letters.

[96]  Optical field measurements for accurate modeling of nonlinear parametric interactions , 2009 .

[97]  J. Fleischer,et al.  Forward four-wave mixing with defocusing nonlinearity. , 2007, Optics letters.

[98]  Charles H. Townes,et al.  Self-steepening of light pulses. , 1967 .

[99]  Jason W Fleischer,et al.  Dispersive shock waves in nonlinear arrays. , 2007, Physical review letters.

[100]  G. Salamo,et al.  Primarily isotropic nature of photorefractive screening solitons and the interactions between them. , 1998, Optics letters.

[101]  J. Kutz,et al.  Nonsoliton pulse evolution in normally dispersive fibers , 1999 .

[102]  O. Bang,et al.  Modulational instability in nonlocal nonlinear Kerr media. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[103]  Mordechai Segev,et al.  Discrete solitons in photorefractive optically induced photonic lattices. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[104]  Niels Grønbech-Jensen,et al.  Dark shock waves in the nonlinear schrödinger system with internal losses , 1997 .

[105]  M. Segev,et al.  Steady-state spatial screening solitons in photorefractive materials with external applied field. , 1994, Physical review letters.