Spatial Optical Solitons

A brief overview of the recent advances in the theoretical and experimental study of self-focusing and self-trapping of light is given. Physical mechanisms of self-trapping and different types of self-trapped beams, spatial optical solitons, and their stability are discussed including solitons of non-Kerr media, self-trapped beams and their spiralling in photorefractive crystals, multi-hump solitons and solitonic gluons, discrete solitons in wave guide arrays, etc. A brief summary of the earlier and more recent experimental observations of spatial solitons, transverse instabilities, and soliton interactions is included as well.

[1]  Y. Kivshar,et al.  Soliton-based optical switching in waveguide arrays , 1996 .

[2]  Hermann A. Haus,et al.  HIGHER ORDER TRAPPED LIGHT BEAM SOLUTIONS , 1966 .

[3]  Friedemann Kaiser,et al.  Spiraling Behavior of Photorefractive Screening Solitons , 1999 .

[4]  Y. Kivshar,et al.  Instabilities of dark solitons. , 1995, Optics letters.

[5]  J. Juul Rasmussen,et al.  Blow-up in Nonlinear Schroedinger Equations-I A General Review , 1986 .

[6]  Donna Strickland,et al.  Resistance of short pulses to self-focusing , 1991 .

[7]  Alexander M. Rubenchik,et al.  Soliton stability in plasmas and hydrodynamics , 1986 .

[8]  Scott A. Diddams,et al.  Investigations of Nonlinear Femtosecond Pulse Propagation with the Inclusion of Raman, Shock, and Third-Order Phase Effects , 1998 .

[9]  E. V. Zemlyanaya,et al.  Vibrations and Oscillatory Instabilities of Gap Solitons , 1998 .

[10]  S A Diddams,et al.  Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media. , 1998, Optics letters.

[11]  Yuri S. Kivshar,et al.  Multicolor solitons due to four-wave mixing , 1998 .

[12]  A. A. Kolokolov,et al.  Stationary solutions of the wave equation in a medium with nonlinearity saturation , 1973 .

[13]  Y. Kivshar,et al.  Peierls-Nabarro potential barrier for highly localized nonlinear modes. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  A. J. Campillo,et al.  Relationship of self‐focusing to spatial instability modes , 1974 .

[15]  Gregory J. Salamo,et al.  Observation of two-dimensional steady-state photorefractive screening solitons , 1995 .

[16]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

[17]  Ranka,et al.  Observation of Pulse Splitting in Nonlinear Dispersive Media. , 1996, Physical review letters.

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

[19]  M Segev,et al.  Interaction between vector solitons and solitonic gluons. , 1999, Optics letters.

[20]  P W Smith,et al.  Continuous-wave self-focusing and self-trapping of light in artificial Kerr media. , 1982, Optics letters.

[21]  Yuri S. Kivshar,et al.  Dark optical solitons: physics and applications , 1998 .

[22]  Y. Kivshar,et al.  Observation of vortex solitons created by the instability of dark soliton stripes. , 1996, Optics letters.

[23]  Y. Kivshar,et al.  Multi-hump optical solitons in a saturable medium , 1999 .

[24]  B. Luther-Davies,et al.  Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium. , 1996, Physical review letters.

[25]  J P Torres,et al.  Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal. , 1998, Optics letters.

[26]  Yuri S. Kivshar,et al.  MULTISTABILITY OF THREE-WAVE PARAMETRIC SELF-TRAPPING , 1997 .

[27]  J. Bjorkholm,et al.  CW self-focusing and self-trapping of light in sodium vapor , 1974 .

[28]  Leon Poladian,et al.  Spiralling spatial solitons , 1991 .

[29]  Cornelia Denz,et al.  Anomalous interaction of spatial solitons in photorefractive media , 1998, Nonlinear Guided Waves and Their Applications.

[30]  M. Segev,et al.  Incoherently coupled soliton pairs in biased photorefractive crystals , 1996, Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference.

[31]  Y. Kivshar,et al.  Scattering and spiraling of solitons in a bulk quadratic medium. , 1998, Optics letters.

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

[33]  Pelinovsky,et al.  Instability of solitons governed by quadratic nonlinearities. , 1995, Physical review letters.

[34]  Trillo,et al.  Stability of Three-Wave Parametric Solitons in Diffractive Quadratic Media. , 1996, Physical review letters.

[35]  P. L. Kelley,et al.  Self-focusing of optical beams , 1965, International Quantum Electronics Conference, 2005..

[36]  Pelinovsky,et al.  Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  Charles H. Townes,et al.  Dynamics and characteristics of the self- trapping of intense light beams. , 1966 .

[38]  Mordechai Segev,et al.  THREE-DIMENSIONAL SPIRALING OF INTERACTING SPATIAL SOLITONS , 1997 .

[39]  F. Kusmartsev Application of catastrophe theory to molecules and solitons , 1989 .

[40]  Barry Luther-Davies,et al.  THREE DIMENSIONAL TRAJECTORIES OF INTERACTING INCOHERENT PHOTOREFRACTIVE SOLITONS , 1999 .

[41]  Y. Kivshar,et al.  Nonlinear theory of soliton-induced waveguides. , 1998, Optics letters.

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

[43]  M Segev,et al.  Dimensionality and size of photorefractive spatial solitons. , 1994, Optics letters.

[44]  Gibbs,et al.  Kaleidoscopic spatial instability: Bifurcations of optical transverse solitary waves. , 1991, Physical review letters.

[45]  C. R. Willis,et al.  Discrete Breathers , 1997 .

[46]  Jason Christou,et al.  Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium , 1995 .

[47]  I. Bialynicki-Birula,et al.  Gaussons: Solitons of the Logarithmic Schrödinger Equation , 1979 .

[48]  D. Christodoulides,et al.  Discrete self-focusing in nonlinear arrays of coupled waveguides. , 1988, Optics letters.

[49]  Y. Kivshar Self-localization in arrays of defocusing waveguides. , 1993, Optics letters.

[50]  J. Moloney,et al.  Instability of standing waves in nonlinear optical waveguides , 1986 .

[51]  M. Segev,et al.  Induced coherence and stable soliton spiraling , 1998, patt-sol/9812005.

[52]  Demetrios N. Christodoulides,et al.  Observation of Multihump Multimode Solitons , 1998 .

[53]  Saffman,et al.  Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices. , 1996, Physical review letters.

[54]  Pelinovsky,et al.  Instability-induced dynamics of dark solitons. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[55]  A. J. Campillo,et al.  Periodic breakup of optical beams due to self‐focusing , 1973 .

[56]  Stegeman,et al.  Observation of two-dimensional spatial solitary waves in a quadratic medium. , 1995, Physical review letters.

[57]  A. Snyder,et al.  Mighty morphing spatial solitons and bullets. , 1997, Optics letters.

[58]  Yuri S. Kivshar,et al.  Nonlinear dynamics of the Frenkel—Kontorova model , 1998 .

[59]  Yuri S. Kivshar,et al.  Stability of multihump optical solitons , 1999, patt-sol/9905006.

[60]  A. V. Mamaev,et al.  Propagation of light beams in anisotropic nonlinear media: From symmetry breaking to spatial turbulence. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[61]  Barashenkov Stability Criterion for Dark Solitons. , 1996, Physical review letters.

[62]  Snyder,et al.  Dynamic spatial solitons. , 1994, Physical review letters.