Guided Modes and Symmetry Breaking Supported by Localized Gain

We review numerous physical phenomena which occur in one- and two-dimensional nonlinear media in the presence of localized gain-defects, and which recently attracted considerable attention. In particular, we discuss stable localized modes in media with linear and nonlinear dissipation; breathers which can be excited in the presence of more than one localized gain channels; vortices. We address the phenomenon of the symmetry breaking in one- and two-dimensional media, resulting in emergence of stable nonsymmetric modes, and analyze possibilities of guiding and switching of waves with help of guiding channels.

[1]  V. Konotop,et al.  Matter solitons in Bose-Einstein condensates with optical lattices , 2002 .

[2]  B. Malomed,et al.  Interaction of a soliton with a localized gain in a fiber Bragg grating. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  van Saarloos W,et al.  Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation. , 1990, Physical review letters.

[4]  Anna Bezryadina,et al.  Observation of two-dimensional surface solitons. , 2007, Physical review letters.

[5]  Hidetsugu Sakaguchi,et al.  Matter-wave solitons in nonlinear optical lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  N. Rosanov,et al.  Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling. , 2005, Physical review letters.

[7]  Lorenzo Spinelli,et al.  Spatial Soliton Pixels in Semiconductor Devices , 1997 .

[8]  L. Torner,et al.  Rotating vortex solitons supported by localized gain. , 2011, Optics letters.

[9]  R. Lefever,et al.  Spatial dissipative structures in passive optical systems. , 1987, Physical review letters.

[10]  B. Malomed,et al.  Stable vortex solitons in the two-dimensional Ginzburg-Landau equation. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  William J. Firth,et al.  Cavity and Feedback Solitons , 2002 .

[12]  Lluis Torner,et al.  Soliton Shape and Mobility Control in Optical Lattices , 2009 .

[13]  B. Malomed,et al.  Stability and interactions of pulses in simplified Ginzburg-Landau equations , 1997 .

[14]  B. Malomed,et al.  Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation. , 2006, Physical review letters.

[15]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[16]  Y. Kivshar,et al.  Observation of discrete vortex solitons in optically induced photonic lattices. , 2004, Physical review letters.

[17]  L. Torner,et al.  Chapter 5 - Optical vortices and vortex solitons , 2005 .

[18]  K. Chow,et al.  Solitons pinned to hot spots , 2010 .

[19]  J. Aitchison,et al.  Gap soliton memory in a resonant photonic crystal , 2005 .

[20]  Kestutis Staliunas,et al.  Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals. , 2008, Physical review letters.

[21]  Sergey V. Fedorov,et al.  Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber , 2003 .

[22]  C. Paré,et al.  Spatial solitary wave in a weakly saturated amplifying/absorbing medium , 1989 .

[23]  Yaron Silberberg,et al.  Discrete Solitons in Optics , 2008 .

[24]  Lluis Torner,et al.  Surface gap solitons. , 2006, Physical review letters.

[25]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[26]  R. Morandotti,et al.  Observation of discrete surface solitons. , 2006, Physical review letters.

[27]  B. Malomed,et al.  Stable solitons in two-component active systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Matthew O Williams,et al.  Light-bullet routing and control with planar waveguide arrays. , 2010, Optics express.

[29]  L. Torner,et al.  Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain. , 2010, Optics letters.

[30]  B. Malomed,et al.  Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating , 2009 .

[31]  Kinks and solitons in the generalized Ginzburg-Landau equation. , 1990 .

[32]  Albert Ferrando,et al.  Soliton topology versus discrete symmetry in optical lattices. , 2005, Physical review letters.

[33]  Observation of Two-Dimensional Surface Solitons in Asymmetric Waveguide Arrays , 2007, 0704.3837.

[34]  D Mihalache,et al.  Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses. , 2010, Physical review letters.

[35]  V. Konotop,et al.  Two-dimensional dissipative solitons supported by localized gain. , 2010, Optics letters.

[36]  W. Firth,et al.  Bifurcation structure of dissipative solitons , 2007 .

[37]  Alain Hache,et al.  Discrete surface solitons. , 2005, Optics letters.

[38]  L. Torner,et al.  Vortex lattice solitons supported by localized gain. , 2010, Optics letters.

[39]  C. Christov,et al.  Dissipative solitons , 1995 .

[40]  Luc Bergé,et al.  Wave collapse in physics: principles and applications to light and plasma waves , 1998 .

[41]  Spatiotemporal surface Ginzburg-Landau solitons , 2008 .

[42]  S. Fauve,et al.  Localized structures generated by subcritical instabilities , 1988 .

[43]  L. Lugiato,et al.  Cavity solitons as pixels in semiconductor microcavities , 2002, Nature.

[44]  L. M. Hocking,et al.  On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[45]  F. Lederer,et al.  Stable dissipative solitons in semiconductor optical amplifiers. , 2003, Physical review letters.

[46]  L. Torner,et al.  Soliton emission in amplifying lattice surfaces. , 2007, Optics letters.

[47]  Michael J. Connelly,et al.  Semiconductor Optical Amplifiers , 2002 .

[48]  Germany,et al.  Patterns and localized structures in bistable semiconductor resonators , 2000, nlin/0001055.

[49]  M. Segev,et al.  Observation of vortex-ring "discrete" solitons in 2D photonic lattices , 2004, Conference on Lasers and Electro-Optics, 2004. (CLEO)..

[50]  B. Malomed,et al.  Discrete vortex solitons. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Malomed,et al.  Stability and interactions of solitons in two-component active systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[52]  A. Siegman,et al.  Propagating modes in gain-guided optical fibers. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[53]  V. Konotop,et al.  One-dimensional delocalizing transitions of matter waves in optical lattices , 2009 .

[54]  Nikolay N. Rosanov,et al.  Spatial Hysteresis and Optical Patterns , 2002 .