Stability of Spatial Optical Solitons

We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based on a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.Comment: 34 pages, 9 figures; to be published in: "Spatial Optical Solitons", Eds. W. Torruellas and S. Trillo (Springer, New York

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons-intrinsically multi-component localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in diffractive and/or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classification and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary significance