Soliton-driven Photonics pp 141-167
This course of lectures is meant to give an idea of what physical effects can be obtained beyond the paraxial approximation in a study of the dynamics of spatial solitons, soliton- like waveguide channels and pulse signals. In description of narrow wave packets featuring a broad space-time spectrum it is often not sufficient to use the approximate parabolic equation which accounts only for a slight diffraction and dispersion spreading. At the same time, analysis of a problem in the nonabridged equations limit is generally quite complicated no matter which method — analytical or numerical -is used, so any new approach is highly valuable. In this work we present some analytical methods for description of the wave fields in inhomogeneous and nonstationary nonlinear media, which allow to design the dynamics of nonparaxial quasi-localized soliton-like wave structures. Using these methods one can largely simplify the initial problem reducing it to the form ready for numerical and, in some cases, analytical solving. Specifically, we focus on two problems here: a) the features of the processes of self-action of soliton-like wave beams and pulse signals in smoothly inhomogeneous slightly nonstationary media, that are related with the nonlinear distortions of propagation paths and the carrier frequency [1, 2], and b) the dynamics of low radiation loss nonlinear wave structures quasi-localized in space (nonlinear leaky modes) . These problems are analyzed for self-consistent soliton-like waveguide channels propagating near the linear-nonlinear media interface (nonlinear quasi-surface waves). To better understand which nonparaxial effects are meant here we need to recall what a paraxial (or quasi-optical) approximation is in itself.
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