Nonlinear guided waves and spatial solitons in a periodic layered medium

Abstract

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response (a nonlinear waveguide) embedded into a periodic layered linear medium, and describe nonlinear localized modes (guided waves and Bragg-like localized gap modes) and their stability. Then, we study modulational instability as well as the existence and stability of discrete spatial solitons in a periodic array of identical nonlinear layers, a one-dimensional nonlinear photonic crystal. Both similarities and differences with the models described by the discrete nonlinear Schrodinger equation (derived in the tight-binding approximation) and coupled-mode theory (valid for the shallow periodic modulations) are emphasized.

10 pages, 14 figures

References in corpus (4)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Self-trapping and stable localized modes in nonlinear photonic crystals
• Stability of Attractive Bose-Einstein Condensates in a Periodic Potential
• Spatial optical solitons in nonlinear photonic crystals

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• Nonlinear Band Gap Transmission in Optical Waveguide Arrays
• Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential
• Solitons in one-dimensional photonic crystals
• Pitch-controlled reorientational nonlinearity in chiral nematic liquid crystals: a reduced-order model for self-focusing and soliton formation
• NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ${\mathbb{R}}^d$