Spatial optical solitons in nonlinear photonic crystals

Abstract

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended Bloch-wave modes and also investigate the existence and stability of bright, dark, and ``twisted'' spatially localized modes in such periodic structures. Additionally, we discuss both similarities and differences of our general results with the simplified models of nonlinear periodic media described by the discrete nonlinear Schrodinger equation, derived in the tight-binding approximation, and the coupled-mode theory, valid for shallow periodic modulations of the optical refractive index.

15 pages, 21 figures

References in corpus (9)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Josephson Junction Arrays with Bose-Einstein Condensates
• Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
• Self-trapping and stable localized modes in nonlinear photonic crystals
• Nonlinear localized waves in a periodic medium
• Discreteness-Induced Oscillatory Instabilities of Dark Solitons
• Creation of gap solitons in Bose-Einstein condensates
• Stability of Attractive Bose-Einstein Condensates in a Periodic Potential
• Parametric localized modes in quadratic nonlinear photonic structures

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• Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schrödinger Equation with a Kronig-Penney Potential
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• Loss of superfluidity in a Bose-Einstein condensate on an optical lattice via a novel classical phase transition
• Exact Localized Solutions of Quintic Discrete Nonlinear Schrödinger Equation
• Perturbation-induced radiation by the Ablowitz-Ladik soliton
• Pulse trapping inside one-dimensional photonic crystal with relaxing cubic nonlinearity
• Theory of spatial mode competition in a fiber amplifier
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• One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity
• Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity
• Critical number of atoms in an attractive Bose-Einstein condensate on an optical plus harmonic traps
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• Discretized optical dynamics in one-dimensionally synthetic photonic lattice
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