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We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap(More)
This paper reviews the latest advances in the area of multi-soliton complexes (MSCs). We present exact analytical solutions of coupled nonlinear Schrr odinger equations, which describe multi-soliton complexes and their interactions on top of a background in media with self-focusing or self-defocusing Kerr-like nonlinearities. We p r e s e n t n umerical(More)
—We overview theoretical and experimental results on spatial optical solitons excited in arrays of nonlinear waveguides. First, we briefly summarize the basic properties of the discrete nonlinear Schrödinger (NLS) equation frequently employed to study spatially localized modes in arrays, the so-called discrete solitons. Then, we introduce an improved(More)
We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and observe the key features of gap solitons that distinguish them from discrete solitons, including a dynamical transformation of gap solitons due to nonlinear interband coupling. We also describe theoretically(More)
We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.
We analyze transmission of a layered photonic structure ͑a one-dimensional photonic crystal͒ consisting of alternating slabs of two materials with positive and negative refractive index. For the periodic structure with zero averaged refractive index, we demonstrate a number of unique properties of the beam transmission observed in strong beam modification(More)
We review both theoretical and experimental advances in the recently emerged field of modulated photonic lattices. These artificial periodic dielectric structures provide a powerful tool for the control of the fundamental aspects of light propagation. Photonic lattices are arrays of coupled optical waveguides, where the light propagation becomes effectively(More)
We study linear guided waves propagating in a slab waveguide made up of a negative-refractive-index material, the so-called left-handed waveguide. We reveal that the guided waves in left-handed waveguides possess a number of peculiar properties such as the absence of the fundamental modes, mode double degeneracy, and sign-varying energy flux. In particular,(More)
Dynamic localization is the suppression of the broadening of a charged-particle wave packet as it moves along a periodic potential in an a.c. electric field 1–3. The same effect occurs for optical beams in curved photonic lattices, where the lattice bending has the role of the driving field, and leads to the cancellation of diffraction 4–8. Dynamic(More)
We demonstrate theoretically and experimentally a novel type of localized beam supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making(More)