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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)

—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)

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 report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the… (More)

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 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)

We reveal a generic connection between the effect of time reversals and nonlinear wave dynamics in systems with parity-time (PT) symmetry, considering a symmetric optical coupler with balanced gain and loss where these effects can be directly observed experimentally. We show that for intensities below a threshold level, the amplitudes oscillate between the… (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 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 predict a sharp crossover from nonlinear self-defocusing to discrete self-trapping of a narrow Gaussian beam with the increase of the refractive index contrast in a periodic photonic lattice. We demonstrate experimentally nonlinear discrete localization of light with defocusing nonlinearity by single site excitation in LiNbO(3) waveguide arrays.