Surface gap solitons at a nonlinearity interface

We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross--Pitaevsky equation. We call these waves the surface gap solitons (SGS). In the case of smooth symmetric periodic potentials, we study analytically bifurcations of SGS's from standard gap solitons and determine numerically the maximal jump of the nonlinearity coefficient allowing for the SGS existence. We show that the maximal jump vanishes near the thresholds of bifurcations of gap solitons. In the case of continuous potentials with a jump in the first derivative at the interface, we develop a homotopy method of continuation of SGS families from the solution obtained via gluing of parts of the standard gap solitons and study existence of SGS's in the photonic band gaps. We explain the termination of the SGS families in the interior points of the band gaps from the bifurcation of linear bound states in the continuous non-smooth potentials.Comment: 23 pages, 6 figures, 3 tables corrections in v.2: sign error in the energy functional on p.3; discussion of the symmetries of Bloch functions on p. 5-6 corrected; derivative symbol missing in (3.5) and in the formula for \mu below (3.6

Observation of surface gap solitons in semi-infinite waveguide arrays

We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya.V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006). We demonstrate strong self-trapping at the edge of a LiNbO_3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.Comment: 4 pages, 5 figure

Lattice-supported surface solitons in nonlocal nonlinear media

We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We find that such solitons feature strongly asymmetric shapes and that they are stable in large parts of their existence domain.Comment: 13 pages, 3 figures, to appear in Optics Letter

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schr\"{o}dinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter -- actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.Comment: Physica D in pres

Nonlinear optics and light localization in periodic photonic lattices

We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals pointing towards practical applications in optical communications and computing, beam shaping, and bio-sensing.Comment: to appear in Journal of Nonlinear Optical Physics & Materials (JNOPM

Interface localized modes and hybrid lattice solitons in waveguide arrays

We discuss the formation of guided modes localized at the interface separat- ing two different periodic photonic lattices. Employing the effective discrete model, we analyze linear and nonlinear interface modes and also predict the existence of stable interface solitons including the hybrid staggered/unstaggered lattice solitons with the tails belonging to spectral gaps of different types.Comment: 11 pages, 5 figures, submitted to Opt. Let

Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices

We report on the experimental observation of two-dimensional surface solitons residing at the interface between a homogeneous square lattice and a superlattice that consists of alternating "deep" and "shallow" waveguides. By exciting single waveguides in the first row of the superlattice, we show that solitons centered on deep sites require much lower powers than their respective counterparts centered on shallow sites. Despite the fact that the average refractive index of the superlattice waveguides is equal to the refractive index of the homogeneous lattice, the interface results in clearly asymmetric output patterns.Comment: 16 pages, 5 figures, to appear in Physical Review