Wormholes in de Sitter branes

In this work we present a class of geometries which describes wormholes in a Randall-Sundrum brane model, focusing on de Sitter backgrounds. Maximal extensions of the solutions are constructed and their causal structures are discussed. A perturbative analysis is developed, where matter and gravitational perturbations are studied. Analytical results for the quasinormal spectra are obtained and an extensive numerical survey is conducted. Our results indicate that the wormhole geometries presented are stable.Comment: 10 pages, 7 figure

Interface solitons in two-dimensional photonic lattices

We analyze localization of light at the interface separating square and hexagonal photonic lattices, as recently realized experimentally in two-dimensional laser-written waveguide arrays in silica glass with self-focusing nonlinearity [A. Szameit {\em et al.}, Opt. Lett. {\bf 33}, 663 (2008)]. We reveal the conditions for the existence of {\em linear} and {\em nonlinear} surface states substantially influenced by the lattice topology, and study the effect of the different symmetries and couplings on the stability of two-dimensional interface solitons.Comment: 3 pages, 4 figures, submitted to Opt. Let

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

Interface solitons in quadratically nonlinear photonic lattices

We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focussing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamics excitation of interface modes shows that, a two-color interface twisted mode splits into two beams with different escaping angles and carrying different energies when entering a uniform medium from the quadratic photonic lattice. The output position and energy contents of each two-color interface solitons can be controlled by judicious tuning ofComment: 6 pages, 8 figure

Discrete surface solitons in two-dimensional anisotropic photonic lattices

We study nonlinear surface modes in two-dimensional {\em anisotropic} periodic photonic lattices and demonstrate that, in a sharp contrast to one-dimensional discrete surface solitons, the mode threshold power is lower at the surface, and two-dimensional discrete solitons can be generated easier near the lattice corners and edges. We analyze the crossover between effectively one- and two-dimensional regimes of the surface-mediated beam localization in the lattice.Comment: 3 pages, 4 figure