Surface modes and breathers in finite arrays of nonlinear waveguides

Abstract

We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one- and two-dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.