Surface modes and breathers in finite arrays of nonlinear waveguides

TL;DR

This paper classifies and analyzes surface modes and breathers in finite arrays of nonlinear waveguides, exploring their stability, bifurcations, and relation to bulk modes in one- and two-dimensional configurations.

Contribution

It provides a comprehensive classification of symmetric and antisymmetric surface modes, introduces surface breathers, and examines their stability and bifurcation behavior.

Findings

Complete set of surface modes classified

Existence of surface breathers demonstrated

Surface modes' stability and bifurcation analyzed

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.