On the continuum limit for a model of binary waveguide arrays

TL;DR

This paper rigorously proves that solutions of discrete binary waveguide array models converge to their continuum limit and establishes the existence of localized standing waves in the continuum model, validating previous physics-based assumptions.

Contribution

It provides a rigorous mathematical proof of the continuum limit for binary waveguide arrays and confirms the existence of localized standing waves in the continuum model.

Findings

Solutions of discrete models converge to the continuum limit.

Existence of localized standing waves in the continuum model.

Validation of formal and numerical physics results.

Abstract

In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal arguments and numerical simulations present in the Physics literature.