Optical surface modes in the presence of nonlinearity and disorder

TL;DR

This paper numerically explores how disorder, nonlinearity, and boundaries influence light localization in finite waveguide arrays, revealing complex behaviors depending on the strength of disorder and nonlinearity.

Contribution

It provides a detailed numerical analysis of edge versus interior localization in nonlinear disordered optical systems, extending understanding beyond linear regimes.

Findings

Weak disorder and nonlinearity require stronger disorder for edge localization.

Strong disorder and nonlinearity favor edge localization over interior.

Localization behavior reverses depending on disorder and nonlinearity strength.

Abstract

We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear Schr\"odinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.