Modal complexity as a metric for Anderson localization

TL;DR

This paper introduces a new metric for Anderson localization in disordered photonic crystals based on the complexity of localized optical modes, derived from experimental phase measurements, providing a quantitative measure of localization.

Contribution

It proposes a novel complexity-based metric for Anderson localization, validated through experimental and theoretical comparison, capturing the degree of localization in disordered media.

Findings

Experimental measurement of mode complexity in photonic crystals.

The proposed metric correlates with localization length.

Validation shows the metric effectively characterizes localization.

Abstract

We present a thorough study of the complexity of optical localized modes in two-dimensional disordered photonic crystals. Direct experimental measurements of complexity were made using an interferometric setup that allowed for extraction of phases and, hence, complex-valued wavefunctions. The comparison of experimental and theoretical results allows us to propose a metric for Anderson localization based on the average value and statistical distribution of complexity. Being an alternative to other known criteria of localization, the proposed metric exploits the openness of the disordered medium and provides a quantitative characterization of the degree of localization allowing for determining the localization length.