Localization of electromagnetic waves in two-dimensional random dielectric systems

TL;DR

This paper rigorously analyzes electromagnetic wave propagation and scattering in 2D random dielectric systems, revealing differences in wave localization depending on the scenario and challenging traditional methods for identifying localization.

Contribution

It provides a detailed comparison of wave localization in regular and random dielectric arrays, highlighting the limitations of conventional approaches.

Findings

Complete bandgaps are identified in regular arrays.

Wave localization behavior differs inside and outside band gaps.

Traditional methods may be ambiguous in detecting localization.

Abstract

We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are discovered. For random arrays, the phenomenon of wave localization is investigated and compared in two scenarios: (1) wave propagating through the array of cylinders; this is the scenario which has been commonly considered in the literature, and (2) wave transmitted from a source located inside the ensemble. We show that within complete band gaps, results from the two scenarios are similar. Outside the gaps, however, there is a distinct difference, that is, waves can be blocked from propagation by disorders in the first scenario, but such an inhibition may not lead to inhibition or wave localization in the second scenario. The study suggests that the traditional method may be ambiguous in discerning localization effects.