Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

TL;DR

This study investigates how electromagnetic waves behave in a two-dimensional random medium, revealing a strong localization regime where waves are trapped, and analyzing the transition from diffusion to localization through numerical solutions.

Contribution

The paper introduces a self-consistent numerical approach to study electromagnetic wave transport and localization in 2D random systems, extending previous models with detailed analysis.

Findings

Identification of a strong localization regime for electromagnetic waves.

Waves are trapped near the source within the localization regime.

Diffusive waves exhibit saturation and exponential decay outside the localization regime.

Abstract

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)