Nonergodic extended phase for waves in three dimensions

TL;DR

This paper reveals that both scalar and electromagnetic waves in three-dimensional disordered media can exhibit a non-ergodic extended phase with fractal modes, challenging the typical localization transition and enabling new wave transport phenomena.

Contribution

It demonstrates the existence of a non-ergodic extended phase for waves in 3D disordered media, including electromagnetic waves, which was previously unrecognized.

Findings

Both scalar and electromagnetic waves show non-ergodic extended phases.

Electromagnetic waves remain in the extended phase at high disorder.

Scalar waves eventually become localized at high disorder.

Abstract

Wave transport in complex media is determined by the nature of quasimodes at the microscopic level. In three dimensional disordered media, waves generally undergo a phase transition from diffusion to Anderson localization, characterized by exponentially localized modes. A remarkable exception are electromagnetic waves, whose vector-like nature prevents Anderson localization to occur. Here we demonstrate that both scalar and vector (electromagnetic) waves exhibit a non-ergodic extended phase characterized by fractal quasimodes, for a broad range of disorder strengths. While electromagnetic waves remain in the non-ergodic extended phase at high disorder strength, scalar waves eventually enter a localized regime. These results pave the way for the engineering of anomalous wave transport phenomena in disordered media without spatial correlations.