Cross density of states and mode connectivity: Probing wave localization in complex media

TL;DR

This paper introduces mode connectivity as a new measure to distinguish between diffusive and localized wave regimes in complex media, using numerical simulations and coherence functions.

Contribution

It proposes a novel connectivity measure based on eigenmodes and demonstrates its effectiveness in identifying wave localization regimes.

Findings

Connectivity discriminates between diffusive and localized regimes.

Second-order coherence function encodes connectivity for practical measurements.

Applicable to all wave types and localization phenomena.

Abstract

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the second-order coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves.