Mean path length invariance in wave-scattering beyond the diffusive regime

TL;DR

This paper demonstrates that the invariance of mean path length, known in diffusive random walks, extends to wave scattering beyond diffusion, including regimes like Anderson localization and photonic band gaps, using microwave experiments.

Contribution

It introduces a novel, robust measurement method for mean path length in wave scattering, applicable beyond diffusive regimes and unaffected by absorption or incomplete data.

Findings

Mean path length invariance holds beyond diffusion, including localization and band gaps.

The new measurement procedure is more robust to absorption and incomplete data.

Experimental verification using microwave setup confirms theoretical predictions.

Abstract

Diffusive random walks feature the surprising property that the average length of all possible random trajectories that enter and exit a finite domain is determined solely by the domain boundary. Changes in the diffusion constant or the mean-free path, that characterize the diffusion process, leave the mean path length unchanged. Here we demonstrate experimentally that this result can be transferred to the scattering of waves, even when wave interference leads to marked deviations from a diffusion process. Using a versatile microwave setup, we establish the mean path length invariance for the crossover to Anderson localization and for the case of a band gap in a photonic crystal. We obtain these results on the mean path length solely based on a transmission matrix measurement through a novel procedure that turns out to be more robust to absorption and incomplete measurement in the localized regime as compared to an assessment based on the full scattering matrix.