Radiant Field Theory: A Transport Approach to Shaped Wave Transmission through Disordered Media

TL;DR

This paper introduces a new field-theoretic transport framework for analyzing wave transmission through disordered media, capturing coherent effects beyond traditional diffusive models and applicable in quasiballistic regimes.

Contribution

The authors develop a novel radiance transport equation that does not rely on isotropy, extending analysis to non-diffusive regimes and incorporating experimental factors like absorption.

Findings

Accurately predicts transmission eigenvalue distribution in quasiballistic regime.

Validates the theory with numerical simulations of microscopic wave equations.

More versatile than DMPK theory, accommodating absorption and incomplete channel control.

Abstract

We present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation for a matrix-valued radiance, analogous to the classical radiative transport equation but capable of capturing coherent effects encoded in the transmission matrix. Unlike the Dorokhov-Mello-Pereyra-Kumar (DMPK) theory, our approach does not rely on the isotropy hypothesis, which presumes uniform angular scattering by material slices. As a result, it remains valid beyond the diffusive regime, accurately describing the transmission eigenvalue distribution in the quasiballistic regime as well. Moreover, the framework is more versatile than the DMPK theory, enabling straightforward incorporation of experimental realities such as absorption and incomplete channel control. These factors are frequently encountered in wave experiments on complex media but have lacked an ab initio theoretical treatment until now. We validate our predictions through numerical simulations based on the microscopic wave equation, confirming the accuracy and broad applicability of the theory.