Transmission through a many-channel random waveguide with absorption

TL;DR

This paper analyzes the statistical distribution of transmittance in many-channel random waveguides with absorption, providing theoretical insights that explain recent experimental results across different absorption regimes.

Contribution

It offers a comprehensive calculation of transmittance distributions in absorbing waveguides, covering both weak and strong absorption regimes, which was not previously achieved.

Findings

Distribution of transmittance is computed for weak absorption.

Complete transmittance distributions are derived for strong absorption.

Results align with recent experimental observations.

Abstract

We compute the statistical distribution of the transmittance of a random waveguide with absorption in the limit of many propagating channels. We consider the average and fluctuations of the conductance T = tr t^{\dagger} t, where t is the transmission matrix, the density of transmission eigenvalues \tau (the eigenvalues of t^{\dagger} t), and the distribution of the plane-wave transmittances T_a and T_{ab}. For weak absorption (length L smaller than the exponential absorption length \xi_a), we compute moments of the distributions, while for strong absorption (L >> \xi_a), we can find the complete distributions. Our findings explain recent experiments on the transmittance of random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].