Electromagnetic wave propagation in random waveguides

TL;DR

This paper analyzes how electromagnetic waves propagate over long distances in random rectangular waveguides with weak permittivity fluctuations, revealing effects like energy transport, mode decoherence, and depolarization due to cumulative scattering.

Contribution

It introduces a stochastic differential equation model for wave modes in random waveguides and applies diffusion approximation to characterize energy transport and wave coherence loss.

Findings

Quantitative description of energy transport in random waveguides

Analysis of mode decoherence and depolarization effects

Validation of diffusion approximation for wave scattering

Abstract

We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly fluctuating electric permittivity. The fluctuations are weak, but they cause significant cumulative scattering over long distances of propagation of the waves. We decompose the wave field in propagating and evanescent transverse electric and magnetic modes with random amplitudes that encode the cumulative scattering effects. They satisfy a coupled system of stochastic differential equations driven by the random fluctuations of the electric permittivity. We analyze the solution of this system with the diffusion approximation theorem, under the assumption that the fluctuations decorrelate rapidly in the range direction. The result is a detailed characterization of the transport of energy in the waveguide, the loss of coherence of the modes and the depolarization of the waves due to cumulative scattering.