Diffusive transport in highly corrugated channels

Abstract

Diffusion in waveguides with spatially modulated profiles is an important topic in modern electromagnetics and optics. Wave dynamics in the high-frequency asymptotics are governed by classical ray dynamics which can be characterised by looking at the diffusion of particles throughout the channel. We study the transport of particles (rays) in a channel with a sinusoidal profile at different values of the corrugation amplitude. We find that below a certain corrugation level the transport is ballistic, beyond this threshold, a diffusion-like behaviour emerges in the asymptotic limit of large times. In this regime particle transport slows down due to the trapping mechanism in the corrugated regions of the channel. We use the analogy with correlated random walks to discuss the observed transport regimes.