High-frequency dynamics of wave localisation

TL;DR

This paper investigates how wave localisation affects pulse propagation in disordered waveguides, revealing a stretched exponential decay in the correlator and the influence of localisation on wave transmission, with effects dependent on symmetry conditions.

Contribution

It provides a detailed analysis of the high-frequency dynamics of wave localisation, including the impact on correlators and the role of time-reversal symmetry breaking.

Findings

Correlator exhibits a stretched exponential tail with large frequency differences.

Localisation multiplies the correlator by a frequency-independent factor.

Breaking time-reversal symmetry removes the localisation effect on the correlator.

Abstract

We study the effect of localisation on the propagation of a pulse through a multi-mode disordered waveguide. The correlator <u(omega1)u*(omega2)> of the transmitted wave amplitude u at two frequencies differing by delta_omega has for large delta_omega the stretched exponential tail ~exp(-sqrt{tau_D delta_omega/2}). The time constant tau_D=L^2/D is given by the diffusion coefficient D, even if the length L of the waveguide is much greater than the localisation length xi. Localisation has the effect of multiplying the correlator by a frequency-independent factor exp(-L/2xi), which disappears upon breaking time-reversal symmetry.