Dynamics of Localization in a Waveguide

This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up as a t −2 tail after N 2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption. 1 L FIG. 1. The top diagram shows the quasi-one-dimensional geometry considered in this review. The waveguide contains a region of length L (dotted) with randomly located scatterers that reflects a wave incident from one end (arrows). The number of propagating modes N may be arbitrarily large. The one-dimensional case N = 1 is equivalent to the layered geometry shown in the bottom diagram. Each of the parallel layers is homogeneous but differs from the others by a random variation in composition and/or thickness.