Dynamics of Weakly Localized Waves

Abstract

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.

Angle dependence of the frequency correlation in random photonic media: Diffusive regime and its breakdown near localization

“…For classical diffusion, the frequency width is proportional to D/ 2 B , which in combination with D = v E B /3 yields the observed inverse linear dependence on B . A renormalization of the diffusion constant 33,35 would lead to a narrowing of the frequency correlation, which is not observed in our experiment.…”

“…(5), however alternative choices of the path length scaling are available to describe other effects such as localization. 33 Experiments on the same porous GaP samples have identified an anomalous cone rounding θ of around 4 mrad. 14 In Fig.…”

“…14 In Fig. 12 33,35 predict a reduction of the diffusion constant in this regime, which should lead to a narrowing of the spectral correlation. This is not observed experimentally in Fig.…”

“…To the first type belongs the cutoff of long light paths and the associated distribution of decay times near localization. 14,33 The second type includes higher-order contributions to the correlation function known as C (2) . 1 Several authors have considered this contribution in a reflection geometry.…”

“…17 It has been pointed out that time-resolved transmission is not expected to yield large modifications for the typical samples under study. 33 The angle-dependent frequency correlation provides a means for accessing the path-length distribution in reflection on much shorter time scales than can be accessed using ultrafast laser pulses. The frequency-resolved technique thus yields information complimentary to picosecond time-resolved experiments, which are usually more involved and not easily extended to studying angle-dependent phenomena.…”