Localization-induced coherent backscattering effect in wave dynamics

Abstract

We investigate the statistics of smgle-mode delay times of waves reflected from a disordered waveguide m the presence of wave locahzation The distribution of delay times is quahtatively different from the distribution in the diffusive regime, and sensitive to coherent backscattering The probability of finding small delay times is enhanced by a factor close to v2 for reflection angles near the angle of incidence This dynamic effect of coherent backscattering disappears m the diffusive regime DOI 10 1103/PhysRevE 63 026605 PACS number(s) 42 25 Dd, 42 25 Hz, 72 15 Rn

Signatures of photon localization

“…The conditional probability distribution P I (φ ′ ) given I for localized waves in transmission is found to exhibit an exponential fall-off, with an asymmetry in the distribution, which increases with decreasing I, and to have a normalized standard deviation of ∆φ ′ / φ ′ ∝ I −0.25 [134]. The distribution, P (φ ′ ), of the single-channel delay time is given by random-matrix theory [132]. In the localized regime, it is found to have a universal quadratic tail, P (φ ′ ) ∝ |φ ′ | −2 [135,136,137].…”

“…For a given value of intensity I the delay time φ ′ is normally distributed with normalized standard deviation, ∆φ ′ / φ ′ = Q/2I, whereas the second-order cumulant correlator vanishes, φ ′ I − φ ′ I = 0. For, ℓ < L < ξ, in the diffusive regime, in the absence of absorption, the probability distribution of the delay times is P ( [130,131] and Q ≈ (L/ℓ) 2 in reflection [130,131,132]. Absorption can be accounted for simply by a change in Q.…”

Dynamics of Weakly Localized Waves

“…A very complete localization theory is random matrix theory [5]. It can describe the transition from weak to strong localization, scaling, absorption, fluctuations, and, recently, also dynamics [7], but the random matrix theory applies only for low-dimensional systems. Supersymmetric theory [8,9] also has a very general range of applicability but does not always give the necessary physical insight to guide experiments.…”

Frequency correlations in reflection from random media

“…V), λ L and λ C , see Eqs. (15,16), are hence dominated by the transversal coordinate x. We thus approximate λ L λ C x sin ϑ, where x = r sin ϕ is expressed in polar coordinates, with uniformly distributed angle ϕ and Gaussian distributed radial coordinate, i.e., P t (r) = (…”

“…Consequently, this dependency of the path length distribution on the backscattering angle leads to a characteristic angular peak of the width of the frequency correlation function [14]. In a previous work on reflection from two-and three-dimensional * Corresponding author: thomas.wellens@physik.uni-freiburg.de random wave guides [15], the narrow angular peak that results in the diffusive regime of weak disorder could not be resolved, due to the discrete scattering channel geometry. On the other hand, however, this work explicitly reports on effects of the transition between the localized and the diffusive regime on the delay time statistics.…”