Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Abstract

Abstract. Previous work has established that the localized regime of wave transport in open media is characterized by a position-dependent diffusion coefficient. In this work we study how the concept of positiondependent diffusion affects the delay time, the transverse confinement, the coherent backscattering, and the time reversal of waves. Definitions of energy transport velocity of localized waves are proposed. We start with a phenomenological model of radiative transfer and then present a novel perturbational approach based on the self-consistent theory of localization. The latter allows us to obtain results relevant for realistic experiments in disordered quasi-1D wave guides and 3D slabs.

Dynamic coherent backscattering of ultrasound in three-dimensional strongly-scattering media

“…Our result is in striking contrast with the surprising large values of v E (approximately 3 − 5 times larger than the velocity of longitudinal waves) previously deduced from the analysis of data for a similar sample in the localization regime [17]. This suggests that the large values of transport velocities observed previously are associated with Anderson localization [30].…”

Intensity of Waves Inside a Strongly Disordered Medium

“…1, I(z) does not decay exponentially with z as one could expect from naive considerations, but instead exhibits a rapid drop near the middle of the slab, while varying much slower near its boundaries. Such a behavior is similar to that found previously in 1D [15][16][17] and quasi-1D [18] media.…”

“…The spatial distribution of the average wave intensity I(r) inside a strongly disordered medium of length L illuminated by a monochromatic wave has been studied theoretically for a one-dimensional (1D) medium [15][16][17] and for a quasi-one dimensional (quasi-1D) waveguide [18]. In both cases, the behavior of I(r) = I(z) differs from a simple exponential decay with the distance z from the sample boundary.…”

Tunable high-index photonic glasses

“…v E can thus be calculated from D, which is accessible via photon time of flight (ToF) measurements [41,43]. How v E is affected by resonant scattering, which of these two quantities (v E and ) dominates D and what controls the Anderson transition is not fully understood in the literature [21,22]. We therefore performed measurements of ToF combined with to characterize the resonant transport behavior in a PG formed by amorphous TiO 2 spheres with r = 228 nm.…”

“…In this study [20], the model was tested against ab initio numerical simulations, earlier experimental data obtained from transmission experiments [11], and experimental results from spectrally resolved coherent backscattering experiments on specially synthesized PS (n PS = 1.6) colloidal glasses. In addition, as pointed out recently [22], it is difficult to distinguish between situations where the photon diffusion constant D is small due to Anderson localization effects leading to small , or due to a small transport energy velocity v E related to Mie resonances. This long-standing issue of the effect of resonant scattering behavior on dynamic scattering properties-i.e., the photon diffusion constant D-and static scattering properties-i.e., the mean-freepath -awaits experimental clarification.…”