Intensity of Waves Inside a Strongly Disordered Medium

Abstract

Anderson localization does not lead to an exponential decay of intensity of an incident wave with the depth inside a strongly disordered three-dimensional medium. Instead, the average intensity is roughly constant in the first half of a disordered slab, sharply drops in a narrow region in the middle of the sample, and then remains low in the second half of the sample. A universal, scale-free spatial distribution of average intensity is found at the mobility edge where the intensity exhibits strong sample-to-sample fluctuations. Our numerical simulations allow us to discriminate between two competing local diffusion theories of Anderson localization and to pinpoint a deficiency of the self-consistent theory.

Anisotropy of localized states in an anisotropic disordered medium

“…Additionally, the transport anisotropy (defined as the ratio of the diffusion tensor's components) has been predicted to be significantly reduced near the mobility edge based on the self-consistent theory of localization [30], challenging earlier conclusions indicating that transport anisotropy is not affected by interference effects [19,20]. Even though this prediction of significantly reduced transport anisotropy has recently been experimentally confirmed for ultrasonic waves propagating in anisotropic networks of aluminum beads [31], the deficiency of the self-consistent theory to correctly describe the scaling properties of wave transport at the mobility edge and in the localized regime even in isotropic media [32] makes an alternative theoretical framework to study the problem of Anderson localization in anisotropic media highly valuable.…”

Multiple Scattering and Random Quasi-Phase-Matching in Disordered Assemblies of LiNbO3 Nanocubes

“…Characterization of the scattering strength returned a minimal value of of 476 ± 6 at 750 nm wavelength, corresponding to an inverse scattering coefficient of 3.9 ± 0.1. This value and the observed decreasing trend with the wavelength makes our samples a promising platform to study the Anderson localization of the SHG in three-dimensional multiple scattering media with second-order nonlinearity, which is an unusual physical scenario . The observed linear scaling of the SHG power with the slab thickness provides the first explicit evidence of RQPM in the multiple scattering regime.…”

“…Differently to the typical RQPM scenario, nonlinear disordered photonic media (NDPM) can have noncentrosymmetric domains that are also scattering sites. Recently, several studies have investigated the SHG generated from a NDPM in the multiple scattering regime focusing on properties, such as the intensity distribution, 18 the polarization dependency, 19 and the nonlinear speckle pattern. 20 Nonetheless, investigating the robustness of the RQPM scaling in the multiple scattering regime presents several experimental challenges.…”

Polarization state transition mechanism of light through turbid media by Monte Carlo simulation

“…Then the transport of light in turbid media is governed by the radiation transport equation (RTE), with an emphasis on the variability of the incident light intensity distribution [7,8]. In highly scattering environments, the RTE can even be simplified to the diffusion equation with analytical solutions [9,10]. The information carried by the spatial intensity distribution of the exiting light has been used to determine the parameters of scattering particles including the size, the anisotropy factor, and the scattering coefficient of turbid media [11,12].…”