Nontechnical Abstract: The scattering of waves, whether acoustic, radio or optical, is an inescapable part of our environment. When this environment is disordered the wave can scatter along many different paths and this can impair our ability to communicate or to image or excite electronic circuits. This project will study the propagation of waves through disordered media using a combination of experimental approaches supplanted by theory and simulations. The effort is a collaboration between the PI and the group of Patrick Sebbah at Bar-Ilan University as part of the NSF/DMR-BSF program. The work will focus on developing a universal description of wave propagation in finite random media and will provide an excellent training ground for students. The results of this work will also have a broad impact on a range of interdisciplinary problems in condensed matter physics, acoustics and optics.
The proposed research extends the range of a universal description of wave propagation from the reflected and transmitted wave at the boundaries of disordered media into the interior of the sample and from samples many times thicker than the mean free path to samples so thin that propagation is nearly ballistic. Phenomenological properties of transmission, such as the extrapolation length, upon which the scaling of transmission depends, will be related to universal parameters such as auxiliary localization lengths of different transmission eigenchannels. These parameters depend only on the ratio of sample length and the localization length and the eigenchannel number. An important aspect of the research is finding the relationship between the transmission eigenchannels, modes of waves in the medium, and solutions of a generalized diffusion equation with a position-dependent diffusion coefficient. The relationship between these approaches provides key clues to the control the wave within random media and disordered metamaterials. Such control of the wave inside disordered media provides a path towards improved imaging, resource exploration, local heating within the body, telecommunications, and low-threshold random lasing. The characteristics of a new class of quasi-one dimensional scattering sample, in which the local density of states vanishes in the interior of the sample, is investigated to understand the relationship of the density of states and localization. This provides new pathways to localizing waves and isolating regions from the surrounding environment.