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Invariance property of wave scattering through disordered media

R. Pierrat,Philipp Ambichl,S. Gigan,A. Haber,R. Carminati,S. Rotter

Published 2014 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance The diffusion of particles and waves through disordered media encompasses a large variety of phenomena, from the motion of insects to the scattering of electrons or light in complex environments. One of the core features of diffusive transport is that the mean length of trajectories traversing a system depends only on the size of the system and of its boundary, which are both independent of the microscopic structure of the underlying medium. Here we show, based on insights from wave-scattering theory, that this fundamental invariance property can be significantly extended beyond the diffusive random walk picture. Our result not only provides an interesting link between all the diverse fields in which wave scattering plays a role but also holds promise for a number of practical applications. A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.

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