Superdiffusive light transport in quenched multiple-scattering media 

Light transport in disordered optical materials is characterized by a
multiple scattering process engendered by random fluctuations of the
refractive index in space. Transport in random media is often
described as a standard diffusive process, assuming that steps between
successive scattering events are small and independent. Deviations
from these assumptions, however, are known to lead to anomalous
transport phenomena [1]. In particular, when the probability to make
very long steps is non-vanishing, transport may become superdiffusive
(i.e. its mean square displacement grows faster than linearly with
time). This work is concerned with light transport in
multiple-scattering media called Lévy glasses [2], in which
fractal-like inhomogeneities of the scattering probability forces
light to propagate superdiffusively [3]. A semi-analytical approach
intended to describe steady-state transport in superdiffusive media of
finite size is first presented [4]. The superdiffusion propagator is
found by solving the fractional diffusion equation in a slab geometry
and used to calculate the coherent backscattering cone in the
superdiffusion approximation. Arbitrary boundary conditions and
truncations in the step length distribution are implemented. The role
of quenched disorder on transport in two-dimensional Lévy glasses is
then investigated by means of Monte Carlo simulations [5]. Quenching
is shown to induce local trapping effects which slow down
superdiffusion and lead to a transient subdiffusive-like transport
regime close to the truncation time of the system. References: [1]
Anomalous transport, Foundations and Applications, edited by
R. Klages, G. Radon, and I. M. Sokolov (Wiley-VCH), 2006. [2]
P. Barthelemy, J. Bertolotti, D. S. Wiersma, ?A Lévy flight for
light,? Nature 453, 495 (2008). [3] J. Bertolotti, K. Vynck,
L. Pattelli, P. Barthelemy, S. Lepri, D. S. Wiersma,
Adv. Funct. Mater. 20, 965 (2010). [4] J. Bertolotti, K. Vynck,
D. S. Wiersma, arXiv:1003.2053 (2010). [5] P. Barthelemy,
J. Bertolotti, K. Vynck, S. Lepri and D. S. Wiersma, Phys. Rev. E 82,
011101 (2010).