69 research outputs found
Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media
Spatial field correlation functions represent a key quantity for the
description of mesoscopic phenomena in disordered media and the optical
characterization of complex materials. Yet many aspects related to the vector
nature of light waves have not been investigated so far. We study theoretically
the polarization and coherence properties of electromagnetic waves produced by
a dipole source in a three-dimensional uncorrelated disordered medium. The
spatial field correlation matrix is calculated analytically using a multiple
scattering theory for polarized light. This allows us to provide a formal
description of the light depolarization process in terms of "polarization
eigenchannels" and to derive analytical formulas for the spatial coherence of
multiply-scattered light
Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations
We develop a model based on a multiple scattering theory to describe the
diffusion of polarized light in disordered media exhibiting short-range
structural correlations. Starting from exact expressions of the average field
and the field spatial correlation function, we derive a radiative transfer
equation for the polarization-resolved specific intensity that is valid for
weak disorder and we solve it analytically in the diffusion limit. A
decomposition of the specific intensity in terms of polarization eigenmodes
reveals how structural correlations, represented via the standard anisotropic
scattering parameter , affect the diffusion of polarized light. More
specifically, we find that propagation through each polarization eigenchannel
is described by its own transport mean free path that depends on in a
specific and non-trivial way
Cross density of states and mode connectivity: Probing wave localization in complex media
We introduce the mode connectivity as a measure of the number of eigenmodes
of a wave equation connecting two points at a given frequency. Based on
numerical simulations of scattering of electromagnetic waves in disordered
media, we show that the connectivity discriminates between the diffusive and
the Anderson localized regimes. For practical measurements, the connectivity is
encoded in the second-order coherence function characterizing the intensity
emitted by two incoherent classical or quantum dipole sources. The analysis
applies to all processes in which spatially localized modes build up, and to
all kinds of waves
Photon echoes in strongly scattering media: a diagrammatic approach
We study photon echo generation in disordered media with the help of multiple
scattering theory based on diagrammatic approach and numerical simulations. We
show that a strong correlation exists between the driving fields at the origin
of the echo and the echo beam. Opening the way to a better understanding of
non-linear wave propagation in complex materials, this work supports recent
experimental results with applications to the measurement of the optical dipole
lifetime in powders
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation
Heterogeneity can be accounted for by a random potential in the wave
equation. For acoustic waves in a fluid with fluctuations of both density and
compressibility (as well as for electromagnetic waves in a medium with
fluctuation of both permittivity and permeability) the random potential entails
a scalar and an operator contribution. For simplicity, the latter is usually
overlooked in multiple scattering theory: whatever the type of waves, this
simplification amounts to considering the Helmholtz equation with a sound speed
depending on position . In this work, a radiative transfer
equation is derived from the wave equation, in order to study energy transport
through a multiple scattering medium. In particular, the influence of the
operator term on various transport parameters is studied, based on the
diagrammatic approach of multiple scattering. Analytical results are obtained
for fundamental quantities of transport theory such as the transport mean-free
path , scattering phase function and anisotropy factor .
Discarding the operator term in the wave equation is shown to have a
significant impact on and , yet limited to the low-frequency regime
i.e., when the correlation length of the disorder is smaller than or
comparable to the wavelength . More surprisingly, discarding the
operator part has a significant impact on the transport mean-free path
whatever the frequency regime. When the scalar and operator terms have
identical amplitudes, the discrepancy on the transport mean-free path is around
in the low-frequency regime, and still above for
no matter how weak fluctuations of the disorder are.
Analytical results are supported by numerical simulations of the wave equation
and Monte Carlo simulations
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