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 $g$, 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 $g$ in a specific and non-trivial way

Transport in quenched disorder: light diffusion in strongly heterogeneous turbid media

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.Comment: 12 pages, 9 figures (significant amount of supplemental information

Weak localization of light in superdiffusive random systems

L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way using light waves. This raises several questions about the influence of superdiffusion on optical interference effects like weak and strong localization. Super diffusive structures have the extraordinary property that all points are connected via direct jumps, meaning that finite-size effects become an essential part of the physical problem. Here we report on the experimental observation of weak localization in L\'evy glasses and compare results with recently developed optical transport theory in the superdiffusive regime. Experimental results are in good agreement with theory and allow to unveil how light propagates inside a finite-size superdiffusive system

Light Transport and localization in two-dimensional correlated disorder

Structural correlations in disordered media are known to affect significantly the propagation of waves. In this Letter, we theoretically investigate the transport and localization of light in 2D photonic structures with short-range correlated disorder. The problem is tackled semianalytically using the Baus-Colot model for the structure factor of correlated media and a modified independent scattering approximation. We find that short-range correlations make it possible to easily tune the transport mean free path by more than a factor of 2 and the related localization length over several orders of magnitude. This trend is confirmed by numerical finite-difference time-domain calculations. This study therefore shows that disorder engineering can offer fine control over light transport and localization in planar geometries, which may open new opportunities in both fundamental and applied photonics research

Global polarizability matrix method for efficient modeling of light scattering by dense ensembles of non-spherical particles in stratified media

We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each other, to planar interfaces and/or to localized light sources. The method consists in finding a small set of fictitious polarizable elements -- or numerical dipoles -- that quantitatively reproduces the field scattered by an individual particle for any excitation and at an arbitrary distance from the particle surface. The set of numerical dipoles is described by a global polarizability matrix that is determined numerically by solving an inverse problem relying on fullwave simulations. The latter are classical and may be performed with any Maxwell's equations solver. Spatial non-locality is an important feature of the numerical dipoles set, providing additional degrees of freedom compared to classical coupled dipoles to reconstruct complex scattered fields. Once the polarizability matrix describing scattering by an individual particle is determined, the multiple scattering problem by ensembles of such particles in stratified media can be solved using a Green tensor formalism and only few numerical dipoles, thereby with a low physical memory usage, even for dense systems in close vicinity to interfaces. The performance of the method is studied with the example of large high-aspect-ratio high-index dielectric cylinders. The method is easy to implement and may offer new possibilities for the study of complex nanostructured surfaces, which are becoming widespread in emerging photonic technologies

Light in correlated disordered media

The optics of correlated disordered media is a fascinating research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This article reviews the theoretical foundations, state-of-the-art experimental techniques and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems -- from short-range correlated photonic liquids, to L\'evy glasses containing fractal heterogeneities, to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. We overview the exciting ongoing research on mesoscopic phenomena, such as transport phase transitions and speckle statistics, and the current development of disorder engineering for applications such as light-energy management and visual appearance design. Special efforts are finally made to identify the main theoretical and experimental challenges to address in the near future.Comment: Submitted to Reviews of Modern Physics. Feedbacks are welcom