Entropy production in multiple scattering of light by a spatially random medium

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works.

Physically Realizable Space for the Purity-Depolarization Plane for Polarized Light Scattering Media

We propose a physically realizable space for the polarized light scattering measurement using the Stokes-Mueller formalism by a purity-index-depolarization-index (PI-P_{Δ}) plane. The parameter PI is defined from indices of polarimetric purity (IPP), which exhibits the overall magnitude of the polarimetric randomness of a medium, while the depolarization index (P_{Δ}) delineates a proper global degree of polarimetric purity and may also refer to the average measure of depolarization power of the scattering medium. Subregions and curves connecting the edge points in the plane are obtained by imposing certain constraints on the IPP; consequently any point on the subregion indicates the information related to a decomposition of the Mueller matrix into its components as a convex sum. From the same set of constraints, complete information about the depolarization index versus the entropy [S(M)-P_{Δ}] diagram is recovered. This work provides a simple geometric representation and a deeper perceptivity of the light scattering media comprising depolarization.

Minkowskian description of polarized light and polarizers

A conventional Stokes description of polarized light is considered in a four-dimensional Lorentzian space, developing a seminal idea of Paul Soleillet [Ann. Phys. (Paris) 12, 23 (1929)]. This provides a striking interpretation for the degree of polarization and the Stokes decomposition of light beams. Malus law and reciprocity theorems for polarizers are studied using this Lorentzian formalism.

Time-domain depolarization of waves retroreflected from dense colloidal media

We report on depolarization measurements of femtosecond pulses retroreflected from dense suspensions of silica microspheres with solid loads increasing from 5% to 54%. Backscattered pulse shapes compare well with predictions of the diffusion theory for all volume fractions, and the inferred values of the transport mean free path agree with independent measurements of enhanced backscattering. The measured degree of polarization decays exponentially with temporal rates that scale with the solid load. It is newly found that, for all solid loads, depolarization sets in for path lengths longer than approximately five transport mean free paths.

Statistics of the normalized Stokes parameters for a Gaussian stochastic plane wave field

<p>The statistics of the normalized Stokes parameters for a stochastic plane wave field that is Gaussian distributed is examined. The resulting probability density functions and lower-order moments generalized those obtained by previous investigators. Results of some numerical calculations are discussed.</p><p>As an application of this analysis, we consider multiple scattering of light by a spatially random medium, composed of uncorrelated spherical pointlike particles, where the description of partially polarized light in terms of normalized Stokes parameters may be useful.</p>

Evolution of the Stokes parameters in optically anisotropic media

The evolution of the Stokes parameters in optically anisotropic media is characterized by a set of coupled nonlinear first-order differential equations. The incident quasi-monochromatic plane-wave field is assumed to be statistically stationary and of arbitrary state of polarization. The optical medium is assumed to be linear, passive, and characterized by a differential Mueller matrix. It is shown that the set of these equations provides an efficient tool for the analysis of the propagation of partially polarized light in anisotropic media. As an example, we analyze the evolution of a beam of light propagating in a cholesteric liquid crystal. We also investigate how an additive temporal randomness on the differential Mueller matrix can modify the evolution of Stokes parameters in this medium.