Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics

We study light scattering by Gaussian-random-sphere particles that are large compared to the wavelength of the incident light using ray optics that, in addition to Fresnellian reflection and refraction, accounts for diffuse scattering. We consider two types of diffusely scattering media. One type of media constitutes a uniform medium inside the particle, i.e. a diffuse internal medium. The second type of media constitutes a layer on the surface of the particle that is thin compared to the particle dimensions and acts as a diffuse external medium mimicking the particle surface roughness. We illustrate the effects of the diffuse media on the scattering characteristics for both cases and show that incorporating diffuse scatterers allows us to explain the scattering matrices measured experimentally for Saharan sand particles large compared to the wavelength.     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Backscattering of linearly and circularly polarized light in randomly inhomogeneous media

The scattering of linearly or circularly polarized light from a semibounded randomly inhomogeneous medium is considered. A new technique for simulating the electromagnetic radiation transport using the Monte Carlo method is proposed, which makes it possible to avoid cumbersome calculation of Muller matrices. Expressions are obtained for the co- and cross-polarized components of backscattered light for incident light of arbitrary polarization. The coherent and incoherent backscattering components are calculated for arbitrary combinations of incident and scattered light polarizations. It is shown that the main contribution to coherent backscattering is from the co- and cross-polarized components for linearly and circularly polarized light, respectively. The backscattering from an optically active random medium is calculated.     

Polarization visualization of scattering media with CW laser radiation

The method of polarization visualization of a multiply scattering medium containing macroinhomogeneities based on analysis of polarization spatial distribution of a scattered linearly polarized light is discussed. The treatment is based on statistical properties of the effective optical path distribution of scattered field components. The influence of media scattering properties and the geometry of the experiment on the inhomogeneity image contrast obtained with use of polarization degree and of normalized scattered intensity of radiation as visualization parameters are discussed, as well as spatial resolution achieved in these both cases. Using the results of theoretical analysis and of the experimental model, the relationship between the shapes of spatial distributions of polarization degree and the intensity of the scattered light is considered as a function of the position of the visualized object (an absorbing half-plane immersed in a plane layer of the scattering medium). The opportunities for enhancing the quality of the images formed in this way are also discussed.     

Reflection and transmission of light through a layer possessing dielectric and magnetic helicities: II. Principal axes of dielectric and magnetic helicities are rotated relative to each other

The transmission and reflection of light are considered in the case of its normal incidence on a layer of a periodically nonuniform medium possessing dielectric and magnetic helicities, with the axes of electrical and magnetic permittivities being rotated relative to each other. A simple algorithm for constructing the solution of the boundary problem for a layer of a helical periodic medium (HPM) of finite thickness is proposed. Jones matrices are constructed and natural polarizations and eigenvalues of the transfer function for the complex amplitude corresponding to natural polarizations are calculated. Numerical analysis is carried out for the case of large (and very large) local anisotropy of the medium. It is shown in particular that a domain of transmission appears between domains of diffraction and specular reflection under certain conditions.     

Impedance theory of sound scattering: General relations

The problem of sound scattering by an elastic body of arbitrary geometry in an acoustic medium is solved by the impedance method. It is shown that, for a complete solution, three impedance matrices are necessary: one of them characterizes the scatterer and the other two, the medium. The scattering matrices and other characteristics of the solution are expressed through the incident field and these three impedance matrices. The necessary general relations are presented, and the most important particular cases are considered. Three new representations of the diffraction field are proposed in the form of a sum of two components obtained as solutions to two simpler boundary-value problems. Original Russian Text ￠ Yu.I. Bobrovnitskiĭ, 2006, published in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 5, pp. 601–606.     

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.     

Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium

We propose an analytical model of the spatio-temporal structure of a short laser pulse transmitted through a layer of an optically inhomogeneous medium with high anisotropy of scattering. The light-field brightness in the medium is represented as a finite series in terms of multiplicities of the small-angle scattering, while the contribution from the higher-order scattering is allowed for as a quasi-diffuse component. The scattered-pulse structure is calculated on the basis of solving the radiative-transfer equation in the small-angle approximation with allowance for the effect of multipath light propagation. Compared with the first approximation of the multiple-scattering theory (attenuated nonscattered light plus the diffuse component), this approach makes it possible to describe more correctly the transformation of the spatio-angular distribution of light in the medium when passing from the single-scattering to multiple-scattering regime, as well as specify the temporal profile of the scattered pulse. The temporal profile of the femtosecond pulse transmitted through a layer of model scattering medium with various concentrations of scatterers is studied experimentally. The blurred-pulse structure is studied with the help of nonlinear optical gating in the case of noncollinear generation of the second harmonic. Good agreement between the theoretical and experimental time profiles of the scattered pulse is shown for the optical-thickness intervals corresponding to both the predominantly low multiplicity scattering and multiple small-angle scattering, which allows us to use the proposed analytical model for solving the inverse problem of the pulse sounding of a homogeneous turbid medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 333–348, April 2008.     

Surface-sensitive polarized Raman spectroscopy of biological tissue

In a two-layer diffusing medium, polarized light directly backscattering off the superficial layer will partially retain its sense of polarization, whereas deeper-probing light will be increasingly depolarized by diffusion. This effect has been studied in both elastic scattering and fluorescence contexts. We apply this method to Raman scattering in two two-layer models with a highly diffusing lower layer of glucose powder and an upper layer of either clear plastic or chicken skin. We employ detection of orthogonal polarization states to generate a Raman spectrum of only the superficial layer by combining the orthogonal signals.     

Simple parametric representations of the polarization optical properties of birefringent biological tissues in reflection polarization spectroscopy

The use of polarization reflection spectroscopy for investigating complex scattering media, including orientationally ordered optically anisotropic elements, requires a special choice of output parameters (represented by spectra) that characterize polarized light scattering by objects under study because the standard characteristics, such as the Mueller matrices, depend on the azimuthal orientation of the medium. We propose compact and convenient sets of experimentally determined output parameters that involve separate detection of co- and cross-polarized components of light scattered by a sample irradiated by a normally incident linearly polarized beam and include characteristics invariant with respect to the azimuthal rotation of the sample.     

Effect of turning of rays on scattering of light in a layered medium

The problem of the scattering of light by random inhomogeneities in a layered medium whose characteristic scale is large compared to the wavelength of light is considered. The attention is mainly focused on the effect that the turning of incident and scattered waves has on light scattering in such a medium. In the mixed (q _⊥, z) Fourier representation, expressions for normal waves, and Green’s function are found, which can be used both far from the turning point, where the fields are described in the WKB approximation, and near this point, where the fields are described using the Airy function. Based on these expressions and using the Kirchhoff method, a general expression for the scattering intensity in the far field of the sample is obtained, which takes into account the turning of the incident and scattered waves in the fluctuating medium. Physical consequences of the calculation results are analyzed. In particular, it is shown that even a comparatively small gradient of the refractive index in the layer leads to a rather appreciable redistribution of the scattering intensity between the forward and backward hemispheres. In this case, the shape of the scattering indicatrix is rather exotic with sharp discontinuities, peaks, and dips whose amplitude is on the order of the intensity itself. Original Russian Text ? A.Yu. Val’kov, A.A. Zhukov, V.P. Romanov, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 4, pp. 647–666.     

Influence of the matrix on boron detection by auger electron spectroscopy (AES)

The difficulties of boron detection by AES in catalysts containing low concentrations of boron can be partially associated with elastic scattering of Auger electrons. In the present work, the Monte Carlo approach is used to estimate the effects of Auger electron collisions in different matrices. Elastic scattering events are described within the partial wave expansion method. The scattering centres are approximated by the Thomas-Fermi-Dirac potentials. It is found that elastic collisions decrease the boron KLL Auger electron signal by up to 10%. In addition, the sampling depth of AES is strongly decreased. This decrease reaches 35% for medium atomic number elements. The values of parameters correcting for elastic scattering effects are determined for boron embedded in 14 elements. An attempt is also made to interpolate the correcting parameters for matrices not considered in the present work.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Light scattering by multilayer ellipsoids in the Rayleigh approximation

A problem of light scattering by multilayer confocal ellipsoids is solved in the Rayleigh approximation. The electric field of a light wave is assumed constant and a set of Laplace equations with the corresponding boundary conditions is considered. The final expression for the polarizability of a particle is represented in the matrix form (2×2 matrices) in terms of parameters of a nucleus and subsequent layers. Numerical calculations of the scattering and absorption efficiencies of small multilayer spheres obtained using the exact (the generalization of the Mie theory) and approximate solutions well agree with each other.     

Propagation and scattering of light in stratified media

The propagation and scattering of light in stratified media are considered. Based on the Maxwell equations, the present approaches to the solution of these problems are formulated in a unified way. The particular features of the wave propagation in stratified media are discussed. Scalar and vector fields are considered. Media with small-and large-scale regular inhomogeneities are examined. The construction of the Green’s function of the wave equation in a spatially homogeneous medium is discussed. Stratified isotropic and anisotropic media are analyzed. The scattering of light in a stratified medium is studied with emphasis on the Kirchhoff method, as this makes it possible to obtain calculation formulas in a form convenient for comparing the theory with the experiment. The propagation of waves in photonic crystals and the formation of forbidden zones in such objects are briefly considered.     

Radiative transfer in plant leaves

A two-layer model of light scattering and absorption in plant phytoelements is considered, which takes into account absorption of light by pigments and water and light scattering by particles of two types: chloroplasts and air cavities. An elementary light scattering event is described using the Mie theory. Multiple light scattering in a leaf is described within the framework of the theory of radiative transfer. The equation of radiative transfer with a strongly anisotropic phase function is solved using the method of addition of layers and the method of reduction to a medium with effective parameters depending on the propagation direction of light. The spectral dependences of reflection and transmission coefficients are calculated in the visible range as functions of the leaf structure.     

Multiple scattering of light transmission in a smoke layer

The visibility in a fire scene decreases because of the existence of smoke produced by the flammable materials. With the growth of smoke concentration, the relationship between light and smoke becomes complicated due to the multiple scattering. In this paper, the radiative transfer equation (RTE) that considers the multiple scattering was applied to calculate the light transmission in a smoke layer. As input parameters of RTE, the single scattering albedo, asymmetry parameter and extinction cross section of single smoke agglomerate were calculated by the discrete dipole approximation (DDA) method. The effects of smoke agglomerate diameter, number density of smoke layer, and the incident light wavelength were considered. The results show that the light transmitted flux decreases with the growth of smoke diameter and number density, and increases with the growth of wavelength. The smoke diameter is dominant among the three parameters, and the light transmitted flux tends to be stable when the wavelength reaches a certain value.     

Role of spatial coherence in polarization tomography

We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix representing the scatterer. We show that, according to the degree of spatial coherence of the beam, the same scattering medium can be represented by different Mueller matrices. This result should serve as a warning for experimentalists.     

Scattering matrices for horizontally oriented ice crystals

Scattering matrices for horizontally oriented ice crystals are calculated with a code based on the geometric optics. The main physical regularities inherent to the scattering matrices are discussed. Degree of polarization of the scattered light is shown to be a qualitative criterion of number of photon trajectories that contribute effectively to the scattered light. The inverse scattering problem of retrieving aspect ratios of the horizontally oriented hexagonal ice plates from polarization of the scattered light in the bistatic sounding scheme has been proposed and discussed.