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.     

Coherent backscattering effects for discrete random media: Numerical and theoretical results

Manifestation of the backscattering enhancement phenomenon in the reflection matrix elements of the coherent component of scattered radiation is considered. The dependence of the coherent backscattering effects on the microphysical properties of the medium scatterers are investigated. It is shown that random media of fractal-like clusters exhibit brightness and polarization opposition effects, which are like those observed for some atmosphereless Solar system bodies. Conditions for a bimodal angle dependence in the degree of linear polarization are discussed and the manifestation of the enhanced backscattering phenomenon in the intensity of scattered radiation is studied.     

Coherent backscattering of singular beams

The phenomenon of coherent backscattering depends on both the statistical characteristics of a random scattering medium and the correlation features of the incident field. Imposing a wavefront singularity on the incident field offers a unique and very attractive way to modify the field correlations in a deterministic manner. The field correlations are found to act as a path-length filter which modifies the distribution of different contributions to the enhancement cone. This effect is thoroughly discussed and demonstrated experimentally for the case of single scale scattering systems.     

Multiple scattering of light by a layer of discrete random medium: backscattering

The problem of multiple scattering of light by a layer of discrete random medium is considered. The medium is supposed to be rarefied with scatterers randomly positioned in the layer. Backscattering of light incident normal to the plane of the layer is considered. The scattering matrix is presented as a sum of three matrices, one of them corresponding to incoherent scattering of light and difference of the other two matrices describing coherent scattering. Equations for the calculation of these matrices are given.     

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.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Enhanced backscattering of polarized light: Effect of particle nonsphericity on the helicity-preserving enhancement factor

We analyze theoretically the effect of particle nonsphericity on the backscattering enhancement factor ζ_hp in the helicity-preserving channel. Using numerically exact T-matrix and vector radiative-transfer codes, we have performed computations for optically semi-infinite homogeneous layers composed of polydisperse, randomly oriented oblate spheroids with the real part of the refractive index equal to 1.2, 1.4, and 1.6, the imaginary part of the refractive index equal to 0 and 0.01, various values of the equal-surface-area-sphere effective size parameter, and aspect ratios 12. Our computations demonstrate that whereas for spheres ζ_hp≡2, for spheroids the helicity-preserving enhancement factor can deviate quite significantly from the value 2. The magnitude of this deviation varies substantially with particle microphysical parameters and illumination geometry.     

Boson peak, flickering noise, backscattering processes and radiative transfer in random media

The method of matrix Green’s functions in the classical theory of electromagnetic waves is stated. This method allows to obtain a closed equation system in the presence of the random media for the calculation both coherent, and incoherent (fluctuating) components of radiation. The density and heterogeneity of scattering media can be arbitrary. The coherent channel is calculated independently. The fluctuating radiation distribution in the medium is developed initially by an interference pattern generated by the coherent channel. The limitations of the processes speed are absent. The theory embraces such phenomena as the boson peak, flickering noise, memory effect, backscattering processes and also conventional radiative transfer equation and Fresnel’s formulae.     

Coherent backscattering: Conceptions and misconceptions (reply to comments by Bruce W. Hapke and Robert M. Nelson)

Although the note by Hapke and Nelson has virtually no relevance to our original publication, it contains a number of statements that are misleading and/or wrong. We, therefore, use this opportunity to dispel several profound misconceptions that continue to hinder the progress in remote sensing of planetary surfaces.     

Numerically exact computer simulations of light scattering by densely packed, random particulate media

Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range [20] and [59], composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.     

Maxwell's equations, radiative transfer, and coherent backscattering: A general perspective

This tutorial paper provides a general overview of the hierarchy of problems involving electromagnetic scattering by particles and clarifies the place of the radiative transfer theory and the theory of coherent backscattering in the context of classical electromagnetics. The self-consistent microphysical approach to radiative transfer is compared with the traditional phenomenological treatment.     

Coherent backscattering of polarized light from a turbid medium

Approximate analytical expressions for the intensities of the polarized components of light reflected from a disordered medium with large discrete particles (larger than the wavelength) have been derived with the use of the method of decoupling of the vector transfer equation that is based on separate treatment of basic and additional polarization modes. The results obtained provide the relation between the peak shape in the angular distribution of the backscattered radiation with a given polarization and the optical characteristics of the medium and are in good agreement with experimental data and numerical calculations.     

Coherent backscattering of a light pulse by a slab of disordered medium

We obtain an exact analytical solution to the problem of the enhanced backscattering of a short pulsed signal from a two- and three-dimensional medium with isotropically scattering centres. The angular spectrum is expressed in terms of the solution to the corresponding stationary problem. The intensity oscillations are shown to appear on the tails of the angular spectrum. The origin of these oscillations is associated with the ballistic phase shift between the interfering waves arriving at the detector. It is shown that the finiteness of the slab thickness influences the magnitude of the backscattering intensity and does not change the shape of the angular spectrum. The range of validity for the diffusion approximation is pointed out.

The results obtained in the paper also contain a generalization of the well known solution to the problem of incoherent transfer to a pulsed signal to the case of two-dimensional disordered media.     

Coherent backscattering by polydisperse discrete random media: exact T-matrix results

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.     

Electromagnetic scattering by a morphologically complex object: Fundamental concepts and common misconceptions

Following Keller (Proc Symp Appl Math 1962;13:227-46), we classify all theoretical treatments of electromagnetic scattering by a morphologically complex object into first-principle (or “honest” in Keller's terminology) and phenomenological (or “dishonest”) categories. This helps us identify, analyze, and dispel several profound misconceptions widespread in the discipline of electromagnetic scattering by solitary particles and discrete random media. Our goal is not to call for a complete renunciation of phenomenological approaches but rather to encourage a critical and careful evaluation of their actual origin, virtues, and limitations. In other words, we do not intend to deter creative thinking in terms of phenomenological short-cuts, but we do want to raise awareness when we stray (often for practical reasons) from the fundamentals. The main results and conclusions are illustrated by numerically-exact data based on direct numerical solutions of the macroscopic Maxwell equations.     

Enhanced backscattering of vortex waves from volume scattering media

The effect of phase vortices on the enhanced coherent backscattering from volume scattering media is studied theoretically and experimentally. The experimental results are well described by a theoretical model based on the diffusion approximation corrected for small path lengths contributions. Based on this approach, a self-referencing method for measuring the optical characteristics of a multiple scattering medium can be developed.     

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.     

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

Abstract

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.     

Angularly resolved backscattering of light from turbid suspensions of dielectric spheres

An analytic expression for the angular dependency of light backscattered from turbid suspensions of dielectric spheres that accounts for multiple-scattering effects is developed. The multiple-scattering model expresses backscattered light as a convolution of the phase function and a kernel representing the effects of forward scattering, multiplied by the optical thickness of the slab. Excellent agreement between Monte Carlo simulations and the analytic expressions is demonstrated for optical thicknesses of 0.1-4. The results are important for goniometric sizing measurements of biological cells and cellular organelles using elastically backscattered light.     

Estimation of light transport parameters in biological media using coherent backscattering

The suitability of using the angular peak shape of the coherent backscattered light for estimating the light transport parameters of biological media has been investigated. Milk and methylene blue doped milk were used as tissue phantoms for the measurements carried out with a He-Ne laser (632.8 nm). Results indicate that while the technique accurately estimates the transport length, it can determine the absorption coefficient only when the absorption is moderately high (α>1 cm⁻¹) for the long transport lengths typical of tissues. Further, the possibility of determining the anisotropy factor by estimating the single scattering contribution to the diffuse background is examined.