Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

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.     

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.     

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.     

The reference wave solution for a two-frequency wave propagating in a random medium

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.     

Exact solution for coherent backscattering of polarized light from a random medium of Rayleigh scatterers

We discuss a rigorous vectorial theory as a model to represent the enhanced backscattering of polarized light from a random medium. The theory is based on the well known relation between the contributions of the ladder and cyclical diagrams to the intensity which allows to express these contributions in terms of radiative transfer theory. The tensor transfer equation for the electromagnetic field in a half-space occupied by point-like scatterers is explicitly solved with the aid of the Wiener-Hopf method. For the case of normal incidence the angular distribution of the backscattered intensity and the enhancement factor are found for arbitrary angles between the incident and detected linear polarizations and the scanning plane. To describe spatial anisotropy of the backscattering cone the half width at half maximum of the intensity is calculated as a function of these angles. Coherent backscattering of circularly polarized light is also considered.     

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.     

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.     

Observation of phase conjugation of light arising from enhanced backscattering in a random medium

We measure the fundamental phase conjugation of a light field arising from enhanced backscattering in a multiple scattering medium. The measurements employ a two-window, time-resolved heterodyne method to suppress specularly reflected light and to determine the transverse Wigner function of the field, yielding joint amplitude and phase information. Using this method, a light field backscattered from an aqueous suspension of polystyrene spheres is found to reverse curvature relative to that of the incident field.     

Moment-screen method for wave propagation in a refractive medium with random scattering

Direct numerical solution of a parabolic equation (PE) for the second moment of the sound field in a refracting medium with random scattering is described. The method determines the mean-square sound pressure without requiring generation of random realizations of the propagation medium. The second-moment matrix is factored into components that are independently propagated with a conventional PE algorithm. A moment screen is periodically applied to attenuate the coherence of the wavefield, much as phase screens are often applied in the method of random realizations. An example involving upwind and downwind propagation in the near-ground atmosphere shows that the new direct method converges to an accurate solution faster than the method of random realizations and is particularly well suited to calculations at low frequencies.     

Spectral moment estimates of broadband backscattering acoustic wave in moving medium

I.IntroductionSincemiddle198o's,theacousticDopplercurrentprofiler(ADCP)hasbeenusedinvariousaspects.Itnormallytransmitsasine-modulatedpulse,thenmeasurestheechoofmanylayersinaprofile.TheDopplerfrequencyshiftofeachlayeriscalculatedwhilethevesseliscruisingandADCPiscontinuallytransmittingpulsesandreceivingechoes.BystatisticallyaveragingtheDopplerfrequencyshiftofeachlayerinmultipletransmissions,theestimateofDopplerfrequencyshiftofthatlayerisobtained,thenthevelocityestimatesofmanydepthbinsinapr…     

Coherent enhancement of light-pulse backscattering by random slab

An exact analytic solution is found for the problem of enhancement of backscattering of a short pulse signal from a slab of finite thickness with isotropic scattering centers.Moscow Engineering-Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 5, pp. 429–442, May, 1993.     

Statistical properties of a wave with random frequency modulation in a dispersive medium

The probability distributions of frequency, intensity, and other parameters of a wave with random frequency modulation propagating in a dispersive medium are determined and studied. In particular, the probability distributions for photon density are found for the limiting cases of linear and quadratic medium dispersion characteristics. It is demonstrated that in the latter case the photon density probability distribution has a singularity produced by the absence of time focusing of the wave in the vicinity of dispersion curve inflection points. The statistics of wave frequency in a multifrequency regime are considered in detail.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1797–1802, December, 1978.The authors thank A. N. Malakhov for his interest in the study.     

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.     

Monte Carlo simulation of the coherent backscattering of electrons in a ballistic system

We study weak localization effects in the ballistic regime as induced by man-made scatterers. Specular reflection of the electrons off these scatterers causes backscattered trajectories to occur, which interfere with their time-reversed path resulting in weak localization corrections to the resistance. Using a semi-classical theory, we calculate the change in resistance due to these backscattered trajectories. We found that the inclusion of the exact shape of the scatterers is very important in order to explain the experimental results of Katine et al.[Superlattices and Microstructures 20 , 337 (1996)].     

Lie-optic matrix algorithm for computer simulation of paraxial self-focusing in a plasma

Propagation algorithm for computer simulation of stationary paraxial self-focusing laser beam in a medium with saturating nonlinearity is given in Lie-optic form. Accordingly, a very natural piece-wise continuous Lie transformation that reduces to a restricted Lorentz group of the beam results. It gives rise to a matrix method for self-focusing beam propagation that is constructed and implemented. Although the results use plasma nonlinearities of saturable type, and a gaussian initial beam, these results are applicable for other media like linear optical fibers and to more general situations.     

Transmission of waves by a nonlinear random medium

We study analytically and numerically the effect of nonlinearity on transmission of waves through a random medium. We introduce and analyze quantities associated with the scattering problem that clarify the lack of uniqueness due to the nonlinearity as well as the localization of waves due to the random inhomogeneities. We show that nonlinearity tends to delocalize the waves and that for very large scattering regions the average transmitted energy is small.