Strong backscattering enhancement for partially convex targets in random media

Earlier work pointed out that the radar cross section (RCS), owing to the double-passage effect on waves propagating through random media, is enhanced by a factor ranging from one up to three. However, our study has manifested numerically a strong enhancement in RCS of targets with concave-convex surfaces in continuous random media, by taking account of boundary conditions of waves on targets. We have found that when a plane wave illuminates a convex portion of the concave-convex conducting target in a random medium, the factor of enhancement oscillates about two with target size. Moreover, this enhancement becomes quite large at certain target shapes and also under a specific condition of target size and spatial coherence length of the incident H-wave. The large enhancement is considered as an anomalous feature in the behaviour of backscattered waves in random media. By analysing the scattering problem for beam-wave incidence on the same target in free space, we manifest the mechanism of such anomalous enhancement.     

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.     

Approximate calculation of coherent backscattering for semi-infinite discrete random media

We describe an approximate method for the calculation of all characteristics of coherent backscattering for a homogeneous, semi-infinite particulate medium. The method allows one to transform a system of integral equations describing coherent backscattering exactly into a system of linear algebraic equations affording an efficient numerical solution. Comparisons of approximate theoretical results with experimental data as well as with benchmark numerical results for a medium composed of nonabsorbing Rayleigh scatterers have shown that the method can be expected to give a good accuracy.     

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 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.     

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.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

Abstract

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Enhanced backscattering in a magnetic field

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ξ(x₁), where the surface profile function ξ(x₁) is a stationary stochastic Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k₊(ω) for a surface polariton of frequency ω propagating in the +x₁-direction is unequal to the (magnitude of the) wavenumber k_-(ω) for a surface polariton of the same frequency propagating in the -x₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x₁-direction but not in the -x₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

Enhanced backscattering in a magnetic field

By infinite-order perturbation theory the authors study the scattering of p-polarized light from a small-amplitude random grating ruled on the surface of a metal or an n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) is a stationary, stochastic, Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂ axis. We find that the position of the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles from the retroreflection direction with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. This is interpreted as due to the breakdown of the coherency between the contribution to backscattering from a given light/surface polariton path and from its time-reversed partner, caused by the removal of time reversal symmetry from the scattering system by the application of the external magnetic field. The latter is manifested by the non-reciprocity of the surface polariton dispersion relation in the presence of the magnetic field.     

Enhanced backscattering in a magnetic field

Abstract

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x ₃=ξ(x ₁), where the surface profile function ξ(x ₁) is a stationary stochastic Gaussian process. The plane of incidence is the x ₁ x ₃ plane, and the magnetic field is directed along the x ₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k ₊(ω) for a surface polariton of frequency ω propagating in the +x ₁-direction is unequal to the (magnitude of the) wavenumber k _?(ω) for a surface polariton of the same frequency propagating in the ?x ₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x ₁-direction but not in the ?x ₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Enhanced backscattering at grazing angles

Backscattering signals at small grazing angles are important for space vehicle atmospheric reentrance and subsurface radar sensing applications. They are also useful in Fourier-transform infrared grazing-angle microscopy. Recently we performed an experimental study of far-field scattering at small grazing angles, in particular, of enhanced backscattering at grazing angles. For a randomly weak rough dielectric film upon a reflecting metal substrate, a large enhanced backscattering peak was measured. Experimental results are compared with small perturbation theoretical predictions.     

Enhanced backscattering of optical vortex fields

The effect of an incident field with a phase screw dislocation (a so-called optical vortex) on the shape of the enhanced backscattering cone was studied theoretically and demonstrated experimentally. We show that the correlation function of the incident field acts as a filter that modifies the shape of the enhanced backscattering cone. The peak value is reduced, and its width is increased as the topological charge of the phase dislocation increases.     

The effect of H-polarization on backscattering enhancement for partially convex targets of large sizes in continuous random media

In our previous work, we have proved that the spatial coherence length (SCL) of the incident waves around the target together with the target configuration play a leading role in the determination of the enhancement in the radar cross-section (ERCS) of a target in a random medium. Owing to the double-passage effect, the ERCS is almost two when the SCL is much smaller or larger than the target size. However, for a SCL comparable with the target size, the ERCS deviates from two, depending on the target parameters and the SCL. The last conclusion was proved only for E-polarization. The polarization of incident waves is one of the key parameters in scattering problems. In this work, we extend our study and investigate the effect of H-polarization on the radar cross-section and the ERCS for large-size targets.     

Coherent backscattering and localization in a self-attracting random walk model

Intensity propagation of waves in dilute 2D and 3D disordered systems is well described by a random walk path-model. In strongly scattering media, however, this model is not quite correct because of interference effects like coherent backscattering. In this letter, coherent backscattering is taken into account by a modified, self-attracting random walk. Straightforward simulations of this model essentially reproduce the results of current theories on “non-classical” transport behavior, i.e. Anderson localization in 1D and 2D for any amount of disorder and a phase transition from weak to strong localization in 3D. However, in the strongly scattering regime corrections are necessary to account for the finite number of light modes due to their non-vanishing lateral extention. Within our model this correction leads to the observation that strong localization does not take place. Received 17 September 2001     

The effect of H-polarization on backscattering enhancement for partially convex targets of large sizes in continuous random media

Abstract

In our previous work, we have proved that the spatial coherence length (SCL) of the incident waves around the target together with the target configuration play a leading role in the determination of the enhancement in the radar cross-section (ERCS) of a target in a random medium. Owing to the double-passage effect, the ERCS is almost two when the SCL is much smaller or larger than the target size. However, for a SCL comparable with the target size, the ERCS deviates from two, depending on the target parameters and the SCL. The last conclusion was proved only for E-polarization. The polarization of incident waves is one of the key parameters in scattering problems. In this work, we extend our study and investigate the effect of H-polarization on the radar cross-section and the ERCS for large-size targets.     

Time-resolved optical backscattering model in highly scattering media

A time-resolved backscattering model, which combines a single large-angle scattering with multiple small-angle scatterings, is used to produce a scattered-light profile about a medium. Inhomogeneity of the medium is included in the model. Some multidimensional integrals can be evaluated analytically.