Numerical studies of the scattering of light from a two-dimensional randomly rough interface between two dielectric media

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered light. These results are obtained for both the case where the medium of incidence is the optically less dense medium, and in the case where it is the optically more dense medium. Optical analogues of the Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than $10^{-4}$.Comment: 25 pages, 14 figure

Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates

Electromagnetic wave scattering from planar dielectric films deposited on one-dimensional, randomly rough, perfectly conducting substrates is studied by numerical simulations for both p- and s-polarization. The reduced Rayleigh equation, which is the integral equation satisfied by the scattering amplitude after eliminating the fields inside the film, is the starting point for the simulation. This equation is solved numerically by considering a random surface of finite length, and by introducing wave number cut-offs in the evanescent part of the spectrum. Upon discretization, a system of linear equations is obtained, and by solving this matrix system for an ensemble of surface realizations, the contribution to the mean differential reflection coefficient from the incoherently scattered field, $<\partial R_\nu/\partial \theta>_{incoh}$ (\nu=p,s), is obtained nonperturbatively. It is demonstrated that when the scattering geometry supports at least two guided waves, $_{incoh}$, has, in addition to the well known enhanced backscattering peak, well-defined satellite peaks in agreement with theory, for most of the parameters considered.Comment: 11 pages and 11 figure

The Design of Random Surfaces with Specified Scattering Properties: Surfaces that Suppress Leakage

We present a method for generating a one-dimensional random metal surface of finite length L that suppresses leakage, i.e. the roughness-induced conversion of a surface plasmon polariton propagating on it into volume electromagnetic waves in the vacuum above the surface. Perturbative and numerical simulation calculations carried out for surfaces generated in this way show that they indeed suppress leakage.Comment: Revtex 6 pages (including 4 figures

GPR clutter amplitude processing to detect shallow geological targets

The analysis of clutter in A-scans produced by energy randomly scattered in some specific geological structures, provides information about changes in the shallow sedimentary geology. The A-scans are composed by the coherent energy received from reflections on electromagnetic discontinuities and the incoherent waves from the scattering in small heterogeneities. The reflected waves are attenuated as consequence of absorption, geometrical spreading and losses due to reflections and scattering. Therefore, the amplitude of those waves diminishes and at certain two-way travel times becomes on the same magnitude as the background noise in the radargram, mainly produced by the scattering. The amplitude of the mean background noise is higher when the dispersion of the energy increases. Then, the mean amplitude measured in a properly selected time window is a measurement of the amount of the scattered energy and, therefore, a measurement of the increase of scatterers in the ground. This paper presents a simple processing that allows determining the Mean Amplitude of Incoherent Energy (MAEI) for each A-scan, which is represented in front of the position of the trace. This procedure is tested in a field study, in a city built on a sedimentary basin. The basin is crossed by a large number of hidden subterranean streams and paleochannels. The sedimentary structures due to alluvial deposits produce an amount of the random backscattering of the energy that is measured in a time window. The results are compared along the entire radar line, allowing the location of streams and paleochannels. Numerical models were also used in order to compare the synthetic traces with the field radargrams and to test the proposed processing methodology. The results underscore the amount of the MAEI over the streams and also the existence of a surrounding zone where the amplitude is increasing from the average value to the maximum obtained over the structure. Simulations show that this zone does not correspond to any particular geological change but is consequence of the path of the antenna that receives the scattered energy before arriving to the alluvial depositsPeer ReviewedPostprint (published version

Scattering Models and Basic Experiments in the Microwave Regime

The objectives of research over the next three years are: (1) to develop a randomly rough surface scattering model which is applicable over the entire frequency band; (2) to develop a computer simulation method and algorithm to simulate scattering from known randomly rough surfaces, Z(x,y); (3) to design and perform laboratory experiments to study geometric and physical target parameters of an inhomogeneous layer; (4) to develop scattering models for an inhomogeneous layer which accounts for near field interaction and multiple scattering in both the coherent and the incoherent scattering components; and (5) a comparison between theoretical models and measurements or numerical simulation

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure