A periodically corrugated interface between vacuum and a high-index dielectric medium supports a p-polarized leaky surface electromagnetic wave whose sagittal plane is perpendicular to the generators of the interface. This wave is bound to the surface in the vacuum region, but radiates into the high-index dielectric medium. We study the excitation of this wave by p-polarized light incident from a prism on whose planar base the highindex dielectric medium in the form of a film is bonded. The unilluminated surface of the film is periodically corrugated, and is in contact with vacuum. Peaks and dips in the dependence of several low-order diffraction efficiencies on the angle of incidence (Wood anomalies) are the signatures of the excitation of the surface wave.

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## Scholarly Works (23 results)

By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.

By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity and the efficiencies of several other diffracted orders when the periodically corrugated surface of an isotropic elastic medium is illuminated by a volume acoustic wave of shear horizontal polarization. These dependencies display the signatures of Rayleigh and Wood anomalies, usually associated with the diffraction of light from a metallic grating. The Rayleigh anomalies occur at angles of incidence at which a diffracted order appears or disappears; the Wood anomalies here are caused by the excitation of the shear horizontal surface acoustic waves supported by the periodically corrugated surface of an isotropic elastic medium. The dispersion curves of these waves in both the nonradiative and radiative regions of the frequency-wavenumber plane are calculated, and used in predicting the angles of incidence at which the Wood anomalies are expected to occur.

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. 〈∂Rν/∂θ〉incoh (ν = p,s), is obtained nonperturbatively. It is demonstrated that when the scattering geometry supports at least two guided waves, 〈∂ν/∂θ〉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.

We study the statistical properties of the scattering matrix S (q/k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x3 = ζ(x1), where the surface profile function ζ(x1) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S (q/k) on the angular intensity correlation function C(q, k/q′, k′) = - , where the intensity I(q/k) is defined in terms of S(q/k) by I(q/k) = L1-1(ω/c)|S(q/k)|2, with L1 the length of the x1 axis covered by the random surface. We focus our attention on the C(1) and C(10) correlation functions, which are the contributions to C(q, k\q′, k′) proportional to δ(q - k - q′ + k′) and δ(q - k + q′ - k′), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C(10) correlation function are determined by exactly the same statistical moment of S(q/k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C(10) correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.

A nonperturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of p- and s-polarized light from a dielectric film with a two-dimensional randomly rough surface deposited on a planar metallic substrate, has been carried out. It is found that satellite peaks are present in the angular dependence of the elements of the mean differential reflection coefficient in addition to an enhanced backscattering peak. This result resolves a conflict between the results of earlier approximate theoretical studies of scattering from this system.

By numerical simulations we study the scattering of s-polarized light from a rough dielectric film deposited on the planar surface of a semi-infinite perfect conductor. The dielectric film is allowed to be either active or passive, situations that we model by assigning negative and positive values, respectively, to the imaginary part (formula presented) of the dielectric constant of the film. We study the reflectance (formula presented) and the total scattered energy (formula presented) for the system as functions of both (formula presented) and the angle of incidence of the light. Furthermore, the positions and widths of the enhanced backscattering and satellite peaks are discussed. It is found that these peaks become narrower and higher when the amplification of the system is increased, and that their widths are linear functions of (formula presented) The positions of the backscattering peaks are found to be independent of (formula presented) while we find a weak dependence on this quantity in the positions of the satellite peaks. © 2001 The American Physical Society.

We show theoretically that the periodically corrugated surface of a high-index dielectric medium can support a leaky surface electromagnetic wave. This wave is bound to the surface in the vacuum, but radiates into the dielectric. Despite this radiative damping, the surface wave can have a long lifetime.

By a computer simulation approach we study the scattering of p- or s-polarized light from a two-dimensional, randomly rough, perfectly conducting surface. The pair of coupled inhomogeneous integral equations for two independent tangential components of the magnetic field on the surface are converted into matrix equations by the method of moments, which are then solved by the biconjugate gradient stabilized method. The solutions are used to calculate the mean differential reflection coefficient for given angles of incidence and specified polarizations of the incident and scattered fields. The full angular distribution of the intensity of the scattered light is obtained for strongly randomly rough surfaces by a rigorous computer simulation approach. © 2010 The American Physical Society.

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectivities for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.