Replacement of ensemble averaging by the use of a broadband source in scattering of light from a one-dimensional randomly rough interface between two dielectric media

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.Comment: 10 pages, 7 figure

The Scattering of Electromagnetic Waves from Two-Dimensional Randomly Rough Perfectly Conducting Surfaces: The Full Angular Intensity Distribution

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.Comment: 15 pages (RevTeX

The Angular Intensity Correlation Functions C(1)C^{(1)} and C(10)C^{(10)} for the Scattering of S-Polarized Light from a One-Dimensional Randomly Rough Dielectric Surface

We calculate the short-range contributions $C^{(1)}$ and $C^{(10)}$ to the angular intensity correlation function for the scattering of s-polarized light from a one-dimensional random interface between two dielectric media. The calculations are carried out on the basis of a new approach that separates out explicitly the contributions $C^{(1)}$ a nd $C^{(10)}$ to the angular intensity correlation function. The contribution $C^{(1)}$ displays peaks associated with the memory effect and the reciprocal memory effect. In the case of a dielectric-dielectric interface, which does not support surface electromagnetic surface waves, these peaks arise from the co herent interference of multiply-scattered lateral waves supported by the in terface. The contribution $C^{(10)}$ is a structureless function of its arguments.Comment: LaTeX, 14 pages including 5 figures. To appear SPIE publicatio

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

The Scattering of Electromagnetic Waves from Two-Dimensional Randomly Rough Penetrable Surfaces

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a two-dimensional rough surface yields a pair of coupled two-dimensional integral equations for the sources on the surface in terms of which the scattered field is expressed through the Franz formulas. By this approach, we calculate the full angular intensity distribution of the scattered field that is due to a finite incident beam of $p$-polarized light. We specifically check the energy conservation (unitarity) of our simulations (for the non-absorbing case). Only after a detailed numerical treatment of {\em both} diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well-satisfied for the non-absorbing case (${\mathcal U}>0.995$), a result that testifies to the accuracy of our approach.Comment: Revtex, 4 pages, 2 figure

Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study

We study by numerical simulations 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 $\epsilon_2$ of the dielectric constant of the film. We study the reflectance ${\cal R}$ and the total scattered energy ${\cal U}$ for the system as functions of both $\epsilon_2$ 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 scale linearly with $\epsilon_2$. The positions of the backscattering peaks are found to be independent of $\epsilon_2$, while we find a weak dependence on this quantity in the positions of the satellite peaks.Comment: Revtex, 9 pages, 9 figure

Waves in gradient metamaterials

This book opens a new avenue to an engendering field of applied physics, located at the “crossing” of modern photonics, electromagnetics, acoustics and material science. It also highlights the concept of “non-locality”, which proves to be not a special feature of quantum phenomena, but is shown to have an important counterpart in classical physics and its engineering applications too. Furthermore, it visualizes the physical results by means of simple analytical presentations, reduced sometimes to the elementary functions