Numerical studies of the transmission of light through a two-dimensional randomly rough interface (original) (raw)
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Optics Express, 2016
The scattering of polarized light from a dielectric film sandwiched between two different semi-infinite dielectric media is studied experimentally and theoretically. The illuminated interface is planar, while the back interface is a two-dimensional randomly rough interface. We consider here only the case in which the medium of incidence is optically more dense than the substrate, in which case effects due to the presence of a critical angle for total internal reflection occur. A reduced Rayleigh equation for the scattering amplitudes is solved by a rigorous, purely numerical, nonperturbative approach. The solutions are used to calculate the reflectivity of the structure and the mean differential reflection coefficient. Optical analogues of Yoneda peaks are present in the results obtained. The computational results are compared with experimental data for the in-plane mean differential reflection coefficient, and good agreement between theory and experiment is found.
Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity
Physical review B, 1984
First-order perturbation theory is applied to calculate scattering of a plane wave from a planebounded, semi-infinite medium where the boundary surface has a roughness perturbation and the scattering medium consists of an isotropic perturbation of the dielectric permittivity. The dielectric perturbation is assumed to fluctuate randomly in the plane parallel to the surface and decay exponentially with depth into the surface. Both the roughness and dielectric permittivity perturbations, which are treated as random variables, can independently cause scattering, and there is generally interference between the two scattered fields. The scattered fields generally depend on the autocovariance functions of the surface roughness and dielectric fluctuations and on the crosscorrelation properties between them. For this reason, the polarization ratio of the pand spolarized scattered light fields depends on the autocovariance and cross-correlation statistical properties. This result is unlike the calculation of scattered fields caused by roughness or dielectric perturbations alone, since in this case the polarization ratios of the scattered fields do not depend on the statistical properties of the perturbation. The numerical results of this work are consistent with experimental measurements where the polarization ratio of light scattered from nominally identical silver films varies widely from surface to surface.
Light scattering from random rough dielectric surfaces
Journal of the Optical Society of America A, 1991
A theoretical and numerical study is made of the scattering of light and other electromagnetic waves from rough surfaces separating vacuum from a dielectric. The extinction theorem, both above and below the surface, is used to obtain the boundary values of the field and its normal derivative. Then we calculate the angular distribution of the ensemble average of intensity of the reflected and transmitted fields. The scattering equations are solved numerically by generating one-dimensional surface profiles through a Monte Carlo method. The effect of roughness a-and correlation distance T on the aforementioned angular distribution, as well as on the reflectance, is analyzed. Enhanced backscattering and new transmission effects are observed, also depending on the permittivity. The ratio o/T is large in all cases studied, and thus no analytical approximation, such as the Kirchhoff approximation (KA) and small perturbation methods, could a priori be expected to hold. We find, however, that the range of validity of the KA can be much broader than that previously found in perfect conductors.
Optics Express, 2012
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.
Journal of the Optical Society of America A, 2014
We present rigorous, nonperturbative, purely numerical solutions of the Rayleigh equations for the scattering of p-and s-polarized light from a two-dimensional randomly rough perfectly conducting surface. The solutions are used to calculate the reflectivity of the surface, the mean differential reflection coefficients, and the full angular distribution of the intensity of the scattered field. These results are compared with previously published rigorous numerical solutions of the Stratton-Chu equations, and very good agreement is found.
Light scattering by randomly rough isotropic dielectric surfaces
Journal of Modern …, 2000
An experimental investigation of the angular distribution of the light scattered by randomly rough, two-dimensional, isotropic dielectric surfaces is presented. T he surfaces, whose pro® les constitute good approximations to Gaussian random processes with Gaussian correlation functions, are fabricated in a photoresist and characterized by means of a mechanical pro® lometer. T he substrates employed in the fabrication of the samples consist of thick parallel plates of ® lter glass that absorb the incident light and whose refractive index is close to that of the photoresist. T his allows us to approximate experimentally a situation in which the light is scattered by a randomly rough interface between two semi-in® nite dielectric media, illuminated from the air side. T he results display features that can be attributed to multiple scattering. In particular, signi® cant amounts of cross-polarized scattered light, as well as an enhanced backscattering peak, were observed in the scattering measurements.
Frontiers in Physics, 2013
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the scattering of p-or s-polarized light from twodimensional dielectric or metallic randomly rough surfaces by calculating the full angular distribution of the co-and cross-polarized intensity of the scattered light. In particular, we present calculations of the mean differential reflection coefficient for glass and silver surfaces characterized by (isotropic or anisotropic) Gaussian and cylindrical power spectra. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization.
Electromagnetic wave scattering from a random layer with rough interfaces II: Diffusive intensity
2003
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical repartition is described by a pair-distribution function. The boundary contribution is included in the Green functions with the help of scattering operators which can represent any existing theory of scattering by rough surfaces. By using a standard procedure, we derive the integral Bethe-Salpeter equation under the ladder approximation and, by differentiation, the vectorial radiative transfer equation. Furthermore, with the help of our formalism, the boundary conditions necessary to solve the radiative transfer equation are expressed in terms of the scattering operators of the rough surfaces. Finally, using the reciprocity properties of the Green functions, we are able to include the enhanced backscattering contributions to take into account every state of polarization of the incident and the scattered waves.
Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study
Physical Review B, 2001
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 ε2 of the dielectric constant of the film. We study the reflectance R and the total scattered energy U for the system as functions of both ε2 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 ε2. The positions of the backscattering peaks are found to be independent of ε2, while we find a weak dependence on this quantity in the positions of the satellite peaks.
Reflection, Scattering, and Diffraction from Surfaces IV, 2014
An approach to inverting experimental light scattering data for obtaining the normalized surface height autocorrelation function of a two-dimensional randomly rough dielectric surface, and its rms height is presented. It is based on the expression for the contribution to the mean differential reflection coefficient from the in-plane, copolarized, light of s-polarization scattered diffusely from such a surface, obtained by phase perturbation theory. For weakly rough surfaces the reconstructions obtained by this approach are quite accurate.