Inversion of in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a two-dimensional randomly rough metal surface (original) (raw)
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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.
Physical Review A, 2016
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional randomly rough dielectric surface when the latter is illuminated by s-polarized light. This result forms the basis for an approach to inverting experimental light scattering data to obtain the normalized surface height autocorrelation function of the surface. Several parametrized forms of this correlation function, and the minimization of a cost function with respect to the parameters defining these representations, are used in the inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the dielectric substrate if it is not known in advance. The input data used in validating this inversion consists of computer simulation results for surfaces defined by exponential and Gaussian surface height correlation functions, without and with the addition of multiplicative noise, for a single or multiple angles of incidence. The reconstructions obtained by this approach are quite accurate for weakly rough surfaces, and the proposed inversion scheme is computationally efficient.
Physical Review A, 2021
An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p-and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.
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.
Resonance effects in multiple light scattering from statistically rough metallic surfaces
Physical Review B, 1992
Multiple scattering of light from one-dimensional random rough metallic surfaces is numerically studied by means of a Monte Carlo simulation method based on the extinction-theorem boundary conditions. Angular and integrated distributions of the mean scattered intensity are computed for several values of the angle of incidence, state of polarization, surface statistical parameters, and dielectric permittivity. Two main regimes are addressed, depending on whether the surface correlation length T is larger or smaller than the wavelength A, . In the first case, we observe enhanced backscattering both for s and p waves, whereas in the latter situation there exist substantial absorption effects under p polarization, linked to the excitation of surface polaritons. In addition, calculations are made of field enhancements on the surface, owing either to surface-polariton excitation in the small-correlation-length case (T & A, ), or to multiple scattering and generation of other kinds of surface wave in the large-correlation-length case (T & A, ).
2002
This paper presents an evaluation of three perturbation theories and the Kirchhoff approximation for calculating the reflectance Í‘the intensity of the coherent componentÍ’ of two-dimensional metallic surfaces with a random roughness distribution. The theoretical results are compared with experimental data obtained on typical samples. The samples were fabricated from photoresist, and their metallized surface profiles are a good match with a Gaussian correlation function and a Gaussian random process. The correlation distances of these surfaces range from approximately one-fifth to two wavelengths of the IR range used in the experiment.
Physical Review A, 2012
We calculate all the elements of the Mueller matrix, which contains all the polarization properties of light scattered from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations for the scattering of p- and s-polarized light from a two-dimensional rough penetrable surface. The ability to model polarization effects in light scattering from surfaces enables better interpretation of experimental data and allows for the design of surfaces which possess useful polarization effects.
Physical Review B
This article demonstrates an elegant method for experimental retrieval of the buried phase information of optical phenomena at metallic-dielectric interfaces, especially surface plasmon polaritons (SPP), employing a model explicitly based on roughness-induced cross-polarization scattering. This inherent roughness of the interfaces within typical SPP Attenuated Total Reflection (ATR) setups leads to two interlinked phenomena: Angular broadening and cross-polarization scattering. The microscopic interface features generate altered polarization vectors which are comparably weak but, because of their orthogonal polarization direction, appreciable within the specularly reflected light. The information contained in this s-polarized light enables us to retrieve the phase information of SPPs through the interference model of cross-polarization scattering described here. On that basis, this article demonstrates the retrieval of phase shifts for multiple silver thicknesses of SPPs generated within an ATR geometry. Additionally, the method permits the evaluation of surface roughness parameters, characterization of the angular broadening of reflection, and determination of the thicknesses of the metallic layers.
Scattering by random rough surfaces: Study of direct and inverse problem
Optics Communications, 2006
In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell's equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier's integral form. The solution is found by using a perturbation method applied to the smooth surface problem; this is fully justified when the defects are of small magnitude. For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation. In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.
Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces
Physical Review A, 2012
We calculate all the elements of the Mueller matrix, which contain all the polarization properties of light scattered from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations for the scattering of p-and s-polarized light from a two-dimensional rough penetrable surface.