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

Abstract

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the Müller 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 both diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well-satisfied for the non-absorbing case (U > 0.995), a result that testifies to the accuracy of our approach. PACS numbers:The scattering of electromagnetic waves from twodimensional randomly rough penetrable surfaces has been studied theoretically for more than five decades. The methods used in these studies in recent years, where attention has been directed toward multiple-scattering phenomena, have been either analytical in nature or computational. Chief among the former methods has been the small-amplitude perturbation theory [1-3], while several different computational methods have been used in solving the scattering problem. In the earliest calculation of this type [4] the system of coupled inhomogeneous integral equations for the tangential components of the total electric and magnetic fields on the rough surface obtained from scattering theory, was converted into a system of inhomogeneous matrix equations by the use of the method of moments [5], which was then solved by Neumann-Liouville iteration [6]. This is a formally exact approach but one that is computationally (and memory) intensive.In subsequent work on this problem approximate solutions of the exact integral equations have been sought. In the sparse-matrix flat-surface iterative approach [7,8] the matrix elements for two close points on the surface are treated exactly, while those connecting two widely separated points are treated approximately, in an iterative solution of the matrix equations.Soriano and Saillard [9] have combined the sparsematrix flat-surface iterative approach with an impedance approximation [10] to calculate co-polarized and crosspolarized bistatic scattering coefficients of aluminum randomly rough surfaces for comparison with results obtained from perfectly conducting surfaces.An approach that combines the fast multipole method [11] and the sparse-matrix flat-surface iterative approach has been developed by Jandhyala et. al [12].Despite these advances, the calculation of the scattering of electromagnetic waves from two-dimensional, penetrable, randomly rough surfaces, remains a computationally intensive problem, in need of further improvements in the methods used to solve it.In this paper we use the Fran...

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