Abstract
The C method is known to be one of the most efficient and versatile tools established for modeling diffraction gratings. Its main advantage is the use of a coordinate system in which the boundary conditions apply naturally and are, ipso facto, greatly simplified. In the context of scattering from random rough surfaces, we propose an extension of this method in order to treat the problem of diffraction of an arbitrary incident beam from a perfectly conducting (PEC) rough surface. For that, we were led to revisit some numerical aspects that simplify the implementation and improve the resulting codes.
Highlights
Actual surfaces are necessarily rough, and the main difficulty encountered in the modeling of their interaction with electromagnetic waves is related to their level of roughness
In the present paper we focus, for the sake of conciseness, on the case of a Gaussian rough surface with Gaussian spectrum made of a perfectly conducting (PEC) material and illuminated by a limited beam
As the lower medium is perfectly conducting, the electric fields are null inside it, and writing the boundary conditions consists in nullifying the tangential components ⌿ or ⌽ according to the polarization, on the surface S given by v = 0
Summary
Actual surfaces are necessarily rough, and the main difficulty encountered in the modeling of their interaction with electromagnetic waves is related to their level of roughness. Two approximate methods have been developed to study rough surfaces with weak roughness and led to analytic expressions of the diffracted intensity in terms of the statistical parameters of the surfaces such as the rms and correlation length lc Among these methods, the most known is the perturbation theory applied to the integral equation of the field [1]. In the so-called resonant domain where the geometrical features of the scattering surface are of the order of magnitude of the wavelength, rigorous solutions of the diffraction problem are necessary This is why exact formalisms have been developed, and one can roughly divide them in two main categories: integral methods [4,5,6,7] and differential methods [8]. The method is tested numerically against usual criteria of energy conservation and our computations are compared to results taken from the literature and based on both integral methods [15] and differential methods [8]
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