Rigorous integral approach to the problem of scattering from a modulated periodic medium obtained through conformal mapping

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Abstract
The method described is an alternative way to solve, by means of a rigorous integral method, the problem of electromagnetic scattering from a typical periodic medium. This medium is issued from a particular conformal mapping that transforms a periodic surface-relief grating into a volume grating bounded by a perfect mirror. Thus the method indirectly solves the problem of scattering from a perfectly conducting rough grating and leads to a single integral equation of the Fredholm type with a simple kernel for each fundamental polarization. Numerical solution of the equation is computed through Gaussian integration, and computing time is less than 1 s per point on a workstation. Application is then made to different types of grating such as cycloidal, blaze, and N-level binary gratings coated with a highly conducting metal such as silver or gold.