An analytical-numerical technique for the scattering problem of a plane wave by a cylinder buried under a rough surface, based on the Cylindrical Wave Approach, is presented. The rough deviations on the interface are dealt with by means of the Small Perturbation Method. Reflection and transmission coefficients are evaluated in a first order approximation, and fields are the sum of a zeroth-order solution, relevant to flat surface, and first-order perturbation fields, associated to the surface roughnesses. Numerical results are obtained through an exact evaluation of the spectral integrals, giving results both in nearand far-field regions, for the case of an interface with sinusoidal profile. The approach is validated through comparisons with the literature, and results showing the effect of geometrical and physical parameters on the scattered field are reported.

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The problem of scattering of electromagnetic waves from a set of cylindrical objects buried beneath a slightly rough surface is undertaken with the cylindrical wave approach as a method of analysis. The small perturbation method is used to compute the scattered field from a rough surface. Numerical results for a rough surface with a sinusoidal profile are obtained with asymptotic evaluation

Abstract-Method proposed by Maslov has been used, to remedy the problem of geometrical optics, for a two dimensional Perfect electromagnetic conductor (PEMC) Gregorian system. It generates an integral form of solution near the caustic that can be evaluated analytically/numerically, or with uniform asymptotic techniques. Away from the caustic it recovers the geometrical optics field. Numerical computations are made to calculate the field around the caustic of a Gregorian system.

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