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Modeling and Predicting Surface Roughness via Transformation Optics

Monte Carlo analysis of surface roughness in electromagnetic scattering problems is presented by using the principles of transformation electromagnetics/optics in finite methods. The main motivation in the proposed approach is to eliminate the need of mesh generation for each surface in repeated Monte Carlo realizations, and hence, to devise a faster model in predicting surface roughness. A single, simple and uniform mesh is employed assuming a smooth surface and ignoring the actual surface, and thereafter, a transformation medium is designed on the smooth surface to make this problem equivalent to the original problem with actual surface. The material parameters of the transformation medium are determined by transforming the smooth surface to the actual surface through a specially-defined coordinate transformation. The technique is demonstrated via various finite element simulations.