Numerical simulations of emission for two-dimensional randomly rough surfaces with an inhomogeneous layered medium are presented. The inhomogeneous layered medium is modeled by a generalized n-layered stratified media. The numerical method was adopted from the physics-based two-grid method (PBTG). To ensure the strict accuracy requirement while to relief the memory and CPU resources, the PBTG in conjunction with the sparse-matrix canonical grid method (SMCG) was used in this paper. In so doing the reflected terms of the dyadic Green's function that accounts for layered media were added into the integral equations governing the surface tangential fields. Since the reflected part of the dyadic Green's function does not contain any singularity, the normal components of the fields remain the same as in the case of homogeneous surfaces. It was found that the elements of Green's tensor are only important to the near-field since they decay very fast as spatial distance goes beyond a few wavelengths. The resulting integral equations are then solved by the Method of Moment (MoM). Comparisons between the inhomogeneous and the homogeneous rough surfaces suggest that the presence of the inhomogeneous layered medium has non-negligible contributions to emission, depending on the dielectric gradient and is polarization dependent.
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