Second-Order Perturbative Solution of Cross-Polarized Scattering From Multilayered Rough Surfaces

An analytical solution for the cross-polarized scattering from multilayered media with an arbitrary number of rough interfaces is presented. The second-order perturbative solutions are summations of the Fourier transform pair products of the roughness profiles, and hence, the problem is initially reduced to two generic problems: one with just a single rough surface with two stratified media above and below it and another with two rough interfaces with three stratified media above, between, and below them. The former helps find the second-order contribution of an individual rough interface while the latter is intended to determine the interaction contribution of two arbitrary rough interfaces. In this paper, the second generic problem is solved using the small perturbation method (SPM) based on the extended boundary conditions (EBC). In this SPM formulation, the stratifications are easily accounted for using the generalized coefficients inserted in the dyadic Green's functions (DGFs). Then, the expressions are simplified to find the solution of the first generic problem which is a special case of the second one. Next, the explicit expressions of the generalized coefficients are introduced to the solutions. Subsequently, the interaction terms of the second and the self-term of the first generic problem are combined to find the desired second-order solution. Finally, using the solution derived, a few numerical examples are presented.