Electromagnetic scattering from multilayer rough surfaces based on extended boundary condition formulation and transition matrix approach

The electromagnetic scattering of rough surface has been investigated extensively for the past decades. There exist analytical solutions to rough surface scattering such as small perturbation method (SPM) or Kirchhoff approximation (KA). These analytical solutions, however, are limited to either small or large roughness regimes. Recent efforts have been put forth to study scattering from multilayer rough surface in the application of deep soil moisture estimation. In this paper, multilayer rough surface scattering is analyzed based on an approach which combines extended boundary condition formulation (EBC) and transition matrix method. From the Floquet theorem, the Floquet modes translate into the coherent reflection and transmission coefficients in their corresponding scattering directions. To account for coherent multiple interactions between rough surface layers, transition matrix approach is used. Each Floquet mode direction is considered a port of a multiport system and network theory is used to characterize cascaded rough surface layers. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resultant Floquet modes in the scattering directions. Therefore, the electromagnetic wave interactions in multilayer rough surfaces are analyzed in a very efficient way by applying EBC to each rough surface and then cascading iteratively transition matrix of each layer interface. Finally, the results are validated against the analytical SPM solution to two-layer rough surface scattering.