Electromagnetic wave scattering from rough layered interfaces: analysis with the small perturbation method and the small slope approximation

We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic field in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitude under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented.