Statistical distribution of the field scattered by rough layered interfaces: formulae derived from the small perturbation method

Abstract

We present a statistical study of electromagnetic wave scattering by a stack of two random rough interfaces that are characterised by Gaussian distributed heights and by exponential correlation functions. These interfaces can be correlated or not. The coherent and incoherent intensities and the statistical distribution of the scattered field in modulus and phase are obtained using the Rayleigh expansion and the small perturbation method. For a structure of finite extension, we show that the modulus follows a Hoyt law and the phase is not uniform. For a structure of infinite extension, whether the interfaces are correlated or not, the modulus of the field follows a Rayleigh law while the phase is uniform.