Scattering of electromagnetic waves from an N-layer dielectric structure with slightly rough boundaries

Random roughness is a representative model for many naturally occurring surface and sub-surface structures such as soil, ice, lakes, and rivers. Rough surfaces are also encountered in smaller scales such as optical instruments that use the surface plasmon resonance (SPR) technique to measure the refractive index of very thin layers of material adsorbed on a thin layer of metal. The knowledge of subsurface properties of layered media such as soil moisture is especially essential in the fields of environmental engineering, hydrology, soil physics, civil engineering, and planetary exploration. Therefore, an analytical, realistic, and fast method for calculating wave scattering from layered media becomes vital, especially because it can be used for inversion of their subsurface properties, where the forward model is evaluated many times, making numerical techniques often not desirable because of their computational burden. We present an analytical approach to finding the scattering coefficients of a general three-dimensional, N-layer dielectric structure with slightly rough boundaries. The solution to the two-layer case has been introduced by the authors in a previous article. The method presented here is the extension of that solution to a general case where all layers are rough and possibly correlated. We show that the first-order solution is achieved by solving two systems of linear equations. This method, in contrast to some of the previous methods, intrinsically takes into account multiple scattering processes between the boundaries, all of which are considered rough simultaneously. Therefore, our method is suitable for being extended to higher orders, because it does not rely on the assumption that each rough boundary contributes to the solution independently of the other boundaries, which is only true for the first-order solution. Another strength of this method is that amplitudes of the fields scattered into the inner layers are obtained simultaneously with thos- - e of the top medium