Scattering and depolarization upon transmission across and multiple reflections from irregular multi-layered structures

In this work the full wave approach (Bahar 1973a, 1973b) is used to predict electromagnetic wave scattering and depolarization upon reflection and transmission through irregular stratified media. The multi-layered structure considered consists of three media (air, coating material, and substrate). They are separated by rough or flat interfaces. The structure is illuminated from air, the random rough surface is at the air-coating interface and the coating-substrate interface is assumed to be flat. The probability density function of the random rough surface is assumed to be represented by a family of gamma functions. The expressions for the scattered fields are developed. These expressions are shown to reduce to the classical results for (uniform) parallel stratified structures that can be expressed in closed form in terms of the Fresnel reflection and transmission coefficients. Combinations of the expressions are averaged over the random rough surface heights and slopes) to yield expressions for the scattered intensities. The polarized intensities are completely represented by the 4 $\times$ 4 Mueller matrix. The Mueller matrix relates the incident Stokes vector to the Stokes vector scattered from the irregular stratified structure. The Stokes vector is a representation of the polarized intensity of power of an electromagnetic wave. Results of this analytical and numerical analysis is intended for two principal applications, remote sensing and thin film technology. The Mueller matrix provides like and cross polarized scattering cross section data as well as relative phase data. Therefore they can be used to obtain the ellipsometric parameters. Modified Mueller matrix elements are also computed because of the explicit relationships between the scattering cross sections and the elements of the Modified Mueller matrix. Illustrative examples are provided to demonstrate the effects of varying the irregular stratified structure parameters (including root mean square (rms) height, rms slope, and correlation length) on the ellipsometric parameters and the backscatter Modified Mueller matrix. Comparisons with measurements of a single interface and stratified medium are shown for the Mueller matrix