Power Reflection from a Lossy One-Dimensional Random Medium

We consider the problem of an electromagnetic plane wave normally incident upon a slab of material whose constitutive parameters are subjected to lossy random perturbations. A transmission line model is adopted, wherein the four distributed parameters are assumed to be strongly mixing random functions of distance along the line. We study the reflection of energy at the input in the diffusion limit, an asymptotic limit involving weak random perturbations and long transmission lines. In the presence of dissipation, the probability density function for the modulus of the reflection coefficient approaches a nontrivial limit as the line length approaches infinity. We compute the mean and fluctuations of the voltage and power reflection coefficients with respect to this limiting density as a function of the dissipation.