MULTIPLE SCATTERING FROM A RANDOM AND INHOMOGENEOUS SLAB
The reflection and transmission functions of an inhomogeneous slab are calculated by labeling the wave by the number of reflections it has undergone in the medium. The Riccati equation, satisfied by the reflected amplitude, is decomposed into a finite set of linear equations by taking into account the number of scatterings taking place inside the medium and is solved by a novel iterative approach. The order-of-scattering reflection functions method presented here and the coupled integral equation approach of the Bremmer solutions for the internal fluxes are set in a unified frame. The solutions of the Riccati equation are computed numerically for the reflection function using the order-of-scattering technique, and it is demonstrated that the method leads to better convergence and stability as compared to usual linearization methods. The Order-of-Scattering Solutions (BVU Series) of the Riccati Equation for the reflection function of an inhomogeneous slab are used to calculate the mean power intensity for a medium having random fluctuations of its dielectric constant. A solution for a Fokker-Planck-like differential equation for the joint probability density of the real and imaginary parts of the reflection function is obtained using a technique due to Van Kampen for nonlinear equations with multiplicative noise. The mean reflected power calculated from the probability density function is in agreement with that derived from the BVU solution. These results are in good agreement with the works of earlier investigators.
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