Scattered field in random dielectric inhomogeneous media : a random resolvent approach

In modeling electromagnetic phenomena randomness of the propagation medium and of the dielectric object should be taken up in the model. The usually applied Monte-Carlo based methods reveal true characteristics of the random electromagnetic field at the expense of large computation time and computer memory. Use of expansion based methods and their resulting algorithm is an efficient alternative. In this paper the focus is on characteristics of electromagnetic fields that satisfy integral equations where the integral kernel has a random component, typically, electromagnetic fields that describe scattering due to dielectric objects with an inhomogeneous random contrast field. The assumption is that the contrast is affinely related to a random variable. The integral equation is of second kind Fredholm type so that its solutions are determined by the resolvent, a random operator field. The key idea is to expand that operator field with respect to orthogonal polynomials defined by the probability measure on the underlying sample space and to derive the properties of the solution from that expansion. Two types of illustration are presented: an inhomogeneous dielectric slab and a 2D dielectric grating with 1D periodicity.