Transient analysis of distributed electromagnetic systems exhibiting stochastic variability in material parameters

The mathematical framework of polynomial chaos is used to develop an FDTD-based model for transient electromagnetic wave interaction with stochastic media. Making use of orthogonal polynomials for the expansion of the stochastic material quantities and the unknown electromagnetic fields in the probability space of interest, a model is put forward that, in principle, allows for the direct calculation of the resulting stochastic electromagnetic response through a standard FDTD integration of a deterministic system with state variables the coefficients in the polynomial chaos expansion of the stochastic electric and magnetic field time histories at the nodes of the finite difference grid. The resulting computer model is demonstrated through the transient simulation of electromagnetic wave interactions with inhomogeneous dielectric regions inside two-dimensional parallel-plate waveguides.