A Stochastic Scattered-Field FDTD Formulation Using a Highly Efficient FDTD Discrete Plane Wave Source for Weak Scattering Environments

A scattered-field only version of the stochastic FDTD formulation is introduced for detecting and quantifying small variations in weakly scattering environments. To broaden the applicability of the formulation, the highly efficient FDTD discrete plane wave source is also presented for a scattered-field only code. The discrete plane wave source, which introduces plane waves into an FDTD grid at the level of machine precision, has previously been presented for total-field scattered-field FDTD formulations, but not yet for scattered-field only FDTD models. Compared to total-field scattered-field models (TFSF), scattered field-only codes permit a slightly reduced total number of grid cells in the model and more efficient computations, they are easier to parallelize onto supercomputers, and they are simpler to use when modeling materials that would normally extend across the TFSF interfaces. To validate the methodologies, we first demonstrate that an FDTD discrete plane wave source within a scattered-field FDTD grid produces results consistent with the TFSF total-field version. Following this, a weakly scattering medium is tested and compared with Monte Carlo results to showcase the utility of the stochastic scattered-field FDTD formulation having a discrete plane wave source.