Modeling of near-field sources in the finite-difference time-domain (FDTD)

A method is outlined to represent near-field sources in the FDTD method by way of spherical wave expansions. Spherical wave modal amplitude functions are time-stepped on alternate 1-dimensional grids (in radius and time) analogous to plane waves in the total/scattered field formulation, with angular functions interpolated later. Initial validation is presented by comparing to the analytic solutions for a spherical resonator, and for an infinitesimal dipole, both showing excellent agreement. A brief discussion on the stability criterion is also presented. This method will allow the modeling of source (e.g. antenna) and scatterer interactions in the near-field without explicitly modeling the source. As a result, the computational resources necessary will be greatly reduced, allowing for faster runtimes and more complicated geometries.