Propagator Methods in Electromagnetics

A propagator is a subclass of Green functions that operate directly on a wave function known throughout a region of space, thereby evolving that wave function to its value at a given future time or, in some cases, to a given spatial distance. In a homogeneous region, the field at any future time and position in space requires only a single propagator calculation. In an inhomogeneous region, a numerical method with a small time increment is required to accommodate changes in waves propagating through position-dependent medium parameters and boundaries. This spatiotemporal incremental application of the propagator is described as a path integral. Several propagator methods have been developed for the electromagnetic field over the last 31 years. These include the Fourier-transform path integral method, stationary phase Monte Carlo method, path integral time-domain method, and propagator method. Each of the first three methods has its limitations, whether spatial, temporal, or dimensional. However, taken as a whole, they lead to the general full-wave propagator method, which is the most significant of all because it features a complete closed-form full-wave Green function solution to the time domain tensor form of Maxwell’s differential equations.