The path integral time-domain method for electromagnetic scattering

Abstract

A full wave analysis of the electromagnetic field in the time-domain derived from R. P. Feynman’s path integral is examined. The propagator, which evolves the fields through successive time steps, comes from a state variable solution to Maxwell’s timedomain differential equations in tensor form. A numerical method o f evaluating the path integral provides analysis of electromagnetic scattering. An investigation of numerical stability and numerical dispersion illustrate attractive features o f this method. A discussion about numerical error in homogeneous regions illuminates another positive trait. Simulating exterior problems and removing the wrap around effect of Fourier Transforms requires an absorbing boundary condition (ABC). Perfectly matched layers and the ‘null boundary’ (unique to this method) provide first step absorbing boundary conditions. Details and examples of the path integral time-domain (PU D) method are presented for one-dimensional and two-dimensional spaces.