Simple Implementation of Arbitrarily Shaped Total-field/scattered-field Regions in Finite- Difference Frequency-domain

The total-field/scattered-field (TF/SF) formulation is a popular technique for incorporating sources into electromagnetic models like the finite-difference frequency-domain (FDFD) method. It is versatile and simplifies calculation of waves scattered from a device. In the context of FDFD, the TF/SF formulation involves modifying all of the finite-difference equations that contain field terms from both the TF and SF regions in order to make the terms compatible. While simple in concept, modifying all of the equations for arbitrarily shaped TF/SF regions is tedious and no solution has been offered in the literature to do it in a straightforward manner. This paper presents a simple and efficient technique for implementing the TF/SF formulation that allows the TF/SF regions to be any shape and of arbitrary complexity. Its simplicity and versatility are demonstrated by giving several practical examples including a diffraction grating, a waveguide problem, and a scattering problem with a cylindrical wave source.