Developments in the Finite-Difference Time-Domain Method for Electromagnetic Modeling

This report presents the derivation and evaluation of concepts in the finite-difference time-domain (FDTD) method for electromagneticmodeling. I show that the incident field time derivative required for the scattered-field method can be obtained from the spatial derivative ofthe incident-field and that a sixth-order central difference equation is a cost effective means to generate the derivative of the incidentfield asopposed to the analytic derivative. I present background on boundary condition concepts starting with one-dimensional FDTD before turning to two-dimensional FDTD where I show that the split-field formulation of the Berenger Perfectly Matched Layer (PML) method can be generalized with other one-dimensional FDTD boundary conditions rather than just lossy material layers. In the development of one-dimensional boundary conditions, I show that the formula for splitting an electromagnetic field into components traveling in opposite directions can be used to develop a series of one-way boundary conditions, which perform better than those developed from the factorization of the wave equation. In the last section of the report, I develop a split-field, one-way boundary condition for two-dimensional FDTD that is far less expensive than the widely used PML methods, which even for two-dimensional FDTD require over 27 different PML/FDTD update equations along with interface equations between the nine different PML/FDTD regions.