Numerical boundary conditions for the fourth-order accurate finite-difference time-domain solution of Maxwell's equations

Development of accurate numerical boundary conditions for metallic boundaries and dielectric interfaces is the key to the proper implementation of high-order finite-difference time-domain (FDTD) methods for Maxwell's equations. In this dissertation, a new set of numerical boundary conditions at perfectly conducting walls and dielectric interfaces is proposed for Fang's fourth-order FDTD schemes. The eigenvalue analysis of the fully discrete systems shows the influence of boundary conditions on the original fourth-order schemes. Numerical experiments using two- and three-dimensional rectangular cavities verify that the proposed numerical boundary conditions preserve the fourth-order accuracy of Fang's schemes. Simulations of electromagnetic wave propagations through rectangular waveguides demonstrate that the enhanced high-order schemes produce much smaller phase errors compared to the second-order FDTD methods. As a consequence, the enhanced fourth-order Fang's schemes reduce the computational cost by more than two orders of magnitude in practical time domain electromagnetic simulations of three-dimensional structures composed of conductors and dielectrics. Applications in nonradiative dielectric (NRD) waveguide structures illustrate the promising capabilities of the enhanced fourth-order FDTD schemes for time domain simulations of electrically long microwave/millimeter wave and optoelectronic devices.