Optimizing the Gaussian excitation function in the finite difference time domain method

A systematic method is presented for determining the optimal pulsewidth and variance of a Gaussian excitation function in the finite difference time domain (FDTD) method. We highlight the interaction of several criteria, such as the stability condition, machine precision limits, the numerical grid cutoff frequency, and the dispersion relation, that play crucial roles in the design of the initial pulse. Optimal Gaussian pulse design is desirable if numerical dispersion, an inherent yet unavoidable property of the standard second-order FDTD Yee algorithm, is to be minimized. A method for determining the phase error of a Gaussian pulse is also presented.