Grid-dispersion error reduction for broadband FDTD electromagnetic simulations

We introduce a general procedure to reduce grid (numerical) dispersion error in broadband finite-difference time-domain (FDTD) simulations based on dispersion filters. Dispersion error functionals are first expanded in a Taylor series that, for a broadband signal, produces larger dispersion- errors for the highfrequency components of the signal. By a change of polynomial basis, modified FDTD update coefficients are obtained in order to minimize the dispersion error over some preassigned frequency band. Moreover, desirable properties such as a local dispersion error that decreases within a frequency band can also be attained. In particular, Butterworth (maximally flat) or Chebyshev polynomial expansions (filters) are considered along with their application toward the optimization of two recently developed high-order FDTD schemes.