Characterization of the Numerical Group Velocity in Yee's FDTD Grid

A method is introduced for the optimization of the numerical group velocity in standard finite-difference time-domain (FDTD) electromagnetic simulations. Through this method analytical expressions for the extrema of are presented for the first time, thus also characterizing its anisotropy. The knowledge of these expressions is hence essential for the evaluation of the anisotropy error in FDTD-based electrodynamics simulations of the propagation of wavepackets in 2D and 3D. This can be of assistance, for example, in the design of error-bounded FDTD simulations with pulsed sources at low computational cost.