Rigorous Analysis of Numerical Phase and Group Velocity Bounds in Yee´s FDTD Grid

We present a systematic derivation of the extreme values of phase and group velocity in Yee´s finite difference time domain (FDTD) lattice with unequal aspect ratios. Using a Lagrange multiplier based approach; we derive necessary conditions that propagation vector components need to satisfy to attain extreme values in phase and group velocity. Knowledge of these extreme values is useful in designing low numerical dispersion FDTD schemes and also seeding numerical inversion routines of FDTD dispersion relations.