Numerical Dispersion in the "Complex-Envelope" FDTD Methods and the Sampling Theorem

The implicit FDTD methods are free of the usual constraint (i.e. the CFL-condition) imposed on the upper limit of the time propagation step in the standard FDTD formulation. Although the time propagation step can be arbitrarily chosen, there are limits set by the Shannon sampling theorem in relation to the numerical phase velocity of wave propagation. It is shown here that they can be further relaxed using the "complex envelope "formulation