Transient modal analysis of quasi-implicit FDTD schemes

Time domain simulations for high-frequency applications are widely dominated by the leapfrog time-integration scheme, especially in combination with finite-difference methods (FDTD) or the finite integration technique (FIT). As an explicit method, however, the leapfrog algorithm is restricted to a maximum stable time step, and recently some alternative, unconditionally stable techniques have been proposed to overcome this limitation. We analyze such schemes using a transient modal decomposition of the electric fields. It is shown that stability alone is not sufficient to guarantee correct results, but additionally important conservation properties have to be met.