On numerical artifacts of the complex envelope ADI-FDTD method

We examine two spurious numerical artifacts of the complex envelope (CE) alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method, viz. spurious charges and anomalous wave propagation (modes with positive phase velocity and negative group velocity). These artifacts are also present in the conventional ADI-FDTD; however, the spurious charges in CE-ADI-FDTD have a fundamental distinction from those of ADI-FDTD: they are static in ADI-FDTD and implicitly time-harmonic in CE-ADI-FDTD. Spurious charges are particularly detrimental to CE-ADI-FDTD simulations because they produce secondary radiation. We also show that spurious charges can be reduced by a fixed-point iterative correction in CE-ADI-FDTD. Index Terms--Alternating-direction-implicit finite-difference time-domain (ADI-FDTD), complex envelope (CE), divergence, spurious mode.