The complex envelope (CE) FDTD method and its numerical properties

The complex envelope (CE) finite-difference time-domain (FDTD) method has been proposed for solving electromagnetic fields of limited frequency-bands. However, it has been formulated often in terms of wave equations. In addition, its numerical properties have not been thoroughly studied. In this paper, a full-wave CE-FDTD method is presented and its numerical stability and dispersion properties are analyzed. It is found that if the carrier frequency is sufficiently high or numerical cell sizes are adequately large, the time step is no longer bounded by the stability condition; otherwise the time step is constrained by a CFL like stability condition. However, through the numerical dispersion analysis, the errors caused by large time step are not acceptable. Thus the CE-FDTD does not present much gain in computation efficiency over the conventional FDTD.