Numerical stability and numerical dispersion of compact conformal mapping 2D-FDTD method used for the dispersion analysis of waveguides

In dispersion analysis of waveguides with particular cross-section by compa ct 2D-FDTD method, using conformal-boundary coordinates can obtain high com putational accuracy. The transformation from conformal-boundary coordinates to rectangular coordinates can be done by conformal mapping technique in o rder to match Yee algorithm. In this paper, numerical stability and numeric al dispersion equation of compact conformal mapping 2D-FDTD (CCM-2D-FDTD) m ethod are derived. It is shown that the upper limit of Courant number for C CM-2D-FDTD is always smaller than 1/root 2. As an example, the dispersion e quation is used to examine the impact of number of cell for circular wavegu ide.