Convergence of FDTD and wavelet-collocation modeling of curved dielectric interface with the effective dielectric constant technique

Abstract

The convergence of the effective dielectric constant (EDC) model of curved dielectric surfaces has been investigated precisely for the finite-difference time-domain (FDTD) as well as for the interpolet-collocation time-domain (ICTD) methods. The EDC is computed by solving the Laplace equation of static electric potential by a finite-difference (FD) method for each cell located on the interface of arbitrary dielectric media. The FD solution of the Laplace equation provides an accurate EDC for arbitrary curved interface with even high contrast of the dielectric constants. It has been demonstrated in this paper that the precisely chosen EDC allows both the FDTD and the wavelet-collocation methods to exhibit second-order convergence for the analysis of not only planar but also curved dielectric interfaces.