Convergence of FDTD and Wavelet-Collocation Modeling of Curved Dielectric Interface with the Effective Dielectric Constants Obtained by Static Field Analysis

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 wavelet-collocation method based on interpolets. The EDCs are computed by solving the Laplace equation of static electric potential by a finite-difference (FD) method for the cells located on the interface of arbitrary dielectric media. The finite-difference solution of the Laplace equation provides accurate EDCs for arbitrary curved interface with even high contrast of the dielectric constants. It has been demonstrated that the precisely chosen ECDs allow both the FDTD and the wavelet-collocation methods to exhibit second-order convergence for the analysis of not only plane boundaries but also curved dielectric interfaces.