Efficient High-Spatial-Order FDTD Analysis of 3D Optical Ring Resonator Filters

A high-spatial-order scheme of the finite-difference time-domain (FDTD) method has been applied to the three-dimensional (3D) full wave analysis of optical dielectric rib-waveguide circuits such as ring resonator filters. Due to the electrically large nature of the 3D optical circuits, the FDTD analysis of them has been significantly restrictive in computation. Precise investigation into the numerical dispersion of high-spatial-order schemes suggests the possibility of employing coarse discretization. By applying the high-spatial-order schemes to those problems, by virtue of their highly linear numerical dispersion property, we have achieved significant reduction in the number of cells compared to the standard FDTD, thus being capable of dealing with larger structures. The accuracy and the required computational resources are also compared. I. INTRO DUCTI ON The dielectric waveguides in optical communication systems typically have very large physical dimensions compared to the wavelength of the transmitted signals, and the numerical full-wave analysis of such waveguides requires very fine discretization to obtain sufficient accuracy, resulting in a significant amount of the required computational resources. Therefore, the beam propagation method (BPM) [1], which is computationally less expensive than other space-discrete methods, has been widely used. However, in the BPM, a wave equation is discretized and reflection is basically not taken into consideration. Moreover, the propagation constants of waves are predetermined in the BPM, and the numerical formulation requires complicated approximations in the analysis of practical structures such as strongly guiding waveguides and longitudinally varying waveguides [2], [3], [4]. For more rigorous analysis, the finite-difference time-domain (FDTD) formulation of Maxwell’s equations [5] has been applied to optical waveguide structures [6]. However, three-dimensional optical waveguide problems are often electrically too large to analyze with the FDTD. Analysis of most of the optical waveguides is restricted by available memory even for the state-of-the-art computers. It has been found recently that wavelets yield very efficient algorithms when applied to numerical