A Wavelet Formulation of Finite Diierence Method: Full Vector Analysis of Optical Waveguide Junctions

We have developed an eecient large-stencil nite-diierence scheme of time-dependent Maxwell's curl equations based on the wavelet-Galerkin formulation in time-domain. The proposed scheme enables, for the rst time within a limited computational resource, full-vector analysis of three-dimensional rib waveguides that are typically used in integrated planar optical devices. The formulation takes advantage of compactly-supported interpolating bases to expand and represent the electric and magnetic elds. Moreover, unlike the well-known beam propagation methods, the numerical scheme is based on the rst-principle algorithm with no explicit approximation, and thus rigorous and versatile for various types of boundary conditions We demonstrate the eeciency of the method by rst analyzing a straight rib waveg-uide and examining the convergence of the results. Then we investigate a Y-shaped junction structure that is electrically too large to analyze with the conventional nite-diierence time-domain scheme.