A wavelet formulation of the finite-difference method: full-vectoranalysis of optical waveguide junctions

摘要

We have developed an efficient, large-stencil finite-differencenscheme of the time-dependent Maxwell's curl equations based on thenwavelet-collocation formulation in the time-domain. The proposed schemenenables, for the first time within a limited computational resource,nfull-vector analysis of three-dimensional rib waveguides that arentypically used in integrated planar optical devices. The formulationntakes advantage of compactly-supported interpolating bases to expand andnrepresent the electric and magnetic fields. Moreover, unlike thenwell-known beam propagation methods, the numerical scheme is based onnthe first-principle algorithm with no explicit approximation, and thusnrigorous and versatile for various types of boundary conditions. Wendemonstrate the efficiency of the method by first analyzing a straightnrib-waveguide and examining the convergence of the results. Then weninvestigate a Y-shaped junction structure that is electrically too largento analyze with the conventional finite-difference time-domain scheme