Three-Dimensional Finite-Element Time-Domain Beam Propagation Method and Its Application to 1-D Photonic Crystal-Coupled Resonator Optical Waveguide

A 3-D finite-element time-domain beam propagation method is described for the first time, to the best of our knowledge, for the analysis of transmission characteristics of any kind of photonic structures. In order to avoid nonphysical reflections from computational window edges, the perfectly matched layer boundary condition is introduced. Furthermore, the present method can treat wideband optical pulses owing to the use of Padé approximation. The validity of this method is verified by numerical simulations of a photonic crystal cavity and a microring resonator. In addition, in order to demonstrate the usefulness of the developed method, a taper waveguide for a highly efficient connection between a straight waveguide and a 1-D photonic crystal-coupled resonator optical waveguide is designed.