Efficient smoothed finite element time domain analysis for photonic devices.

Abstract

In this paper, a new finite element method (FEM) is proposed to analyse time domain wave propagation in photonic devices. Dissimilar to conventional FEM, efficient "inter-element" matrices are accurately formed through smoothing the field derivatives across element boundaries. In this sense, the new approach is termed "smoothed FEM" (SFETD). For time domain analysis, the propagation is made via the time domain beam propagation method (TD-BPM). Relying on first order elements, our suggested SFETD-BPM enjoys accuracy levels comparable to second-order conventional FEM; thanks to the element smoothing. The proposed method numerical performance is tested through applicating on analysis of a single mode slab waveguide, optical grating structure, and photonic crystal cavity. It is clearly demonstrated that our method is not only accurate but also more computationally efficient (far few run time, and memory requirements) than the conventional FEM approach. The SFETD-BPM is also extended to deal with the very challenging problem of dispersive materials. The material dispersion is smartly utilized to enhance the quality factor of photonic crystal cavity.