Matrix-Free Time Domain Gradient Smoothing Method With Stretched-Coordinates Perfectly Matched Layer for Analysis of Photonic Devices

Abstract

In this article, the gradient smoothing method is introduced for the first time to the time domain analysis of photonic devices. The proposed method combines the advantages of finite difference and finite element methods. It is capable of accurately modelling irregularly-shaped geometries by dividing the computational domain into elements like the finite element method. While it naturally produces a diagonal matrix for the field discretization similar to the finite difference method which makes it a perfect method for explicit time marching schemes. The beam propagation method with explicit time discretization is adopted for the propagation in time. Additionally, a novel stretched coordinate perfectly matched layer with two auxiliary equations is developed for the proposed method. The numerical aspects of the proposed method are demonstrated through the analysis of different photonic integrated structures.