Galerkin descontínuo no domínio do tempo aplicado a problemas com múltiplas escalas em nanofotônica

Abstract

The constant increase in the need for technological resources that bring higher rates of transmission, processing, and storage of data, drives the study of the properties of electromagnetic propagation in nanoscale devices. Thus, we find in the literature a significative number of scientific researches for this purpose. With the advanced hardware available nowadays and the increasing development of numerical methods, research using numerical models simulations are becoming more common around the world. One of the most promising photonic devices is the planar guide, based on two-dimensional photonic crystals. Numerical methods in the time domain can simulate propagation in these guides revealing peculiar characteristics, such as slow light. Among the problems encountered in the modeling of nanophotonic devices are problems with multiple scales. Numerical methods have difficulty adjusting to different scales. The DGTD is a promising method in the treatment of problems with multiple scales since it uses unstructured meshes in domain discretization. However, in the standard version, the time integration can bring a big computational cost. Therefore, researchers have been proposed local time stepping strategies (LTS). Although the existing LTS methods are efficient, they still have limitations and do not exploit the full potential of spatial discretization DG. Therefore, it is possible to develop more efficient LTS strategies. The LTS strategy developed here is based on the linear multistep strong stability preserving method (SSPMS). However, in principle, it can be applied to any single stage method. To test the strategy, we applied on electromagnetic wave propagation on photonic crystals planar guides. The results validate and demonstrate the multiclass strategy efficiency.