Spectral Methods and Domain Decomposition for Nanophotonic Applications

Nanophotonic applications often involve large-scale problems with excessive demand on computational resources. We develop a domain decomposition method (DDM) to reduce computer memory and central processing unit (CPU) time requirements by combining the spectral element method (SEM) and the spectral integral method (SIM) for large-scale finite periodic structures. The interior scattering subdomains within each period are modeled by the SEM while the exterior scattering problem is modeled by the SIM. The interactions between neighboring subdomains are modeled by the frequency-domain version of the Riemann solver. Numerical convergence of the Riemann solver is fast and weakly dependent on the size of the system. Two sets of examples demonstrate the typical nanophotonic applications: The first periodic system is a vertical coupling waveguide based on a photonic crystal slab which opens a way to construct and simulate optical circuits. The second periodic system is a finite-sized metamaterial with an effective negative refractive index, whose edge effects are visualized and analyzed.