High-order accurate numerical simulation of monochromatic waves in photonic crystal ring resonators with the help of a non-iterative domain decomposition

A photonic crystal ring resonator (PCRR) is a micro-scale optical device that combines a closed-loop waveguide with a light input and output. PCRRs are constructed with periodically placed scattering rods where the exclusion of rods is used to form the path of a waveguide. We simulate PCRRs numerically using a non-iterative domain decomposition approach that is insensitive to jumps in material properties, in particular, those between the scattering rods and surrounding medium. To approximate the governing Helmholtz equation, we use a compact fourth-order accurate finite difference scheme combined with the method of difference potentials (MDP). The MDP renders exact coupling between the decomposition subdomains and maintains high-order accuracy for non-conforming boundaries/interfaces on regular grids.