Analysis of 2-D dielectric-waveguide-coupled optical ring resonators using a transmission-line formulation

A rigorous and fast method for a Fourier-based analysis of 2-D dielectric-waveguide-coupled optical ring resonators (ORRs) is presented. As a first step, the structure under investigation is periodically repeated along a specific direction. The resulting periodic structure is then analyzed using a transmission-line formulation (TLF). For a sufficiently long period, the solutions of the resulting periodic structure converge with those of the actual structure. As will be demonstrated, the simulation time for the analysis of a sample ORR of high-index contrast at a single frequency point amounts to a few seconds without remarkable computing resources. Our results are in close agreement with those of the pseudospectral time-domain (PSTD).