A comparison of modeling methods for ring resonator circuits.

We have previously introduced a "compound ring resonator circuit," in which several ring resonator (RR) cavities are coupled in a loop, and analyzed the resulting configuration with the coupling of modes in space (CMS) technique. In this work we compare the accuracy, simplicity and calculation time of three standard procedures, namely the FDTD, and the methods of coupling of modes in time (CMT) and CMS in the context of a two-dimensional (2D) complex ring resonator circuit. This provides a far more effective benchmark of the relative advantages of the methods than the analysis of far simpler structures performed by other authors. As part of these calculations, we further discuss the relationship between the power loss coefficients in the CMS and the CMT models. We verify that the CMT yields accurate and rapid results for small coupling coefficients and losses even for large waveguide circuits containing multiple rings.