Reflection properties of coupled-ring reflectors

The reflection properties of a coupled-ring reflector (CRR) are analyzed using the transfer matrix method. The CRR is composed of two coupled rings that are coupled to a bus waveguide. Depending on the combination of the cross-coupling ratios of the couplers, the reflection spectrum shape changes greatly. In the lossless case, the reflection spectrum has four peaks when the ring-bus coupling ratio is small. When the ring-bus coupling ratio is more than half and the ring-ring coupling is very small, the four peaks broaden, forming a single peak with still considerably narrow reflection spectrum, which makes the CRR attractive in applications requiring compact reflectors such as for single-mode laser diodes. The dependence of the propagation and insertion losses of the couplers on the reflection spectrum is also investigated, and the design guidelines are presented.