Analysis of Coupled Microring Resonators in Sheared Lattices

We present a field coupling method for analyzing coupled microring resonators (CMRs) in sheared 2-D lattices. Shearing has the effect of imparting phase shifts to certain coupling elements in the lattice, and is shown to be a simple way for realizing negative couplings in CMR networks. We mathematically show that the operation of shearing can be described by a similarity transformation on the field coupling matrix of the microring network. The analysis presented can be generalized to account for the position dependence of the coupling junctions of arbitrary 2-D CMR networks.