Canonic Design of Parallel Cascades of Symmetric Two-Port Microring Networks

A method for obtaining the optimal canonic design of optical filters based on parallel-cascaded arrays of symmetric two-port microring networks is presented. The approach is based on the all-pass decomposition of the parallel-cascaded microring architecture, whereby the filter is transformed into an equivalent sum-difference all-pass microring circuit via a similarity transformation of the transfer matrix. The sum-difference transformation also helps reveal important properties of the parallel-cascaded microring architecture, such as the doubly complementary nature of its transfer functions, and the existence and uniqueness of the canonic form of parallel-cascaded arrays of symmetric microring networks.