Exact Realization of Optical Transfer Functions With Symmetric Transmission Zeros Using the Double-Microring Ladder Architecture

Arrays of parallel-cascaded microring doublets with inter-stage differential phase shifts are proposed for realizing general optical filter transfer functions whose zeros are located on or symmetrically distributed about the imaginary j omega-axis. Compared to previously proposed microring filters capable of realizing transmission zeros, the double-microring ladder architecture has the advantages in that it is compact and requires only synchronously tuned microring resonators with nonnegative coupling coefficients. Furthermore, the building blocks of the filter are simple symmetric microring doublets, which can be separately optimized to achieve good fabrication tolerance and repeatability. A procedure for exactly synthesizing the device given a prescribed transfer function is developed in both the s- and z-domains. Examples of an optical elliptic filter and a linear-phase filter with flat-top spectral responses in both the amplitude and group delay are presented to illustrate the applications of the proposed ladder filter architecture. Sensitivity analysis also shows that the device is robust with respect to microring loss as well as variations in the coupling parameters and phase shift factors.