Predistortion techniques for synthesizing coupled microring filters with loss

A general method based on the predistortion technique is presented for determining the optimum coupling parameters of multiple-coupled microring filters in the presence of known uniform resonator loss. The technique involves predistorting the filter transfer function by shifting its poles and zeros to compensate for loss in the microring resonators due to material absorption, surface roughness scattering, coupling loss and bending loss. It is shown that by sacrificing some in-band insertion loss, both the amplitude and group delay responses of the filter can be recovered when loss is present. Application of the method to synthesizing lossy microring filters in both the digital z-domain and analog s-domain will be presented. The proposed technique is general in that it can be applied to both amplitude and phase filters constructed of coupled microresonators in the most general two-dimensional coupling topology.