Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters-a tutorial overview

This tutorial describes the transmission, group delay time and quadratic dispersion properties of the four basic building blocs of optical filters built using ring resonators. These building blocs are single-ring resonators in either two-port (all-pass) or four-port (add/drop filter) configuration. The effect of waveguide and coupler loss is included throughout. Explicit expressions to compute the complex amplitude of the circulating wave in the ring, the Q factor, the finesse and the insertion loss are also given. Attention is drawn to the similarities between the ring resonator the Fabry-Pe´rot resonator and the Gires-Tournois interferometer. Material properties and fabrication technology are not reviewed.