Elements of an optical microring resonator Dielectric optical waveguides The vectorial wave equations The Effective Index Method and solutions of the 1D slab waveguide Waveguide dispersion Propagation loss Optical modes in bent dielectric waveguides Conformal transformation of bent waveguides Resonant modes in microdisks and microrings Full-vectorial analysis of bent waveguides Coupling of waveguide modes in space The coupled mode equations Solution of the coupled mode equations Fabrication of microring resonators Summary Analytical models of microring resonators Resonance spectrum of an uncoupled microring resonator Power coupling description of a microring resonator The add-drop microring resonator The all-pass microring resonator Phase and group delay responses of a microring resonator Energy coupling description of a microring resonator Relationship between energy coupling and power coupling formalisms Summary Coupled microring optical filters Periodic arrays of microring resonators Periodic arrays of all-pass microring resonators Periodic arrays of add-drop microring resonators Arrays of serially coupled microring resonators Transfer functions of coupled microring optical filters Cascaded all-pass microring filters Serially coupled microring filters Energy coupling analysis of serially coupled microring filters Energy coupling synthesis of serially coupled microring filters Power coupling analysis of serially coupled microring fil