Abstract

An optical ring resonator is a fundamental element of an integrated photonic circuit due to its ability to confine optical waves. Composed of a dielectric waveguide closed in a loop, the periodic geometry of the ring allows for the build-up of high-intensity electric fields at particular wavelengths of light known as resonances. These resonances can be used for applications in fields such as non-linear optics, biosensing, and high-precision spectroscopy. The intended operation of a ring resonator is often limited by the underlying material dispersion of the ring’s waveguide. To counteract these effects, the dispersion of the waveguide can be designedly engineered via precise geometric patterning of the material. In this work, several dispersion engineering methods are proposed. In particular, condensed matter theories including Bloch’s theorem, the Su-Schrieffer-Heeger model, and synthetic dimensions are applied to the periodic dielectric function of the ring. Using these principles, photonic analogs of band structures, topologically-protected edge states, coupled degenerate two-level systems, and a synthetic modal dimension in an optical ring resonator will be shown.