Rotation-induced evolution of far-field emission patterns of deformed microdisk cavities

A critical issue that hinders the development of chip-scale optical gyroscopes is the size dependence of the Sagnac effect, which manifests as a rotation-induced phase shift or frequency splitting between two counterpropagating waves or resonances, and is proportional to the size of the optical system.We show numerically and theoretically that the far-field emission patterns (FFPs) of optical microdisk cavities depend strongly on rotation and can therefore provide an alternative approach. At low rotation speed where resonant frequencies barely shift with rotation (i.e., a negligible Sagnac effect), the FFPs already exhibit a significant rotation-induced asymmetry, which increases linearly with the rotation speed. We further identify the basic requirements to maximize this effect, including distinct output directions for the clockwise and counterclockwise waves in a cavity mode, as well as a vanishing frequency splitting between one such mode and its symmetry related partner mode. Based on these requirements, we propose several microcavity shapes that display orders of magnitude enhancement of the emission sensitivity to rotation and could stimulate a new generation of optical gyroscopes with small footprints and on-chip integrability.