Dispersion engineering by rotational symmetry breaking in an optical microcavity.

Dispersion engineering is pivotal for nonlinear optics, yet it often faces challenges posed by material and structural limitations. Here, we establish rotational symmetry breaking as the guiding principle for dispersion engineering in optical microcavities. Through boundary deformation, multi-branch global dispersion emerges in island modes, and local dispersion is controlled via resonance-assisted tunneling between quasi-whispering gallery modes. Enabled by the global dispersion, the optical parametric oscillation is predicted in blue-violet light spectrum with high efficiency (>55%) and large frequency separation (>180 THz). Using the local dispersion engineering, the doubly-resonant enhancement of second-harmonic generation is regulated by the resonance-assisted tunneling.