Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion.

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ ⁽²⁾ and χ ⁽³⁾ frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳10 ⁴ , small modal volumes V≳(λ/2n) ³ , and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.