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 ${\chi }^{(2)}$ and ${\chi }^{(3)}$ frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and 2D slab microcavities exhibiting long lifetimes $Q\gtrsim {10}^4$, small modal volumes $V \gtrsim (\lambda/2n)^3$, 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.