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

Abstract

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 2D slab microcavities exhibiting long lifetimes $Q \gtrsim 10^4$, small modal volumes $V \gtrsim (λ/2n)^3$, 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.