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

## TL;DR

This paper uses advanced topology-optimization techniques to design complex, wavelength-scale resonators with high quality factors and small modal volumes, significantly improving nonlinear frequency conversion efficiency in integrated photonic devices.

## Contribution

It introduces novel topology-optimized designs for multi-track ring resonators and 2D microcavities with enhanced nonlinear overlaps and high Q-factors, advancing integrated nonlinear photonics.

## Key findings

- Achieved Q-factors greater than 10^4 in designed resonators
- Demonstrated small modal volumes near the diffraction limit
- Maximized nonlinear overlaps for efficient frequency conversion

## Abstract

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.