Cavity-enhanced second harmonic generation via nonlinear-overlap optimization

TL;DR

This paper introduces a topology optimization method for designing photonic structures that significantly enhance second-harmonic generation efficiency by optimizing frequency matching, mode lifetime, and nonlinear overlap, leading to superior SHG performance.

Contribution

The authors develop a novel topology optimization approach that simultaneously maximizes frequency matching, mode lifetime, and nonlinear overlap in photonic cavities, enabling high-efficiency SHG.

Findings

Achieved modes with Q > 10^4 and small modal volumes.

Demonstrated orders of magnitude increase in SHG efficiency.

Supported various material platforms with optimized structures.

Abstract

We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that seek to maximize Purcell factors at individual frequencies is that our method not only aims to achieve frequency matching (across an entire octave) and large radiative lifetimes, but also optimizes the equally important nonlinear--coupling figure of merit $\bar{\beta}$, involving a complicated spatial overlap-integral between modes. We apply this method to the particular problem of optimizing micropost and grating-slab cavities (one-dimensional multilayered structures) and demonstrate that a variety of material platforms can support modes with the requisite frequencies, large lifetimes $Q > 10^4$, small modal volumes $\sim (\lambda/n)^3$, and extremely large $\bar{\beta} \gtrsim 10^{-2}$, leading to orders of magnitude enhancements in SHG efficiency compared to state of the art photonic designs. Such giant $\bar{\beta}$ alleviate the need for ultra-narrow linewidths and thus pave the way for wavelength-scale SHG devices with faster operating timescales and higher tolerance to fabrication imperfections.