Optimal third-harmonic generation in an optical microcavity with $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities

TL;DR

This paper investigates the interplay of direct and cascaded nonlinear processes in microcavities for third-harmonic generation, revealing how interference can be optimized to enhance conversion efficiency and proposing a design rule for high-efficiency harmonic generation.

Contribution

It provides a detailed analysis of the interference effects between $ ext{chi}^{(2)}$ and $ ext{chi}^{(3)}$ nonlinearities and offers a practical design guideline for optimizing third-harmonic generation in microcavities.

Findings

Interference between direct and cascaded processes can be exploited to improve efficiency.

Optimizing cavity resonance and coupling mitigates nonlinear saturation.

A general design rule for efficient high-order harmonic generation is proposed.

Abstract

Third-harmonic generation can be realized via both $\chi^{(3)}$ and cascaded $\chi^{(2)}$ nonlinear processes in a triply-resonant microcavity. It is still unknown how these processes interfere with each other and the optimization of the conversion efficiency still remains as a question. In this work, the interplay between the direct third-harmonic generation and the cascaded process combining of the second-harmonic generation and the sum-frequency generation are investigated. It is found that the interference effect between these two processes can be used to improve the conversion efficiency. By optimizing the cavity resonance and the external coupling conditions, the saturation of the nonlinear conversion is mitigated and the third-harmonic conversion efficiency is increased. A design rule is provided for achieving efficient third-harmonic generation in an optical microcavity, which can be generalized further to the high-order harmonic generations.