Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities

TL;DR

This paper provides a theoretical analysis of third-harmonic generation in doubly resonant Kerr cavities, highlighting their efficiency, complex nonlinear behaviors, and methods to optimize harmonic conversion using tailored input pulses.

Contribution

It introduces a comprehensive theoretical framework for nonlinear dynamics in doubly resonant Kerr cavities, including efficiency enhancement and control of multistable states.

Findings

Doubly resonant cavities significantly reduce power requirements for harmonic generation.

The system can achieve 100% conversion efficiency at a critical input power.

Complex nonlinear phenomena like multistability and limit cycles are present.

Abstract

We describea theoretical analysis of the nonlinear dynamics of third-harmonic generation ($\omega\to3\omega$) via Kerr ($\chithree$) nonlinearities in a resonant cavity with resonances at both $\omega$ and $3\omega$. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of $\sim V/Q^2$ where $V$ is the modal volume and $Q$ is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a critical input power. However, we show that it also exhibits a rich variety of nonlinear dynamics, such as multistable solutions and long-period limit cycles.We describe how to compensate for self/cross-phase modulation (which otherwise shifts the cavity frequencies out of resonance), and how to excite the different stable solutions (and especially the high-efficiency solutions) by specially modulated input pulses.