Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities

We describea theoretical analysis of the nonlinear dynamics of third-harmonic generation ($ω\to3ω$) via Kerr ($\chithree$) nonlinearities in a resonant cavity with resonances at both $ω$ and $3ω$. 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.

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