Nonlinear harmonic generation and devices in doubly resonant Kerr cavities

We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation (ω→3ω) via Kerr (χ⁽³⁾) 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 ∼V∕Q², 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- and 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.