### Abstract

We demonstrate theoretical conditions for highly efficient degenerate four-wave mixing in triply resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ω_{0}-Δω can, in the presence of pump light at ω_{0}, be converted with quantum-limited efficiency into an output shifted signal of frequency ω_{0}+Δω, and we derive expressions for the critical input powers at which this occurs. We find the critical powers in the order of 10 mW, assuming very conservative cavity parameters (modal volumes ~10 cubic wavelengths and quality factors ~1000). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting "quantum" arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.

Original language | English (US) |
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Article number | 033834 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 83 |

Issue number | 3 |

DOIs | |

State | Published - Mar 30 2011 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*83*(3), [033834]. https://doi.org/10.1103/PhysRevA.83.033834