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We demonstrate theoretical conditions for highly-efficient degeneratefour-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ ageneral and accurate temporal coupled-mode analysis in which the interaction oflight in arbitrary microcavities is expressed in terms a set of couplingcoefficients that we rigorously derive from the full Maxwell equations. Usingthe coupled-mode theory, we show that light consisting of an input signal offrequency $\omega_0-\Delta \omega$ can, in the presence of pump light at$\omega_0$, be converted with quantum-limited efficiency into an output shiftedsignal of frequency $\omega_0 + \Delta \omega$, and we derive expressions forthe critical input powers at which this occurs. We find that critical powers inthe order of 10mW assuming very conservative cavity parameters (modal volumes$\sim10$ cubic wavelengths and quality factors $\sim1000$. The standardManley-Rowe efficiency limits are obtained from the solution of the classicalcoupled-mode equations, although we also derive them from simplephoton-counting "quantum" arguments. Finally, using a linear stabilityanalysis, we demonstrate that maximal conversion efficiency can be retainedeven in the presence of self- and cross-phase modulation effects that generallyact to disrupt the resonance condition.

Degenerate four-wave mixing in triply-resonant Kerr cavities