Degenerate four-wave mixing in triply-resonant Kerr cavities

Details Degenerate four-wave mixing in triply-resonant Kerr cavities Degenerate four-wave mixing in triply-resonant Kerr cavities

2010-11-26

arxiv.org/abs/1011.5845v1

Phys. Rev. A 83, 033834 (2011)

Physics

Optics

13 pages, 8 figures. To appear in Physical Review A

Scientific paper

10.1103/PhysRevA.83.033834

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 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 $\omega_0-\Delta \omega$ can, in the presence of pump light at $\omega_0$, be converted with quantum-limited efficiency into an output shifted signal of frequency $\omega_0 + \Delta \omega$, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes $\sim10$ cubic wavelengths and quality factors $\sim1000$. 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.

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