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arXiv · 1011.5845

Degenerate four-wave mixing in triply-resonant Kerr cavities

David Ramirez·Alejandro W. Rodriguez·Hila Hashemi·J. D. Joannopoulos·Marin Soljačić·Steven G. Johnson
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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 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 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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David Ramirez, Alejandro W. Rodriguez, Hila Hashemi, J. D. Joannopoulos, Marin Soljačić, Steven G. Johnson. 2010-11-26. Degenerate four-wave mixing in triply-resonant Kerr cavities. https://doi.org/10.1103/physreva.83.033834

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