Degenerate four-wave mixing in triply-resonant Kerr cavities

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 ${\omega }_0-\Delta \omega$ 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 $\sim 10$ cubic wavelengths and quality factors $\sim 1000$. 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.

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

References in corpus (6)

• 1 Low power continuous-wave nonlinear optics in silica glass integrated waveguide structures
• Parametric gain and wavelength conversion via third order nonlinear optics a CMOS compatible waveguide
• Photonic quasicrystals for general purpose nonlinear optical frequency conversion
• Ultra-low power nonlinear optics in a high Q CMOS compatible integrated micro-ring resonator
• Tailoring optical nonlinearities via the Purcell effect
• Random quasi-phase-matched second-harmonic generation in periodically poled lithium tantalate

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