Photon conversion processes in dispersive microcavities: Quantum-field model

We present a simple quantum-field model for photon frequency conversion processes in dispersive dielectric microcavities, allowing practical calculations of conversion rates and efficiency optimization. The model incorporates the effect of dispersion into the structure of spatial cavity eigenmodes, while the material nonlinear properties enter the calculations through the coupling coefficients. Similar to the radiative atomic transitions, cavity photon-to-photon decay rates are derived for stimulated and spontaneous photon conversion. The phase matching requirement for a nonlinear process in a cavity is shown to be translated into a nonlinear mode overlap, manifesting the momentum conservation in a k space spanned by the cavity eigenmodes. We illustrate the efficiency of the model by calculating degenerate two-photon and three-photon parametric down-conversion rates and analyze the photon lifetime dependence on various cavity and material parameters.