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Quantum Electronics and Laser Science Conference

¿Photon emission by photon¿ model for spontaneous frequency conversion in dispersive dielectric microcavities

Alex Hayat, Meir Orenstein

Published May 1, 2007• 0 citations
Publisher

Abstract

We develop a quantum-field model for photon conversion in dispersive cavity, incorporating dispersion into spatial eigenmodes. Direct calculations of spontaneous photon-tophoton decay rates that cannot be done conventionally are reported.
DOI
10.1109/qels.2007.4431443

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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 kkk 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.
We consider spontaneous emission in dielectric microcavities with multiple resonances that may overlap in both position and frequency. By projecting the Green tensor onto a set of quasimodes associated with the resonances, we derive the reduced spontaneous emission rate. To demonstrate the accuracy and computational efficiency of our approach, we model spontaneous emission in a two-dimensional photonic crystal with two coupled defects. Employing a quantum mechanical interpretation, we show that the spontaneous emission involves both direct decay into the individual quasimodes and photon transfer between the quasimodes. The quantum path interference between these different emission channels can cause the spontaneous emission rate to differ dramatically from the rate obtained by the summation over resonant line shapes. We also show how our approach can be used to determine the emission into particular quasimodes of multiple-resonance microcavities.
A recently developed scheme [S. Scheel, L. Kn\"oll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)] for quantizing the macroscopic electromagnetic field in linear dispersive and absorbing dielectrics satisfying the Kramers-Kronig relations is used to derive the quantum local-field correction for the standard virtual-sphere-cavity model. The electric and magnetic local-field operators are shown to become approximately consistent with QED only if the polarization noise is fully taken into account. It is shown that the polarization fluctuations in the local field can dramatically change the spontaneous decay rate, compared with the familiar result obtained from the classical local-field correction. In particular, the spontaneous emission rate strongly depends on the radius of the local-field virtual cavity.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.