Parametric fluorescence and second-harmonic generation in a planar Fabry-Perot microcavity

In this work we develop a quantum theory of second-order nonlinear optical processes such as parametric fluorescence and second-harmonic generation (SHG), generated by a strong electromagnetic field in an active medium placed in a microcavity. Fields are quantized and expanded in terms of a suitable set of cavity normal modes. In the first part of this work we consider a single many-level quantum system (an atom or molecule), which interacts with all the radiation field modes (spontaneous emission). We show how vacuum fluctuations affect both SHG and parametric processes. For SHG, we demonstrate that the presence of the microcavity allows the introduction of the concept of coherence length, even for a medium made of a single molecule. In the second part of this paper we discuss the case of a uniform distribution of emitting dipoles. For this configuration we calculate the differential extinction coefficient, and discuss the dependence of the emitting power on the microcavity's parameters. Finally we suggest the possibility of realizing a micro-optical parametric oscillator.