Dynamics of non-linear optical processes

TLDR: In this article, the authors studied the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms.

Abstract: We study the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms. In a short-time approximation some conservation laws are derived and the existence of the Glauber-Sudarshan weighting function is discussed. It is shown in the second harmonic generation case that good coherence of the incident radiation is lost proportionally to the intensity in interaction while the second harmonic radiation has tendency to be coherent. The effects of the spontaneous emission of the medium and of the physical vacuum are also discussed. In this approximation the statistics is generally described by the superposition of coherent and chaotic fields with correlated components.