Non-equilibrium Transitions in Sub/second Harmonic Generation

Abstract

In this paper we present a quantum statistical analysis of a non-linear optical system with a mode coupled to its second harmonic, studied semiclassically in a previous paper. Quantum fluctuations are included via a Fokker-Planck equation for a generalized P representation. The spectrum of the light is shown to split into two peaks for critical values of the input fields. It is found that under certain conditions the non-classical effect of photon antibunching is possible in the steady state. In certain limits exact solutions for the generalized P representation are possible which allows an estimate of lifetimes in the metastable region to be calculated.