Abstract

The degenerate parametric oscillator has been in recent years the subject of great interest as a nonlinear system able to produce a large amount of squeezing [1]. Quantum treatments of optical parametric oscillation were presented early by Graham and Haken [2], Drummond, McNeil and Walls [3]. In this paper, the process of sub-harmonic generation is studied, involving the nonlinear interaction of a light field mode (the pump b) at frequency 2Ω with its sub-harmonic (the signal a) at frequency Ω in a nonlinear crystal (characterised by a second-order susceptibility η) placed inside an optical cavity. An external classical pumping ε_b is applied to drive the system to a non-equilibrium steady state. The coupling of the internal field modes to the external continuum of modes is modeled through the transmitivity of the cavity mirror leading to the relaxation of the pump and the signal modes (relaxation rates γ_b, γ_a).

© 1996 Optical Society of America