Photon-counting statistics of the degenerate parametric oscillator in the transient regime: The factorial moments method

Photon-counting statistics of a subthreshold degenerate parametric oscillator (DPO) are studied in the transient regime. The field produced by the parametric oscillator is expressed in terms of two independent real Gaussian variables. We use this property of the field variables to derive analytically the generating function for the photoelectron statistics. From this generating function one general expression for the factorial moments is obtained, and expressions for the first and second factorial moments and variance are presented. Using the Mandel-Q parameter we show that the statistics is Super-Poissonian for the DPO in the transient regime. Some curves are presented to illustrate the behavior of the variance and the Mandel-Q parameter.