Low frequency spectrum of vacuum squeezed radiation to be used in GW antennas

We generalize the Collett and Gardiner model for the generation of vacuum squeezed radiation by degenerate optical parametric oscillators. We account for fluctuating pump, cavity with time varying length and nonlinear crystal phase matching temperature. The equation of motion of the intracavity field is integrated by WKB approximation by introducing a set of random functions. Relying on this result we calculate the low frequency spectrum of the quadrature amplitude, a quantity essential for assessing the photon noise reduction in interferometric gravitational wave antennas using vacuum squeezed light.