Statistical properties of the intensity fluctuation of a saturation laser model driven by cross-correlation additive and multiplicative noises are investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution Pst(I), the relaxation time Tc, and the normalized variance λ2(0) of the system. By numerical computation, we discussed the effects of the cross-correlation strength λ, the cross-correlation time τ, the quantum noise intensity D, and the pump noise intensity Q for the fluctuation of the laser intensity. Above the threshold, λ weakens the stationary probability distribution, speeds up the startup velocity of the laser system from start status to steady work, and attenuates the stability of laser intensity output; however, τ strengthens the stationary probability distribution and strengths the stability of laser intensity output; when λ < 0, τ speeds up the startup; on the contrast, when λ > 0, τ slows down the startup. D and Q make the relaxation time exhibit extremum structure, that is, the startup time possesses the least values. At the threshold, τ cannot generate the effects for the saturation laser system, λ expedites the startup velocity and weakens the stability of laser intensity output. Below threshold, the effects of λ and τ not only relate to λ and τ, but also relate to other parameters of the system.
Stationary and dynamical properties of finite N-unit Langevin models subjected to multiplicative noises
