Intensity correlation function and associated relaxation time of a saturation laser model with cross-correlated noises for the case of nonzero correlation time

Considering a saturation laser model with cross-correlated additive and multiplicative noises, we derive the stationary probability distribution function P-st(I), the stationary intensity correlation function C(s) and the associated relaxation time T-c by virtute of the Novikov theorem and Stratonovich's decoupling ansatz. Based on numerical computation, we discuss the effects of the correlation strength lambda, the cross-correlation time tau, and the noises intensity. The correlation strength lambda attenuates the probability distribution and increases the intensity fluctuation of the laser system. The correlation strength lambda and the noise intensity D and Q speed up the relaxation of the system from an arbitrary state to the steady state and enhance the stability of the laser intensity output. For the case of negative correlation ( lambda < 0), the cross- correlation tau enhances the probability distribution, decreases the intensity fluctuation, slows down the relaxation of the system from an arbitrary state to the steady state, and decreases the stability of the laser intensity output; by contrast, the effects of the cross-correlation time tau on P-st(x), C(s), and T-c are entirely opposite for (lambda > 0).