Stationary properties of a saturation laser stochastic system with time delay

Stationary properties of a saturation laser stochastic system with the time delay are investigated. Making use the method of the small time delay approximation, we obtain the analytic expressions of the stationary probability distribution Pst(I) of the laser intensity, the nth power of the laser intensity 〈In〉, the normalized variance λ2(0), and the normalized skewness λ3(0) of the system. By numerical computation, we discuss effects of the delay time and the feedback strength on the stationary probability distribution Pst(I), the mean value of the laser intensity 〈I〉, the normalized variance λ2(0) and the normalized skewness λ3(0). Above threshold the laser system possesses the efficient laser intensity output, and the delay time and the feedback strength enchances the laser intensity output of the saturation laser system. The delay time increases the stability of the laser intensity output. In contrast, the feedback strength weakens the stability.