The relaxation time of a single-mode dye laser system driven by cross-correlated additive and multiplicative noises

The relaxation time Tc of the intensity correlation function is investigated in a single-mode dye laser system driven by cross-correlated additive and multiplicative white noises. The expression for Tc is obtained by using the projector-operator method. And then the effects of correlation intensity between noises λ and correlation time between noises τ on Tc are studied. Numerical results show that the correlation intensity λ speeds up the intensity fluctuation decay of laser slightly above threshold in the presence of nonzero τ. Meanwhile, when λ>0, τ suppresses the intensity fluctuation of laser. But when λ>0, τ enhances the intensity fluctuation of laser. Moreover, the effects of λ and τ on the intensity fluctuation also depend on the noise intensity ratio R and net gain coefficient a0.