Intensity correlation function and relaxation time of a single-mode laser driven by cross-correlated noises for the case of nonzero correlation time

We consider a single-mode laser model driven by correlated quantum and pump noise and study the effects of the cross correlation time tau between noises on the steady-state intensity correlation function and the associated relaxation time. Based on an approximated Fokker-Planck description of the laser model and the Stratonovich-like ansatz, we find the steady-state probability distribution function P-st(I), the steady-state intensity correlation function K(s) and the associated relaxation time T. From numerical computations we found the following: (l) tau suppresses the fluctuation of the laser intensity for the case of positively correlated noises (i.e. the correlation strength between noises (lambda. > 0) and increases the intensity fluctuation for the case of negatively correlated noises (lambda > 0); (2) tau slows down the decay of the intensity correlation for the case of lambda > 0 but speeds up the decay for the case of lambda < 0. The effects of tau on P-st(I), k(s) and T are entirely opposite for lambda < 0 and for lambda > 0.