The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR). Results show that cross-correlation intensity \lambda enforces the SR of the system. The position of the peak on the SNR-\tau curves moves to the right direction along with the increase of \lambda (\tau is the self-correlation time of the multiplicative colored noise). We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-\lambda curves.

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s). C(s) is derived by means of the projection operator method. The effects of the self-correlation time \tau1 of the additive colored noise, \tau2 of the multiplicative colored noise, and the effect of the cross-correlation time \tau0 between the two noises on C(s) are discussed by numerical calculation. For the case of positive correlation (\lambda>0), it is found that when a0>0 the normalized intensity correlation function C(s) increases with the increase of \tau0 or \tau2, and with value of \tau0 or \tau2 becoming larger, C(s) comes to saturation. With increasing the self-correlation time \tau1 of the additive noise, a minimum and a maximum will appear on curve of C(a) as a0>0. If a0<0, C(s) decreases with the increase of \tau0, \tau1, and \tau2.

A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time 'tau' and the cross-correlation intensity 'lambda' between noises on the normalized intensity correlation function C(s). It is found that if 'lambda'>0 ('lambda'<0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time 'tau', and at large value of 'tau', the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when 'lambda' is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when 'lambda' becomes smaller and smaller.