FIRST-ORDER-LIKE TRANSITION FOR COLORED SATURATION MODELS OF DYE-LASERS - EFFECTS OF QUANTUM-NOISE

A multidimensional form of the unified colored-noise approximation is applied to obtain the Fokker-Planck equation for intensity distributio ns of dye-laser models simultaneously driven by colored pump noise and quantum noise. The stationary intensity distributions (SID's) of thes e models are calculated. The first-order-like transitions (FOLT's) of the models are studied and compared. With the help of the combination of Sturm's theorem and Descarte's rule of signs, the following conclus ions on the FOLT are obtained. (1) In the limit of white pump noise (t he correlation time of the pump noise tau=0), the FOLT disappears for the colored loss-noise model with saturation whereas it does not disap pear for the colored gain-noise model. (2) The dependence of the FOLT on tau is intensely affected by the quantum noise. If quantum noise is neglected, the first critical curve which separates the regions of si ngle extremum and double extrema of the SID does not change with tau. However, when the quantum noise is considered, the : first critical cu rve does change with tau. (3) When tau --> infinity, the area of regio n II in which the SID varies monotonically contracts and tends to zero . Therefore the FOLT disappears in the models. (4) It is found that wh en the strength of the quantum noise P varies (tau is fixed), the crit ical curves also change.