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 distributions of dye-laser models simultaneously driven by colored pump noise and quantum noise. The stationary intensity distributions (SID's) of these 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 conclusions on the FOLT are obtained. (1) In the limit of white pump noise (the correlation time of the pump noise tau=0), the FOLT disappears for the colored loss-noise model with saturation whereas it does not disappear 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 single extremum and double extrema of the SID does not change with tau. However, when the quantum noise is considered, the : first critical curve does change with tau. (3) When tau --> infinity, the area of region II in which the SID varies monotonically contracts and tends to zero. Therefore the FOLT disappears in the models. (4) It is found that when the strength of the quantum noise P varies (tau is fixed), the critical curves also change.