Saturation Effects and the Colored Pump Noise in a Dye Laser

We investigate the statistical properties of two single-mode dye-laser models-the colored-loss-noise model and the colored-gain-noise model. Analytic expressions of the probability,the mean and the variance of the steady-state laser intensity are obtained through the unified expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find that when the cavity decay rate for the electric field is large and the pump parameter a₀ is small, the differences of the results of the two laser models are small. Otherwise, the differences are large. And the correlation time of the noise has very obvious influence on the results of the two models.