FIRST-ORDER CORRECTION TO THE UNIFIED COLORED-NOISE APPROXIMATION AND DYE-LASER TRANSIENTS

We develop a first-order theory of the unified colored-noise approximation. It can be applied to general multidimensional systems driven by colored noise (the Ornstein-Uhlenbeck noise). A general formula for the first-order correction is derived, which is used for investigating the transient process of a dye laser. For the colored cubic model and colored gain-noise model of a dye laser, the Fokker-Planck equations are derived based on the general formula of first-order theory. The first-order corrections of the mean first-passage times for the models are obtained. We compare the results with numerical simulations, and show that the present results have greatly improved the results obtained by the original unified colored-noise approximation. © 1994 The American Physical Society.