Effects of a dye laser with correlations between additive and multiplicative noise: Transient properties

The transient properties of a single-mode dye laser with correlations between additive and multiplicative white-noise terms are investigated theoretically. The mean, variance, and skewness of first-passage-time distributions for the white-noise-loss model and the white-noise-gain model are obtained. We find that (1) the mean first-passage time for the two models is not affected by the strength {λ} of the correlation between additive and multiplicative noise terms; (2) as {λ} is increased, the magnitudes of the variance and skewness of the two models are increased; and (3) under the same {λ} and the same pump level, the variance and skewness of the white-noise-gain model are larger than those of the white-noise-loss model.