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Physical Review A

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

Ya Jia, Cao Li, Wu Da-Jin

Published Apr 1, 1995• 45 citations
Publisher

Abstract

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 \ensuremath{\lambda} of the correlation between additive and multiplicative noise terms; (2) as \ensuremath{\lambda} is increased, the magnitudes of the variance and skewness of the two models are increased; and (3) under the same \ensuremath{\lambda} 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.

DOI
10.1103/physreva.51.3196

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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 \ensuremath{\lambda} of the correlation between additive and multiplicative noise terms; (2) as \ensuremath{\lambda} is increased, the magnitudes of the variance and skewness of the two models are increased; and (3) under the same \ensuremath{\lambda} 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.
We have derived the approximate formulas of the mean, variance, and skewness of the first-passage-time distribution for the colored-loss-noise model and the colored-gain-noise model of the dye laser by virtue of the best Fokker-Planck-equation approximation. Comparing the colored-loss-noise model with the colored cubic model, it is shown that our analytic results are in good agreement with the numerical simulation given by Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)]. We find that the prefactor of the pump fluctuation term can curb the variance and skewness of the first-passage-time distribution. In the regime 0.8${\mathit{I}}_{0}$1, where I0{\mathit{I}}_{0}I0​ denotes the relative laser intensity, the best Fokker-Planck equation predicts that as the laser intensity is increased, the increases of the variance and skewness of the first-passage-time distribution for the colored saturation models are slower than those of corresponding white saturation models.
Statistical properties of dye laser transients are analyzed by first-passage-time technique. Both pump and quantum fluctuations effece the establishment of steady states in a dye laser. These two kinds of noise play different roles in laser transients. Meanwhile it is difficult to discern them since the pump fluctuations are six orders of magnitude larger than the quantum noise. In this paper a model of single mode dye laser with pump fluctuations simplified by white noise is presented and the analytic results of the mean, variance and skewness of first-passage-time distributions are obtained through a Fokker-Planck equation. Compared with experimental measurements and curves from Monte Carlo simulations, excellent agreement is obtained.
A single-mode dye-laser model incorporating pump white noise through gain-parameter fluctuations is analyzed. It includes a fluctuating saturation term. Intensity fluctuations, a first-order-like transition, and intensity correlation functions are calculated and discussed. It is found that effects previously claimed to be a consequence of the presence of colored noise in the context of loss-noise models can be also explained by white gain noise, except for the existence of two time regimes in the early decay of intensity correlation functions.
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 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.
Laser fluctuations are measured and characterized with a new technique based on the concept of first-passage-time distributions. This first-passage-time technique makes it possible to discern quantum noise in a dye laser even in the presence of pump fluctuations that are many orders of magnitude larger. We report new analytic and experimental results for the mean, variance, and skewness of the first-passage-time distributions. The analytic results agree well with numerical computations and experimental measurements. Our technique is particularly suited to the quantitative description of laser fluctuations above threshold; it complements the conventional photoelectric counting and correlation methods which are valuable for lasers below and near threshold but are difficult to implement for lasers far above threshold. The limits of validity of the theory containing a cubic nonlinearity are examined in the context of passage-time measurements. The effects of multiplicative noise and saturation on the variance of the intensity fluctuations are also discussed. A new signature of multiplicative noise is predicted.