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Physical Review A

Effects of saturation in the transient process of a dye laser. II. Colored-noise case

Cao Li, Wu Da-Jin, Xueli Luo

Published May 1, 1992• 22 citations
Publisher

Abstract

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 ${\mathit{I}}_{0}$ 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.

DOI
10.1103/physreva.45.6848

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Physical Review A•Dec 1, 1988•45 citations
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 0.8I0{\mathit{I}}_{0}I0​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.
A unified colored-noise approximation is applied to calculate the stationary intensity probabilities of colored-gain-noise and colored-loss-noise models for dye lasers with saturation effects. We compare the results of the unified colored-noise approximation with the predictions of the best Fokker-Planck equation for the stationary intensity probability of a colored-gain-noise model, and find that the results of the unified colored-noise approximation agree better with simulation results than the results of the best Fokker-Planck equation. The first-order-like transition of colored-gain-noise and colored-loss-noise models with saturation effects is discussed and compared. It is found that the emergence of the first-order-like transition is related to the saturation element in the fluctuation term of the dye-laser model for white pump noise, and the occurrence of the first-order-like transition is only due to the existence of colored pump noise in the loss-noise models for dye lasers with saturation effects.
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.
We carry out numerical simulations of the evolution and steady-state properties of a dye laser operating near resonance. The model we use is fully two dimensional (i.e., it includes the intensity and the phase of the radiation) and does not involve the usual low-intensity expansions commonly used in the literature. The equation for the complex electric field is driven by white additive noise (quantum fluctuations due to spontaneous emission) and by colored multiplicative noise (fluctuations of the gain parameter). We note that the simulations agree with the experimental results of Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)] for parameter values used in their experiments. We compare the simulation results with predictions of the ``best Fokker-Planck equation'' (BFPE) for the steady-state distribution of the laser intensity and find remarkable quantitative agreement for large ranges of parameters values, even for values that are in principle beyond the range of validity of this equation. We conclude that the BFPE can be safely invoked to make predictions for this system.
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.
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.