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Communications in Theoretical Physics

Intensity Correlation, Relaxation Time, Intensity Fluctuation and First-Order-Like Transition of Dye Laser

Tie-Hai Jiang, Wu Da-Jin, Cao Li

Published Apr 1, 1993• 0 citations
Publisher

Abstract

Statistical properties of dye laser are studied by using the colored gain-noise model which has been presented recently. We calculate the intensity correlation function and relaxation time driven by colored pump noise and white spontaneous-emission noise simultaneously. Intensity fluctuation and first-order-like transition are analyzed too in this paper. It is found that the colored gain-noise model can describe well the anomalous statistical properties of dye laser.

DOI
10.1088/0253-6102/19/3/295

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Statistical properties of dye laser are studied by using the colored gain-noise model which has been presented recently. We calculate the intensity correlation function and relaxation time driven by colored pump noise and white spontaneous-emission noise simultaneously. Intensity fluctuation and first-order-like transition are analyzed too in this paper. It is found that the colored gain-noise model can describe well the anomalous statistical properties of dye laser.
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.
The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times \ensuremath{\tau} larger than the deterministic relaxation time td{\mathit{t}}_{\mathit{d}}td​, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.
Predictions for dye-laser intensity correlation functions of a stochastic model incorporating colored gain-noise fluctuations are discussed and compared with the predictions of the model incorporating loss-noise fluctuations. It is shown that differences between the two models are generally masked by the finite correlation time of the noise. Important differences are shown to exist well above threshold when the correlation time of the colored noise is of the same order or smaller than the cavity decay time. A new algorithm for the simulation of stochastic equations with colored noise is used and discussed.
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.
We consider a single-mode dye-laser model with gain parameter fluctuations modeled by a white noise. The decay of the intensity correlation function C(t) is analyzed with the use of a method based on the combination of the low- and high-frequency expansions of the Laplace transform of C(t). The correlation function is approximated by a superposition of two decaying exponentials. Numerical simulations show that this approximation is accurate. We analyze the relaxation of C(t) in the domain of parameters, gain parameter close to the pump parameter, in which the white-gain-noise model reproduces the initial slow decay of C(t). It is found that the intensity correlation function does not show two separated time scales as observed experimentally.
Recent theoretical analyses of the single-mode laser with colored-noise pump fluctuations have allowed the detailed prediction of the short-time behavior of the intensity autocorrelations of such a laser. In particular, a rounding off of the intensity correlation function on the time scale of the correlation time of the pump fluctuations has been predicted. We present results from experiments performed on a single-mode dye-laser system that clearly confirm these predictions. Numerical simulations of the laser Langevin equations including the colored-noise pump fluctuations are used to fit the experimental results.