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Physical Review A

Intensity correlation functions for dye lasers with white gain noise

J. M. Noriega, Luis Pesquera, M. A. Rodrguez

Published Apr 1, 1991• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.43.4008

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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.
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.
By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. T3.
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.