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Physical Review A

Statistical fluctuations in laser transients

Shijun Zhu, Anthony W. Yu, Rajarshi Roy

Published Nov 1, 1986• 152 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.34.4333

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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.

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Introduction The investigation of the coherence properties of light sources has traditionally involved the study of correlation functions of different orders of the electric field (Born and Wolf, 1975; Mandel and Wolf, 1965). Field and intensity correlation functions have been measured for laser light (for a review, see Lax and Zwanziger, 1973) and have been compared with predictions obtained from quantum laser theory (Haken, 1970, 1981; Lax, 1969; Louisell, 1973; Sargent, Scully and Lamb, 1974). This was, in fact, one of the major confirmations of the correctness of the basic formalism of quantum laser theory. Most of the experiments that probed the coherence properties of lasers were, however, carried out on a very limited variety of lasing media. Interest was also centered on the regime of operation near threshold, where the light from the laser is extremely weak; hence photoelectron counting and correlation techniques were developed for the measurement of coherence properties of the laser light. While these early experiments were performed with the main intent of testing the basic theory, the large variety of lasers now available, and their ever more demanding applications, make it necessary to develop new methods for the measurement and analysis of laser fluctuations. These techniques should be applicable to the measurement of noise in high power lasers; at the same time, in order to delineate the limits of usage, they must be sensitive enough to quantitatively determine the quantum mechanical sources of noise which may lie buried in external noise that is many orders of magnitude larger.

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Physical Review Letters•Dec 16, 1985•112 citations
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.
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 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.
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.
Introduction The investigation of the coherence properties of light sources has traditionally involved the study of correlation functions of different orders of the electric field (Born and Wolf, 1975; Mandel and Wolf, 1965). Field and intensity correlation functions have been measured for laser light (for a review, see Lax and Zwanziger, 1973) and have been compared with predictions obtained from quantum laser theory (Haken, 1970, 1981; Lax, 1969; Louisell, 1973; Sargent, Scully and Lamb, 1974). This was, in fact, one of the major confirmations of the correctness of the basic formalism of quantum laser theory. Most of the experiments that probed the coherence properties of lasers were, however, carried out on a very limited variety of lasing media. Interest was also centered on the regime of operation near threshold, where the light from the laser is extremely weak; hence photoelectron counting and correlation techniques were developed for the measurement of coherence properties of the laser light. While these early experiments were performed with the main intent of testing the basic theory, the large variety of lasers now available, and their ever more demanding applications, make it necessary to develop new methods for the measurement and analysis of laser fluctuations. These techniques should be applicable to the measurement of noise in high power lasers; at the same time, in order to delineate the limits of usage, they must be sensitive enough to quantitatively determine the quantum mechanical sources of noise which may lie buried in external noise that is many orders of magnitude larger.