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Physical Review A

Intrinsic third-order correlations in laser light near threshold

Mario Corti, Vittorio Degiorgio

Published Oct 1, 1976• 17 citations
Publisher

Abstract

We present an experimental investigation of the third-order intensity correlations in the light from a single-mode intensity-stabilized He-Ne laser in the threshold region. Accurate results were obtained by utilizing a fast digital correlator operating in real time. The computation of the intrinsic third-order correlations requires also a knowledge of the second-order intensity correlation which was measured under the same operating conditions. The experimental data are in agreement with recent theoretical computations based on the usual Van der Pol model of the laser oscillator. A new definition of the intrinsic correlations, which seems more appropriate for the interpretation of the experimental results, is discussed.

DOI
10.1103/physreva.14.1475

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Third-order intensity correlations in laser light

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Exact Photocount Statistics: Lasers near Threshold

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A previously constructed laser model with quantum (noncommuting) noise sources was shown to lead near threshold to a quantum rotating-wave Van der Pol oscillator. A full dynamical correspondence between quantum and classical random processes allows one to compute the average of any time-ordered, normal-ordered operator function by averaging the associated function of classical random variables. Numerical calculations for the associated classical Van der Pol oscillator of the steady-state distribution, the total intensity fluctuations, and the linewidth versus operating point were amply confirmed experimentally. Measurements (and calculations) of higher than two-time correlations were sparse and contradictory. Photocount distributions, at times short compared to the intensity correlation time, confirm only the steady state of the laser. Photocount distributions at intermediate and longer times are difficult to compute because they involve multitime correlations of high ($\ensuremath{\infty}$) order. By providing an exact solution for photocount distributions and their moments for all times, we expected to stimulate measurements near threshold which would provide an adequate test of the Van der Pol laser model. Comparison of the results reported here with recent photocount experiments of Meltzer, Davis, and Mandel and of Jakeman, Oliver, and Pike provides gratifying agreement and confirmation of our statistical understanding of laser fluctuations near threshold.

Physical Review A•Feb 1, 1973•44 citations
We present an experimental investigation of the third-order intensity correlations in the light from a single-mode intensity-stabilized He-Ne laser in the threshold region. Accurate results were obtained by utilizing a fast digital correlator operating in real time. The computation of the intrinsic third-order correlations requires also a knowledge of the second-order intensity correlation which was measured under the same operating conditions. The experimental data are in agreement with recent theoretical computations based on the usual Van der Pol model of the laser oscillator. A new definition of the intrinsic correlations, which seems more appropriate for the interpretation of the experimental results, is discussed.
We have calculated the third- and higher-order (multitime) cumulants of the intensity of single-mode laser light using the rotating-wave van der Pol (RWVP) model. Our results indicate a distinctly nonexponential time dependence of the cumulants slightly below threshold and an oscillatory time dependence somewhat above threshold. One can interpret this oscillatory behavior as showing that the larger fluctuations above the mean decay more rapidly than those below the mean. Measurements of the third-order intensity cumulants above threshold would be desirable to check for this behavior and to provide a more rigorous test of the RWVP model than the second-order intensity correlation.
In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from 110\frac{1}{10}101​ to 10 times threshold intensity. The experimental results are compared with theoretical predictions based on solutions of a Fokker-Planck equation. We stabilized the intensity of a He-Ne cw gas laser by means of a long-time-constant servo system which controlled the cavity length. Using a fast photomultiplier as detector, we recorded the photoelectron count distribution within a short counting time (3 \ensuremath{\mu}sec) while the photomultiplier was exposed to the laser light. From the photoelectron count distribution measurement, we calculated second, third, and fourth normalized cumulants of the intensity probability density function of the light field. The normalized cumulant is a measure of "pure" correlations among photons because the contributions from lower-order correlations are removed. The statistics of the photoelectron count distribution shows that the intensity fluctuations at about 110\frac{1}{10}101​ threshold are nearly those of a Gaussian field, and continuously approach those of a constant-amplitude field as the intensity is raised to about 10 times threshold. The normalized second, third, and fourth cumulants of the intensity probability density function of the laser light were also measured at 17 and 42% of threshold intensity as the counting time was increased from 3 to 1000 \ensuremath{\mu}sec. The results agree with predictions computed under the assumption that the dependence of the correlation functions on the time variables is the same as for Gaussian light.
The form and the decay time of the intensity correlation function of the light from a single-mode He:Ne laser have been measured in the neighborhood of threshold. The experiments were performed at several predetermined values of the pump parametera, ranging froma = -1toa = 4. By combination of the experimental results with the theoretically predicted eigenvalues appearing in the expansion of the correlation function, it was possible also to determine the amplitudes of the first two terms in the expansion over the same range. The experimental results are found to be substantially in agreement with the nonlinear oscillator theory of the laser, without adjustment of any arbitrary scaling parameters.
A previously constructed laser model with quantum (noncommuting) noise sources was shown to lead near threshold to a quantum rotating-wave Van der Pol oscillator. A full dynamical correspondence between quantum and classical random processes allows one to compute the average of any time-ordered, normal-ordered operator function by averaging the associated function of classical random variables. Numerical calculations for the associated classical Van der Pol oscillator of the steady-state distribution, the total intensity fluctuations, and the linewidth versus operating point were amply confirmed experimentally. Measurements (and calculations) of higher than two-time correlations were sparse and contradictory. Photocount distributions, at times short compared to the intensity correlation time, confirm only the steady state of the laser. Photocount distributions at intermediate and longer times are difficult to compute because they involve multitime correlations of high ($\ensuremath{\infty}$) order. By providing an exact solution for photocount distributions and their moments for all times, we expected to stimulate measurements near threshold which would provide an adequate test of the Van der Pol laser model. Comparison of the results reported here with recent photocount experiments of Meltzer, Davis, and Mandel and of Jakeman, Oliver, and Pike provides gratifying agreement and confirmation of our statistical understanding of laser fluctuations near threshold.