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Physical Review Letters

Time-Dependent Photoelectric Counting Statistics for a Q -Switched Laser Near Threshold

David W. Meltzer, L. Mandeļ

Published Oct 26, 1970• 40 citations
Publisher

Abstract

The time-dependent variation of the photoelectric counting probability has been measured for a $Q$-switched single-mode laser, whose steady state is in the neighborhood of the threshold of oscillation. The mean and the variance of the instantaneous light intensity, at various times and for various pump parameters, are derived and found to be in very good agreement with the values predicted by Risken and Vollmer.

DOI
10.1103/physrevlett.25.1151

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The time-dependent variation of the photoelectric counting probability has been measured for a QQQ-switched single-mode laser, whose steady state is in the neighborhood of the threshold of oscillation. The mean and the variance of the instantaneous light intensity, at various times and for various pump parameters, are derived and found to be in very good agreement with the values predicted by Risken and Vollmer.
The time evolution of the optical field produced by a QQQ-switched He:Ne laser has been investigated experimentally, in the neighborhood of the threshold of oscillation. The experiment was based on a measurement of the variation of the photoelectric counting probability with time, following the turn-on of the laser. QQQ switching was achieved with the help of an external mirror to extinguish the laser, and a Pockels cell to switch out the mirror. The working point of the laser could be held anywhere in the threshold region, by use of a feedback arrangement which controlled the cavity length, and therefore the atomic gain. Results are presented showing the evolution of the mean light intensity, the variance of the light intensity, and the counting probability with time, for several different values of the laser pump parameter. The results are found to be in very good agreement with the calculations of Risken and Vollmer, based on a rotating-wave van der Pol oscillator model of the laser.
With the help of a fast digitizer, the probability distribution of the light intensity of a single-mode dye laser has been measured photoelectrically, for various working points of the laser, from well-below to well-above threshold. In the region below threshold the laser exhibits short spiking and a double-peaked probability distribution with large value at zero intensity. A plot of most probable vs mean light intensity shows a discontinuity suggestive of a first-order phase transition. The experimental results are compared with Monte Carlo solutions of the equations of motion, with both additive spontaneous emission noise and multiplicative Ornstein-Uhlenbeck pump noise, and reasonable agreement is found.
The equations of motion for an inhomogeneously broadened laser operating off resonance in the neighborhood of threshold are solved. It is shown that the effects of detuning cannot be described just by a frequency-dependent laser pump parameter, but that the laser characteristics are modified in other ways also. The relative intensity fluctuations and the correlation time of the laser are calculated as a function of mean intensity and frequency, and it is shown that both are affected by detuning. These theoretical conclusions are then confirmed quantitatively by direct photoelectric counting and two-time correlation measurements of a He:Ne laser.
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.