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Physics Letters A

Photon bunching in a laser at threshold.

C. O. Alley, Ren Fang Chang, Robert W. Detenbeck, U. Hochuli, Victor Korenman

Published Aug 14, 1967• 0 citations
OpenAlex

Abstract

He-Ne laser light intensity distribution cumulants for nonlinear oscillation threshold operation

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Second-harmonic generation (SHG) has been predicted to be very sensitive to photon bunching. Because of its two-photon nature SHG would be more efficient with bunched than with random or antibunched photon sequences of the same mean intensity. We use this phenomenon to demonstrate the bunching of photons in time. The fundamental beam, derived from a laser operating near threshold, was focused into a 90° temperature phase matched nonlinear crystal. The operating point of the laser was varied in the neighborhood of threshold, and a feedback loop stabilized its intensity at each operating point. It is well known that the character of laser light changes in passing the threshold of laser action. Underlying photon sequences are bunched below threshold and random above threshold.
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.