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Journal of physics. A, Proceedings of the Physical Society. General

Comparison of semi-classical and quantum theories for a single-mode laser

L. Allen

Published Jul 1, 1969• 4 citations
Publisher

Abstract

The dependence on cavity Q of the intensity of a single-mode laser above threshold is examined for the quantum and semi-classical theories due to Scully and Lamb (1967), and Stenholm and Lamb, respectively. The two theories predict different functional dependencies, but comparison with previously published results show that both theories are satisfied for the small relative excitations possible in a He-Ne laser.

DOI
10.1088/0305-4470/2/4/003

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
The dependence on cavity Q of the intensity of a single-mode laser above threshold is examined for the quantum and semi-classical theories due to Scully and Lamb (1967), and Stenholm and Lamb, respectively. The two theories predict different functional dependencies, but comparison with previously published results show that both theories are satisfied for the small relative excitations possible in a He-Ne laser.
The results of the semi-classical theory for the laser are compared with the results of the quantum theory given by Scully and Lamb (1967). It is found that the spatial structure of the cavity mode leads to important corrections. For moving atoms the cavity mode is smeared, and a generalized form of the Scully-Lamb theory (for resonance between the atomic transitions and the cavity mode) leads to agreement with the semi-classical theory. The photon distribution for the case with moving atoms is obtained and compared with the results of the Scully-Lamb theory.
The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.
The question of how the light output of a laser and its fluctuations depend on the optical-cavity length at a given frequency is investigated theoretically for a laser oscillating in a single Gaussian mode. The treatment is quantum mechanical, and is based on the Scully-Lamb laser model, except that a perturbation expansion is used and possible cooperative atomic effects are included. It is shown, with the help of some reasonable approximations, that the probability distribution of the photon-occupation number can be cast into a form that is similar to the Scully-Lamb formula, but with coefficients that depend on cavity length in a more complicated way. Curves are presented that illustrate the behavi\`or and should lend themselves to experimental test.