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

On the quantum theory of a laser with inhomogeneous broadening

D.O. Riska, Stig Stenholm

Published Mar 1, 1970• 14 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/3/2/011

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
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 theory of a laser developed by Scully and Lamb (1967) is reformulated to include the effects of atomic motion and detuning. The equations are solved to fourth order in the atom-field coupling constant. An approximate treatment of the mode structure is shown to reproduce the results of Lamb's semi-classical theory in the Doppler limit. In addition the photon distribution may be studied as a function of the detuning. The width of the photon distribution is found to increase monotonically with increasing detuning.
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 results of the Riska-Stenholm quantum theory for an inhomogeneously broadened laser are re-derived without using the Doppler limit approximation which restricts the utility of this theory. The photon distribution peak is seen to occur at a significantly lower photon number and the threshold condition is dependent on Yablku, where Yab is the relaxation parameter and ku the Doppler parameter. The dimensionless intensity parameter is obtained and the results are compared with the existing theories of Riska and Stenholm and of Scully and Lamb.