Quantum Theory of an Optical Maser. V. Atomic Motion and Recoil

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Abstract
A quantum theory of an optical maser was developed in the first paper of this series, in which the active medium is made up of static two-level atoms excited in their upper level while the damping atoms are taken in their lower level. The theory was extended in the fourth paper by generalizing to finite atomic and cavity temperatures, and the frequency pulling and pushing relations were also derived. In the present paper we extend the work of the previous papers by allowing the lasing atoms to have thermal motion. Recoil of the atoms due to photon emission or absorption is also considered, and its effect on the laser threshold and operating frequency is given. The influence of the atomic motion on the photon statistics, frequency shift, and line shape of the laser radiation is shown explicitly.