Effect of optical-cavity length on laser photon statistics

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Abstract
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 behaviòr and should lend themselves to experimental test.