Theory of a Zeeman ring laser: General formalism

A theory of a ring laser subject to a uniform, axial dc magnetic field is given in extension of the two-mirror standing-wave treatment by Sargent, Lamb, and Fork. The active medium consists of thermally moving atoms that have two electronic levels with arbitrary angular momenta. The electric field is treated classically for two circular polarizations of opposite sense in a cavity with any degree of cavity anisotropy. Losses due to backscattering are also included. In addition, the results of a generalized treatment are given which includes arbitrarily oriented magnetic field, a general state of electric field polarization, varying isotopic abundance, and hyperfine structure. The self-consistency requirement is used to obtain amplitude- and frequency-determining equations for multimode operation as functions of laser parameters. A general calculational technique, the "perturbation tree," is introduced in the calculation of the third-order component of the population matrix, greatly simplifying the algebra involved by allowing it to be abstracted in tabular form.