Abstract
Expressions are developed in this paper which describe the behavior of a gas laser having generalized polarization characteristics. It is found that degeneracies of the atomic energy levels play an important part in determining the behavior of such a laser since significant terms occur in the nonlinear polarization which are attributable to an oscillatory mixing of these levels. As a result, it is found, for example, that for single-mode operation the field intensity is greatest for either plane or circular polarization depending upon whether a $\ensuremath{\Delta}j=\ifmmode\pm\else\textpm\fi{}1$ or $\ensuremath{\Delta}j=0$ atomic transition is involved in the laser action. For two-mode operation, on the other hand, the behavior depends in a complicated way both on the polarization states of the oscillations and on the degree of degeneracy of the energy levels. This behavior is discussed in a number of special cases.
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