On the physical meaning of the "Two nondegenerate levels" atomic model in nonlinear calculations

Two results, obtained by different methods, are given for the nonlinear interaction of two electromagnetic waves of different polarizations in a population inverted medium. In the first and rigorous approach, the degeneracy of the levels is taken into account. The second method, used previously by other authors for similar calculations, involves the use of nondegenerate levels and averaging over an assumed continuous distribution of dipole orientations. By comparing the two results, the validity and physical significance of the second "classical" method is investigated. It is found that, in general, this approach gives incorrect results. However, it corresponds physically to and is valid for the case of
\DeltaJ=O
and
J
large. In addition, it gives correct results for parallel polarizations of the fields and any
J
values.