Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals

Using classical fields and the density-matrix formalism, we analyze the nonlinear characteristics of a gas laser amplifier subject to an axial magnetic field, operating with two optical-frequency signals of arbitrary polarization. Perturbational solutions, valid for relatively weak intensities, are obtained which describe the saturation interaction of the signals and the generation of combination tones. An arbitrary amount of Doppler broadening is considered throughout. The simple $J=1\mathrm{}\to J=0\mathrm{}$ model is found convenient to describe the physical processes taking place. In general, however, the interactions are found to depend on the $J$ values of the levels. We find that only saturation and no combination-tone generation occurs for two opposite circularly polarized signals, while both effects are, in general, present for two linearly or elliptically polarized fields. The limiting case of zero magnetic field is examined separately. It is also found that in many cases the medium is made effectively anisotropic by the nonlinear interactions. Applications to measurements of atomic parameters such as $J$ values, $g$ values, and lifetimes are discussed.