Nonlinear Effects in Optical Pumping of Atoms by a High-Intensity Multimode Gas Laser. General Theory

The optical pumping of atoms by a multimode gas laser, in the presence of a magnetic field, is studied theoretically. The atoms are described by their density matrix, which is expanded on an irreducible tensorial set. The atomic relaxation is assumed to be isotropic. In order to avoid the usual perturbation theory, we use the so-called "Broad-Line approximation" (BLA). BLA is valid when the width of the "Bennett hole" created by one laser mode in the velocity distribution of the excited atoms is comparable to the spacing between modes; under these conditions, the atomic response does not depend on the velocity and the multimode laser irradiation is equivalent to a broad-line excitation. For the atomic system, BLA leads to a set of coupled equations which is valid at arbitrary intensities of the laser field and which depends on this field through a unique parameter, $\gamma$. This parameter can be understood as a laser-induced transition probability. In this article, we analyze the nonlinear effects which can be deduced from this theory, for any value of the angular momenta involved in the laser transition: Hanle-effect broadening, alignment coupling, saturation resonances on the populations are shown. The exact calculations, valid at arbitrary laser intensities for $J=1\mathrm{}\leftrightarrow J=0\mathrm{}$, $J=1\mathrm{}\leftrightarrow J=1\mathrm{}$, and $J=1\mathrm{}\leftrightarrow J=2\mathrm{}$ transitions, and the corresponding experimental results will be presented in forthcoming papers.