Nonlinear Faraday Rotation in Samarium Vapor

Studies of the nonlinear Faraday effect (rotation of the plane of polarization in a longitudinal magnetic field) on resonance atomic transitions have been reported in a number of theoretical and experimental papers [1-9]. The nonlinear effect manifests itself at moderate laser intensities in the absence of atomic collisions. It leads to narrow peaks in the magnetic field dependence of Faraday rotation in the region of small fields. The rotation angles on these peaks may exceed the linear contribution by many orders of magnitude. In addition, the nonlinear rotation exhibits a vastly different dependence on laser detuning. The main mechanisms responsible for nonlinear Faraday rotation are related to the laser light-induced coherences between the Zeeman components of atomic states and also to the Bennett structures within the atomic velocity distributions. The simplest systems where coherence effects can be observed are the so-called Vand Λ-systems. Coherence of Zeeman sub-levels with M= + 1 arises here due to stimulated absorption and emission. The origin of optical rotation can be understood from a simple classical picture. Linearly polarized radiation induces in the medium an oscillating dipole moment. In the presence of a longitudinal magnetic field this moment precesses around the field direction causing rotation of the polarization plane of the radiation. This effect is similar to the Hanle effect (see e.g. [10] ). The magnitude of optical rotation is maximal when, during the coherence relaxation time, the oscillating dipole moment rotates by an angle of the order of a radian. Thus, peaks arise in the magnetic field dependence of optical rotation with a width determined by the Zeeman coherence relaxation rate. For Λ-systems with metastable lower states this rate can be much smaller than the natural width of the transition. Consider the influence of Bennett structures on Faraday rotation. In the presence of a magnetic field, left and right circularly polarized photons interact in general with different velocity groups of atoms. The arising Bennett structures (an example of such structure is the velocity distribution for the J=O level in a V-system is sketched in fig. 1) are shifted in opposite directions with respect to the velocity groups resonant to the right and left circular polarizations. This causes a difference in refractive indices for the two circular components and leads to the Faraday rotation. The corresponding peaks in the magnetic