Laser pumping and magneto-optical rotation of the light polarization plane in a cell with an antirelaxation coating of the walls: I. Statement and solution of the problem

Abstract

A general solution of the Boltzmann kinetic equations for the atomic density matrix in a long cylindrical cell with an antirelaxation coating of the walls under conditions of laser pumping in a magnetic field is obtained. The theory involves only one relaxation parameter—the coefficient K refl of the diffusion reflection of polarized atoms from the cell walls. The solution consists of two terms. The first term is proportional to K refl and describes the contribution to the atomic polarization made by multiple passages of atoms through the pumping beam after their reflection from the walls with the antirelaxation coating. The second term does not depend on K refl and describes the polarization formed during a single passage of atoms through the pumping beam. This solution allows one to calculate the Stokes parameters for the pumping beam transmitted through the cell that are measured in experiments on magneto-optical rotation of the light polarization plane.