Quantitative investigation of the resonant nonlinear Faraday effect under conditions of optical hyperfine pumping

We extend our previous discussion of the resonant nonlinear Faraday effect in terms of the precession of an induced quadrupole moment to the realistic experimental situations where depopulation, repopulation, and hyperfine optical pumping contribute. We derive, to lowest order in the light intensity, an analytical expression for the magnetorotation angle near an electric-dipole resonance in an atomic medium of arbitrary spins. We find excellent quantitative agreement with absolute measurements performed on the Cs ${\mathit{D}}_2$ line.