Modulated Hanle signals in partially coherent fields

The fluorescence emitted by atoms whose excited states have Zeeman structure is studied for the case of excitation by partially coherent optical sources whose amplitudes are weakly modulated at a low frequency $\Omega$. The temporal fluctuations in lasers are taken into account exactly by using the phase-diffusion model of the laser. Analytical results for the modulated fluorescence are presented for the case of weak fields. It is shown that the shape of the fluorescent signal is extremely sensitive to the bandwidth of the field; for example, one gets resonances at a Larmor frequency equal to $\mathcal{s}=\frac{\pm \Omega }{2}(0,\pm \Omega )$ for broadband (monochromatic) fields. Various limiting cases are treated, and in the limit of very broadband fields, results reduce to those of Corney and Series. The fluorescence is studied both as a function of the modulation frequency and as a function of the magnetic field. Numerical studies of the modulated Hanle signals in intense fields reveal resonant structures in the modulation-frequency scan at $\Omega =0,\pm {\alpha }_0$, $\pm 2{\alpha }_0({\alpha }_0^2={\mathcal{s}}^2+2\mathrm{}{\alpha }^2)$ due to the dynamical Stark splitting of the various energy levels, with the strength of the resonances depending on the direction of detection.