Transit-time effects in optically pumped coupled three-level systems

A density-matrix calculation of the line shape for an optically pumped coupled three-level system subjected to two traveling wave-laser fields with Gaussian intensity profiles is presented to third-order in perturbation theory. A closed-form expression for the line shape in the extreme transit-time limit is obtained. The line shape of the narrow resonance (Raman-type processes) is found to be an exponential function of the detuning, with half-width at half maximum ΔHWHM(Hz)0.98(u2πD) (D is the intensity 1/e diameter and u is the thermal speed). The saturation intensity is also modified by the transit rate γₜ=√2uD (rad/sec).