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

Abstract

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 ${\ensuremath{\Delta}}_{\mathrm{HWHM}}^{(\mathrm{Hz})}\ensuremath{\simeq}0.98(\frac{u}{2\ensuremath{\pi}D})$ ($D$ is the intensity $\frac{1}{e}$ diameter and $u$ is the thermal speed). The saturation intensity is also modified by the transit rate ${\ensuremath{\gamma}}_{t}=\frac{\sqrt{2}u}{D}$ (rad/sec).