Absorption of a Gaussian laser mode in a molecular beam

This paper presents a calculation of the depth of the saturation dip observed when laser radiation of a Gaussian ${\mathrm{TEM}}_{00}$ mode is absorbed in a thermal molecular beam or in a very-low-pressure gas. Transit-time broadening is assumed to be the only broadening mechanism, with neglect of collisions and other relaxations. There is no restriction to small saturation parameters. The absorption experienced by one molecule has been calculated via the optical Bloch equations. Averaging over all relevant parameters of the molecular trajectory and the laser field followed. To get a reference for the saturation, from which to measure the dip depth, simply twice the absorption from a running-wave field has been taken, which therefore also had to be calculated in addition to the calculation of the absorption in a standing wave. Preliminary experiments have been carried out for comparison, and the data agree very well with the calculated shape of the curve and the absolute values of the calculated dip depth. From the laser-power scaling factor, necessary to fit the experimental data to the universal theoretical curve, the dipole moment can be derived without having to know such hard-to-determine quantities as absorber density, partition function, collision relaxation rate, or even the diameter of the laser beam.