Dipole saturated absorption modeling in gas phase: Dealing with a Gaussian beam

With the advent of new accurate and sensitive spectrometers, cf. combining optical cavities (for absorption enhancement), the requirement for reliable molecular transition modeling is becoming more pressing. Unfortunately, there is no trivial approach which can provide a definitive formalism allowing us to solve the coupled systems of equations associated with nonlinear absorption. Here, we propose a general approach to deal with any spectral shape of the electromagnetic field interacting with a molecular species under saturation conditions. The development is specifically applied to Gaussian-shaped beams. To make the analytical expressions tractable, approximations are proposed. Finally, two or three numerical integrations are required for describing the Lamb-dip profile. The implemented model allows us to describe the saturated absorption under low pressure conditions where the broadening by the transit-time may dominate the collision rates. The model is applied to two specific overtone transitions of the molecular acetylene. The simulated line shapes are discussed versus the collision and the transit-time rates. The specific collisional and collision-free regimes are illustrated, while the Rabi frequency controls the intermediate regime. We illustrate how to recover the input parameters by fitting the simulated profiles.