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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France, Aug. 28 - Sept. 1, 2023}}}
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\title{MODELING OF SATURATED ABSORPTION IN GAUSSIAN BEAM}

\author{\underline{\FirstName PATRICK \LastName DUPR\'E}}
\address{Laboratoire Interdisciplinaire Carnot de Bourgogne, 9 Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France}

\category {3}
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If the Saturated Absorption resonance modeling has generated an abundant
literature when it is based on ``monochromatic'' ElectroMagnetic
Fields (EMF), the time of interaction of the molecules with the impinging
EMFs due to the finite transit path is quasi exclusively considered
under the approximation of a decay rate of the population, providing
Lorentzian resonance shapes. If the reasons of this over simplification
can be understood, they largely miss the real interaction resonance
shape. Actually, numerous transverse profiles of the EMF are Gaussian
shaped, hence, this shape is experienced by the traveling molecules
at low pressure when they cross the EMFs. An accurate description
of the interaction is crucial for analyzing the collisional processes
under these circumstances (the radiative processes can be ignored
in the Infrared range). Under low pressure conditions, those include
inelastic collisions (probably not dominant), Velocity Changing Collision,
Phase Interrupt Collisions or Resonant Collisions.

We will try to discuss a model based on a 2-level system under weak
saturation, including the recoil effect and the different collisional
processes under a Gaussian EMF. Analytical solutions can be obtained
for a specific Doppler shift. Then, only a Doppler shift numerical
integration is required.
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