General theory of frequency modulated selective reflection. Influence of atom surface interactions

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Abstract
We calculate the modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened

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