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Journal de physique

Spectral narrowing of selective reflection

Martin F. H. Schuurmans

Published Jan 1, 1976• 114 citations
Publisher

Abstract

A theory for the spectral narrowing of selective reflection near a resonance line of an atomic vapor is developed. The narrowing is ascribed to transient polarization behaviour of vapor atoms associated with wall collisions. For normally incident light the reflectivity of a glass-vapor interface is calculated both for diffuse and for specular wall collisions and for a symmetric distribution of atomic velocities. The theoretical results are compared with recent experimental results.

DOI
10.1051/jphys:01976003705046900

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A theory for the spectral narrowing of selective reflection near a resonance line of an atomic vapor is developed. The narrowing is ascribed to transient polarization behaviour of vapor atoms associated with wall collisions. For normally incident light the reflectivity of a glass-vapor interface is calculated both for diffuse and for specular wall collisions and for a symmetric distribution of atomic velocities. The theoretical results are compared with recent experimental results.
The theory of the thin-vapor-layer linear optical properties is presented for the case of specular reflection of atoms colliding with the walls. The effects of light absorption and the shift in the resonance frequency are taken into account by means of self-consistent calculation of the field and polarization in a gaseous medium. The obtained formulas reproduce the complex dependence of the spectral line profile on the gas layer thickness and allow one to determine numerically the exact values of the ``blueshift.'' It was shown that, despite the low vapor concentration, the resonance shift is on the same order of magnitude as the width of the spectral lines.
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.
A theory of selective reflection (SR) of a light beam from the interface of a dielectric medium and a dense atomic vapor is presented. Following another earlier work on this subject [J. Guo et al., Opt. Commun. 110, 732 (1994)], we calculate the atomic density matrix and the transmitted field in the vapor self-consistently. We extend our previous theory to include an attractive atom-dielectric wall interaction and multiple atomic transitions. We examine the limits at which the conventional SR theories, which are based on the assumption of a plane-wave field in the vapor, start to fail. It is shown that at or above vapor densities of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3, the frequency shifts of the SR line shape due to the local-field correction (Lorentz-Lorenz shift), the atom-wall interaction, and the nonexponential attenuation of the field in the vapor can have comparable orders of magnitude, and the proper determination of all these effects is essential for calculating the correct SR signals. A comparison of the theoretical SR spectra with an experimental result for a Rb vapor with a density of order 1017{10}^{17}1017/cm3{\mathrm{cm}}^{3}cm3 is also presented. \textcopyright{} 1996 The American Physical Society.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
Hot alkali metal vapors enclosed in submicron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at the nanoscale. Here, we propose an approach for calculating the eigenmodes of a thin vapor layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blueshift and deformation of the spectral line shapes of reflection, transmission, and absorption. We also demonstrate that the eigenmodes of the thin vapor layer can be calculated independently of the choice of optical boundary conditions. This greatly extends the applicability of the constructed theory for the development of miniature atomic sensors.