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Physical Review A

Origin of the “blueshift” in selective reflection spectroscopy and its partial compensation by the local-field correction

T. A. Vartanyan, Antoine Weis

Published May 16, 2001• 17 citations
Publisher

Abstract

The theory of selective reflection from the interface of a dielectric medium and an atomic vapor is reconsidered. Both the local-field correction and the nonexponential decay of the electromagnetic field inside the vapor are accounted for in a purely analytical form. It is shown that the large influence of both effects on the shift of the spectral line is due to an interference between contributions from atoms moving towards the reflecting surface and from those moving away. We show that the local-field correction reduces the blueshift due to the field decay by one-third of its value. A simple formula relating the shift of the maximum of the reflection spectrum to the transition dipole moment and the number density of the atoms is given.

DOI
10.1103/physreva.63.063813

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The theory of selective reflection from the interface of a dielectric medium and an atomic vapor is reconsidered. Both the local-field correction and the nonexponential decay of the electromagnetic field inside the vapor are accounted for in a purely analytical form. It is shown that the large influence of both effects on the shift of the spectral line is due to an interference between contributions from atoms moving towards the reflecting surface and from those moving away. We show that the local-field correction reduces the blueshift due to the field decay by one-third of its value. A simple formula relating the shift of the maximum of the reflection spectrum to the transition dipole moment and the number density of the atoms is given.
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.
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 discuss the properties of selective reflection spectroscopy at the interface between a resonant vapor and a complex dense medium, such as a metallic film layered on a dielectric substrate. We show that in the approximation of a low-density vapor, the signal mixes up the absorptive and dispersive components of the "effective resonant susceptibility" of the vapor, with the mixture amount governed by simple laws of linear optics. Preliminary experiments performed at the interface between Cs vapor (D2, 852-nm line) and a silver-coated glass window are reported, that show qualitatively the effect of the atom-surface van der Waals interaction.
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.
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).