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Physical Review A

Selective reflection from a dense atomic vapor

Jingzhong Guo, J. Cooper, Alan Gallagher

Published Feb 1, 1996• 46 citations
Publisher

Abstract

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 ${10}^{17}$/${\mathrm{cm}}^{3}$, 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 ${10}^{17}$/${\mathrm{cm}}^{3}$ is also presented. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1130

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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 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.
Perpendicular reflection of low-power, near-resonant radiation at a sapphire--Rb-vapor interface (selective reflection) has been measured for Rb densities of $3\ifmmode\times\else\texttimes\fi{}{10}^{14}--3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At the lowest density the eight hyperfine components are essentially isolated, and at the highest pressure they are highly blended. The data have been fitted to a coherent superposition of the reflected field amplitudes of the eight components, including the well-known starting transient and wall interaction. At low to moderate densities this yields a good fit to the data, and a result for the Rb-Rb collisional shift. At the higher densities the rapid attenuation of the incident field has a major effect on the reflection spectrum, and an approximation to this is included in the calculation, assuming exponential attenuation at the equilibrium-vapor rate. This provides improved fits to the data and allows the apparent Lorentz-Lorenz plus collisional shift to be evaluated. However, the data do not fully fit this calculation, and a complete self-consistent-field calculation appears necessary to fully understand the high-pressure results.
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.
The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.
We have experimentally investigated the selective reflection of the $P\ensuremath{-}D$ transition in a high-density rubidium vapor and shown it to be sensitive to the exact spatial distribution of PPP-state atoms near the dielectric-vapor interface. This distribution results from the radiative and nonradiative transport of excitation and from wall-quenching collisions of excited-state atoms and is highly inhomogeneous. Selective reflection thus acts as a probe of the spatial dispersion in the vapor. The resulting spectra have been analyzed to show that the broadening due to $S\ensuremath{-}D$ collisions contributes considerably to the self-broadened linewidth of the $P\ensuremath{-}D$ transition.
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.