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Annual Meeting Optical Society of America

Lorentz red shift and self-broadening of atomic potassium vapor

Jeffery J. Maki, Robert W. Boyd, Michelle S. Malcuit, John E. Sipe

Published Jan 1, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1990.fff3

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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 studied the resonant optical response of a dense atomic potassium vapor under conditions such that the response is strongly influenced by local-field effects. Our experimental results are in good agreement with the predictions of theory. We have also discovered a collision-induced shift of the potassium resonance lines given by \ensuremath{\Delta}${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}\mathrm{o}\mathrm{l}=}$\ensuremath{\beta}N, where \ensuremath{\beta}=-5.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ cm3{\mathrm{cm}}^{3}cm3 for the 4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2P1/2{\mathit{P}}_{1/2}P1/2​ transition and where \ensuremath{\beta}=-3.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ cm3{\mathrm{cm}}^{3}cm3 for the 4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2P3/2{\mathit{P}}_{3/2}P3/2​ transition.
We have observed attenuated total reflection at a glass/rubidium vapor interface in high precision. The atom density was from $3.8\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.7\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ and the angle of incidence was from 48.4 to 64.8\ifmmode^\circ\else\textdegree\fi{}. Redshift and broadening of the reflection spectra were observed. The redshift depended on atom density, angle of incidence, light polarization and hyperfine structure. The observed broadening was attributed to the self-broadening of the resonance line. Calculation based on the Fresnel formula with a local index for the susceptibility of the vapor, which included the Lorentz local field correction and the modification of the wave vector of the evanescent light by the optically dense atomic vapor, was found to be in reasonable agreement with the experimental results.
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.
Absorption spectrum of the evanescent light at a glass/Rb vapor interface has been observed with atom density from 9 ×10 19 m -3 to 5 ×10 20 m -3 . Absorption is as high as 60% at the peak of a hyperfine structure split line. The absorption spectrum of the experiment is compared with that of the calculation based on Fresnel's relation on the assumption of a homogeneous electric susceptibility of the vapor. Near the critical angle the calculation which incorporates the Lorentz–Lorenz local-field correction reproduces the experimental red shift only partly.
We study the frequency derivatives of selective reflection from high-density rubidium vapor using a hole-burning technique. Saturation dips are observed inside the self-broadened line shapes. The line self-broadening is a combination of static width and collision width. By analyzing saturation dips, we can separate power broadening and collision width. Our experimental results support the theory of inhomogeneous dipole-dipole induced broadening of transitions in a dense atomic gas, published by J. A. Leegwater and S. Mukamel [Phys. Rev. A 49 (1994) 146].