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Physical Review A

Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection

賢 東條, Masahiro Hasuo

Published Jan 31, 2005• 39 citations
Publisher

Abstract

The absorption line strengths of electric-dipole-forbidden (magnetic dipole and electric quadrupole) transitions have been calculated in the evanescent light field that accompanies the total reflection of light. Owing to the complex wave and polarization vectors of the evanescent light, the apparent oscillator strength is enhanced from that in the propagating light and the enhancement for the electric quadrupole transition depends on the polarization vector of the incident light. Separation of the contribution from each component of the wave and polarization vectors is proposed with a magnetic-sublevel-resolved measurement for the $(s\text{\ensuremath{-}}d)$ electric quadrupole transition.

DOI
10.1103/physreva.71.012508

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Precision measurement of the oscillator strength of the cesium 6S1∕22→5D5∕22 electric quadrupole transition in propagating and evanescent wave fields

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Hyperfine-structure-resolved absorption spectra of the $6\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}5\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ of cesium atoms have been observed with a temperature-controlled cell and a diode laser. From a comparison with the absorption of the ${D}_{2}$ transition at the same atom density range, the oscillator strength of the electric quadrupole transition was determined to be $(4.69\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. Reflection spectra of the same transition have also been observed in the partial and total reflection regimes with a reflection cell. An increase in the apparent oscillator strength was observed for total reflection with an increase in the angle of incidence, by a factor up to 1.5 at ${\ensuremath{\theta}}_{c}+83.8\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$ and 2.4 at ${\ensuremath{\theta}}_{c}+107.5\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$ for $s$ and $p$ polarizations, respectively, where ${\ensuremath{\theta}}_{c}$ is the critical angle. The observed enhancement is ascribed to the incidence-angle-dependent wave vector and polarization vector of the evanescent wave.

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Precision measurement of the oscillator strength of the cesium-6 S-2(1/2)-> 5 D-2(5/2) electric quadrupole transition in propagating and evanescent wave fields

S Tojo, Fujimoto, T, Masahiro Hasuo

•Jan 1, 2005•0 citations
The absorption line strengths of electric-dipole-forbidden (magnetic dipole and electric quadrupole) transitions have been calculated in the evanescent light field that accompanies the total reflection of light. Owing to the complex wave and polarization vectors of the evanescent light, the apparent oscillator strength is enhanced from that in the propagating light and the enhancement for the electric quadrupole transition depends on the polarization vector of the incident light. Separation of the contribution from each component of the wave and polarization vectors is proposed with a magnetic-sublevel-resolved measurement for the (s\ensuremath-d)(s\text{\ensuremath{-}}d)(s\ensuremath-d) electric quadrupole transition.
Hyperfine-structure-resolved absorption spectra of the $6\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}5\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ of cesium atoms have been observed with a temperature-controlled cell and a diode laser. From a comparison with the absorption of the D2{D}_{2}D2​ transition at the same atom density range, the oscillator strength of the electric quadrupole transition was determined to be $(4.69\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. Reflection spectra of the same transition have also been observed in the partial and total reflection regimes with a reflection cell. An increase in the apparent oscillator strength was observed for total reflection with an increase in the angle of incidence, by a factor up to 1.5 at ${\ensuremath{\theta}}_{c}+83.8\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$ and 2.4 at ${\ensuremath{\theta}}_{c}+107.5\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$ for sss and ppp polarizations, respectively, where ${\ensuremath{\theta}}_{c}$ is the critical angle. The observed enhancement is ascribed to the incidence-angle-dependent wave vector and polarization vector of the evanescent wave.
We have observed for the first time reflection spectra of an electric quadrupole transition for the cesium atom ($6\text{ }^{2}S_{1/2}\mathrm{\text{\ensuremath{-}}}5\text{ }^{2}D_{5/2}$) line at an angle of incidence from ${\ensuremath{\theta}}_{c}\ensuremath{-}11.9$ to ${\ensuremath{\theta}}_{c}+107.5\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$, where ${\ensuremath{\theta}}_{c}$ is the critical angle for total reflection. From a comparison with the calculated absorption in the attenuated total reflection, the oscillator strengths for sss and ppp polarizations were found to increase with an increase in the angle of incidence by a factor up to 1.5 at ${\ensuremath{\theta}}_{c}+83.8\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$ and 2.4 at ${\ensuremath{\theta}}_{c}+107.5\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$, respectively, in the experiment. The dependences of the observed enhancement on the angle of incidence were in good agreement with the calculated ones for the oscillator strength of the quadrupole transition in the evanescent light.
Summary form only given. Although it is often assumed that all light-matter interactions at optical frequencies are mediated by electric dipole transitions, strong optical-frequency magnetic dipoles do exist. In fact, we see magnetic dipole emission every day from the many lanthanide ions (such as erbium, europium, and terbium) that help to illuminate everything from fluorescent lighting to telecom fiber amplifiers. Higher-order processes such as magnetic dipole and electric quadrupole transitions also play an important part in the light emission from transition metal ions and semiconductor quantum dots. Nevertheless, most applications have overlooked the device implications of these electric-dipole-forbidden transitions throughout the visible and near-infrared regime, and their contributions to many important emitters have not been fully characterized.In this presentation, we will experimentally characterize the "forbidden" transitions in a range of solid-state emitters and investigate their applications and implications for nanophotonics. We will examine the electric dipole approximation commonly used to describe light-matter interactions and discuss naturally occurring systems that exhibit higher-order magnetic dipole and electric quadrupole emission. We will illustrate how these nanoscale quantum transitions can provide both a new way to probe magnetic light-matter interactions and a new degree of design freedom for active electronic and photonic devices. Specifically, we will demonstrate how the different symmetries of multipolar transitions can be exploited to identify, quantify, and control light emission, even at sub-lifetime scales. Despite similar radiation patterns, magnetic and electric dipole emitters have different symmetries with respect to polarization and phase. Thus, in an inhomogeneous environment, we can tailor interference effects and the local density of optical states to selectively enhance either electric or magnetic dipole emission [1,2]. To examine the scope of such higher-order transitions, we will present quantum mechanical calculations that identify all the magnetic dipole and electric quadrupole emission lines in the trivalent lanthanide series in the visible to near-infrared spectrum [3]. Then, we will present an energyand momentum-resolved spectroscopy technique to directly quantify the electric and magnetic dipole contributions from any mixed transition. [4] Using energy-momentum spectroscopy, we will experimentally examine the higher order transitions in lanthanide ions [4,5], transition metal ions [6], and epitaxial quantum dots [7]. If time permits, we will then show how the symmetry differences between magnetic and electric dipoles can be used to address specific electronic states [6] and to dynamically tune emission spectra at sub-lifetime-scales [8].
Modern studies have confirmed the possibility of making atomic mirrors using quadrupole-active atomic transition evanescent waves. The reflection process has been shown to be enhanced to approach specular behavior in several ways. In this study, we considered the atomic mirror due to the optical quadrupole potential generated by two counter-propagating optical Gaussian beams. This arrangement provides good enhancement for the evanescent field in the vacuum above the surface, which can be used as an atomic mirror. A high-quality atomic mirror should reflect the atoms specularly while maintaining the coherence of the de Broglie wave function. We focused on a particular atomic transition in Cs, which is a dipole-forbidden but quadrupole-allowed transition. We illustrate the optical quadrupole potential and suggest that quadrupolar transitions generally ignored in atom optics exist for exploitation. This study investigated the conditions facilitating atomic mirrors using typical experimentally accessible parameters.
We investigate the electric quadrupole interaction of an alkali-metal atom with guided light in the fundamental and higher-order modes of a vacuum-clad ultrathin optical fiber. We calculate the quadrupole Rabi frequency, the quadrupole oscillator strength, and their enhancement factors. In the example of a 87Rb^{87}\mathrm{Rb}87Rb atom, we study the dependencies of the quadrupole Rabi frequency on the quantum numbers of the transition, the mode type, the phase circulation direction, the propagation direction, the orientation of the quantization axis, the position of the atom, and the fiber radius. We find that the root-mean-square (rms) quadrupole Rabi frequency reduces quickly but the quadrupole oscillator strength varies slowly with increasing radial distance. We show that the enhancement factors of the rms Rabi frequency and the oscillator strength do not depend on any characteristics of the internal atomic states except for the atomic transition frequency. The enhancement factor of the oscillator strength can be significant even when the atom is far away from the fiber. We show that, in the case where the atom is positioned on the fiber surface, the oscillator strength for the quasicircularly polarized fundamental mode HE11{\mathrm{HE}}_{11}HE11​ has a local minimum at the fiber radius $a\ensuremath{\simeq}107$ nm, and is larger than that for quasicircularly polarized higher-order hybrid modes, transverse electric modes, and transverse magnetic modes in the region a<498.2a<498.2a<498.2 nm.