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Physical Review A

Forward-scattering magneto-optical effects

Isao Hirano

Published Nov 1, 1995• 3 citations
Publisher

Abstract

A general equation is constructed for magneto-optical spectra. The incident laser beam has an arbitrary polarization and its direction is arbitrary relative to the magnetic field. The analyzer has an arbitrary extinction ratio function. The Faraday and Voigt formulas are deduced as special solutions. From the generalized Faraday formula, the absorption spectra of ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ light are measured without influence of the birefringence. The circular dichroism is estimated. The measured spectra clearly show the frequency shifts of ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ light. The magnitude of the shift for a magnetic field of 0.015 T is twice as large as the Doppler width for the Cs ${\mathit{D}}_{2}$ line. These shifts are induced by the Larmor precession defined by the fine-structure g factor. The Larmor precession does not induce a real shift of Zeeman levels, but induces a phase shift of optical coherence through the Rabi frequency.

DOI
10.1103/physreva.52.3594

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A general equation is constructed for magneto-optical spectra. The incident laser beam has an arbitrary polarization and its direction is arbitrary relative to the magnetic field. The analyzer has an arbitrary extinction ratio function. The Faraday and Voigt formulas are deduced as special solutions. From the generalized Faraday formula, the absorption spectra of \ensuremathσ+{\mathrm{\ensuremath{\sigma}}}^{+}\ensuremathσ+ and \ensuremathσ\ensuremath−{\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}\ensuremathσ\ensuremath− light are measured without influence of the birefringence. The circular dichroism is estimated. The measured spectra clearly show the frequency shifts of \ensuremathσ+{\mathrm{\ensuremath{\sigma}}}^{+}\ensuremathσ+ and \ensuremathσ\ensuremath−{\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}\ensuremathσ\ensuremath− light. The magnitude of the shift for a magnetic field of 0.015 T is twice as large as the Doppler width for the Cs D2{\mathit{D}}_{2}D2​ line. These shifts are induced by the Larmor precession defined by the fine-structure g factor. The Larmor precession does not induce a real shift of Zeeman levels, but induces a phase shift of optical coherence through the Rabi frequency.
A general equation is constructed for the magneto-optical spectra of the forward-scattered light observed through an analyzer when an absorption cell in a homogeneous magnetic field is illuminated by a linearly polarized laser beam at an arbitrary angle to the field direction. The Faraday effect and the Voigt effect are deduced as special solutions of this general equation. For the case of Voigt geometry, \ensuremath{\pi}-polarized light whose plane of polarization is parallel to the applied magnetic field gives a simple absorption profile. \ensuremath{\sigma}-polarized light oscillating perpendicularly to the static magnetic field contains an interference term between right and left circularly polarized light as well as absorption terms. For these eigenwaves (\ensuremath{\pi},\ensuremath{\sigma}) for the Voigt effect, the spectral shapes are independent of the angle of the analyzer, only their intensity is modified by the angle. For the general case, experimental results for cesium vapor and theoretical spectra show good agreement.
Magneto-optical spectra were observed for the dilute gas phase of the Cs metal. The non-linear Faraday effect was investigated with a frequency tunable laser diode of weak intensity. Theoretical spectral profiles were obtained via optical coherence derived from the density matrix formalism. As a result of the analysis, it was ascertained that the coherent Larmor precession of atoms induces a broadening and a phase shift in the optical coherence in opposite directions for sigma + and for sigma - light. This effect originates from off-diagonal elements of the Hamiltonian.
An experiment on nonlinear laser spectroscopy and magneto-optics at the Advanced Undergraduate Laboratory at Berkeley is described. The experiment consists of three parts. In the first part, students learn to operate a diode laser system and characterize its performance using a Fabry–Perot spectrum analyzer. In the second part, Doppler-broadened laser-induced fluorescence and Doppler-free saturated absorption spectra of the rubidium D2 line (780 nm) are recorded and analyzed. Finally, in the third part of the experiment, which we describe in greater detail, the near-resonant magneto-optical rotation is investigated. Nonlinear light-atom interaction leads to spectacular manifestations of the resonant Faraday effect—polarization plane rotation in a magnetic field applied along the direction of light propagation radically different from the linear case. In particular, narrow (∼30 Hz) effective line widths are observed in this experiment corresponding to a rotation enhancement by some seven orders of magnitude compared to the linear Faraday rotation.
Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance
We investigated the resonant magneto-optic spectra of the Rb D2 transition in the Voigt configuration (transverse magnetic field). To resolve the hyperfine structure of the Voigt-effect spectrum, we used a tunable single-mode GaAlAs diode laser as a light source. Elliptically polarized light with a small ellipticity was incident upon a Rb vapor cell placed in a magnetic field. The polarization change caused by magnetically induced optical anisotropy was detected by use of a birefringent prism placed behind the vapor cell. The Voigt-effect line profiles were measured for various degrees of light ellipticity and analyzer offset angle. The measured profiles were compared with the theoretical expression.
The resonant magneto-optic spectra of the Rb D2 transition in the Voigt configuration was measured by using a tunable, narrow-band, single-mode GaAlAs diode laser. The elliptically polarized laser beam with a small ellipticity Δα was incident upon Rb vapor in a transverse magnetic field of 0.75 T. The polarization change caused by magnetically induced optical anisotropy was analyzed with a birefringent prism placed behind the sample with a small offset angle Δθ from the perfectly crossed direction. The Voigt-effect signal had a Zeeman splitting of 50 GHz. The spectral intensity distribution of the signal, determined by the interference between the hyperfine components of 85Rb and 87Rb, was dependent on Δα, Δθ, and the number density of atoms. The theoretical prediction1 for the Voigt-effect line profiles for various Δα and Δθ agreed with the experimental result. The minimum detectable density of Rb atoms was limited by statistical fluctuations of photon counts.