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Physical Review A

Forward scattering magneto-optical spectra of the Cs D2 line

Isao Hirano

Published Dec 1, 1994• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.4650

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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.
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 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.
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.
We give a theory of magneto-optic rotation and pseudorotation spectra for forbidden transitions. The case considered is that of a weak magnetic field at an arbitrary angle to the direction of light of low intensity passing through a dilate atomic vapour. The theory is applied to the 1279 nm M1 transition in atomic lead and the 1283 nm M1/E2 transition in atomic thallium. Experimental Voigt and Faraday effect data for lead measured in a sensitive optical polarimeter provide confirmation of the predicted profiles.
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