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Journal of Physics B Atomic Molecular and Optical Physics

Magneto-optic rotation for an arbitrary field direction

N. H. Edwards, S J Phipp, P. E. G. Baird

Published Sep 28, 1995• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/28/18/009

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Journal of Physics B Atomic and Molecular Physics•Apr 14, 1980•57 citations
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.
For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.
We give a density-matrix account of an atom in a dilute vapor which is subject to a magnetic field and through which is propagating plane-polarized monochromatic light with frequency in the vicinity of a transition between levels of total angular momenta J=0J=0J=0 and 1, where the degeneracy may be in either the upper or lower level. The master equation approach allows saturation effects to be treated in a nonperturbative manner, and collisions are included within the context of the impact approximation. The particular case of the Voigt effect in a $(\stackrel{\ensuremath{\rightarrow}}{1}0)$ transition (lower level J=1J=1J=1) is considered in detail, and contrasted with that in $(\stackrel{\ensuremath{\rightarrow}}{0}1),$ already published; in the absence of collisions, the $(\stackrel{\ensuremath{\rightarrow}}{1}0)$ rotation spectrum is of Lorentzian form at all intensities, while if collisional relaxation is much faster than radiative decay, it takes the same form as for the $(\stackrel{\ensuremath{\rightarrow}}{0}1)$ case. The rotation produced by a magnetic field of arbitrary direction and the effects of atomic motion are also discussed.
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
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.
The authors give the theory of optical Faraday rotation and circular dichroism for a transition of mixed magnetic-dipole and electric-quadrupole character in the presence of hyperfine structure. The results are applied to two transitions of atomic bismuth, lambda 647.6 nm (J j = 3 / 2 to J j = 5 / 2 ) and lambda 875.5 nm (J j = 3 / 2 to J j = 3 / 2 ). They have studied the Faraday rotation profiles of these lines under high resolution; the results confirm the theoretical predictions and for each transition give a value for the ratio, chi , of the electric-quadrupole and magnetic-dipole reduced matrix elements, (J j //( omega /4 square root 3)(-2er 2 C (2) )//J i ) and (J j // mu //J i ). They obtain chi =-0.60(2) for lambda 647.6 nm and chi =+0.13(7) for lambda 875.5 nm, to be compared with the theoretical values -0.65 and +0.11 respectively.