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Journal of Physics B Atomic Molecular and Optical Physics

Theory of Faraday rotation produced by atoms near a Jg= 1/2 to Je= 1/2 transition

F Schuller, Derek N. Stacey, Richard B. Warrington, K. P. Zetie

Published Sep 14, 1995• 5 citations
Publisher

Abstract

An analytical expression is derived for the Faraday rotation occurring in a dilute atomic vapour for monochromatic light of any intensity tuned near an absorption transition between two levels, each with total angular momentum J= 1/2 . Collisional effects are included within the framework of the impact approximation. The result is discussed in terms of simple physical mechanisms; it is shown that optical pumping effects play an important role.

DOI
10.1088/0953-4075/28/17/016

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An analytical expression is derived for the Faraday rotation occurring in a dilute atomic vapour for monochromatic light of any intensity tuned near an absorption transition between two levels, each with total angular momentum J= 1/2 . Collisional effects are included within the framework of the impact approximation. The result is discussed in terms of simple physical mechanisms; it is shown that optical pumping effects play an important role.
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.
We present a simple quantitative description of the lowest-order nonlinear Faraday effect of an atomic vapor by modeling the effect as a Hanle-type precession of the quadrupole moment induced by optical pumping. This gives the medium the symmetry of uniaxial birefringence, and the Faraday rotation is expressed in terms of this birefringence. We obtain expressions for transitions between states of arbitrary angular momenta; the new expressions match results obtained earlier for the case of depopulation pumping. The novel aspects are that only level populations intervene and that no explicit use of sublevel coherences is made. We present experimental verifications of the equivalence of light-induced birefringence and the nonlinear Faraday effect.
We extend our previous discussion of the resonant nonlinear Faraday effect in terms of the precession of an induced quadrupole moment to the realistic experimental situations where depopulation, repopulation, and hyperfine optical pumping contribute. We derive, to lowest order in the light intensity, an analytical expression for the magnetorotation angle near an electric-dipole resonance in an atomic medium of arbitrary spins. We find excellent quantitative agreement with absolute measurements performed on the Cs D2{\mathit{D}}_{2}D2​ line.
The absorptive and dispersive properties of a Doppler-broadened vapour of rubidium atoms is investigated. A detailed model of the atom-light interaction is developed and found to be in excellent agreement with experiment in the regime where the interacting light field is sufficiently weak such that it does not significantly alter the medium through which it propagates. The importance of using a weak beam to probe atomic systems is discussed, and a method of characterising how weak such a beam has to be is provided. The theoretical model is applied to both situations of illumination by continuous-wave and pulsed light, the latter situation providing a demonstration of the slow light effect. This phenomenon is a manifestation of the dispersive properties of the medium and is shown to exist over a particularly large frequency range, compared to the absorption spectrum, in thermal vapours. Off-resonant interactions are studied, in which incident laser-light is detuned from resonance to such a degree that Doppler-broadening can be neglected. We quantify the extent to which the light needs to be detuned to be in this regime, and provide approximations to the line-shape function developed in earlier parts of the thesis. The approximate line-shapes are much easier to manipulate and allow a more intuitive understanding of the atom-light interaction. In the second part of the thesis we study the Faraday effect and related phenomena which are an expression of the birefringent properties of the atom-light system. Beginning with a theoretical and experimental investigation of the Faraday rotation of a weak continuous-wave beam, we move on to the consideration of pulsed light. Optically-induced birefringence via the application of an intense continuous-wave pumping field is demonstrated experimentally, and the theoretical plausibility of controlling the polarisation state of a weak pulsed field mediated via intense pulsed light is shown.
Whereas mechanical rotation of a transparent solid induces rotation of the plane of linear polarization of a light beam, for a dilute vapor this mechanical Faraday effect must disappear. By studying the structure of the collision operator that is familiar in the unified theory of spectral line broadening, we demonstrate that a nonzero effect arises for a vapor of absorbing atoms embedded in a buffer gas. The size of the effect is easily compared with the magnetic Faraday effect, when the angular velocity is replaced with the Larmor precession frequency. Then, the mechanical effect is smaller by a factor of the order of the collision frequency multiplied with the duration of a collision. Furthermore, the mechanical effect is a linear combination of the frequency derivative of a (collision-broadened) dispersion curve and the derivative of an absorption curve.
The Faraday rotation and circular dichroism of dilute gases in longitudinal magnetic fields and subject to strong radiation fields are studied. The use of irreducible tensorial sets as bare-atom states which are then dressed by the laser field allows a simple incorporation of the various multipole relaxation rates into the theory. The treatment considers magnetic fields which produce Zeeman shifts much smaller than inverse collision times but which may be greater or smaller than the multipole relaxation rates. Doppler broadening is also considered. Explicit expressions are given for dipole transitions in a two-level system with arbitrary angular momentum for strong and weak magnetic fields.