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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Non-linear magneto-optical polarization rotation in dark and bright coherent states

Z. D. Grujić, Marina M. Mijailović, Aleksandar J. Krmpot, Bratimir M. Panic, Dejan Pantelić, B. M. Jelenkovic

Published Mar 2, 2007• 0 citations
Publisher

Abstract

We have measured non-linear Faraday effects for dark and bright long-lived Zeeman coherences in the D2 resonance line of 85Rb, for linearly polarized input laser light. Zeeman coherence in the bright state show enhanced nonlinear effects, larger values for the angle of polarization rotation and higher rates of the polarization rotation, similar to recent results for higher refractive index and dispersion in the bright state of Cs 1. Dark and bright states also show different dependence of both polarization rotation angle and of polarization rate on the laser intensity, while the resonance width for both states varies similarly with the laser intensity. We show small enhancement of such non-linear effects when the laser beam diameter increases from 1 mm to 5 mm. Ellipticity of transmitted laser beam vary strongly for amplitudes of the external magnetic field smaller then 50 mG, but the maximum value of the ellipticity remains below &pgr;/300.

DOI
10.1117/12.726884

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We have measured non-linear Faraday effects for dark and bright long-lived Zeeman coherences in the D2 resonance line of 85Rb, for linearly polarized input laser light. Zeeman coherence in the bright state show enhanced nonlinear effects, larger values for the angle of polarization rotation and higher rates of the polarization rotation, similar to recent results for higher refractive index and dispersion in the bright state of Cs 1. Dark and bright states also show different dependence of both polarization rotation angle and of polarization rate on the laser intensity, while the resonance width for both states varies similarly with the laser intensity. We show small enhancement of such non-linear effects when the laser beam diameter increases from 1 mm to 5 mm. Ellipticity of transmitted laser beam vary strongly for amplitudes of the external magnetic field smaller then 50 mG, but the maximum value of the ellipticity remains below &pgr;/300.
We show that long-lived bright Zeeman coherence that is responsible for absorption enhancement and steep anomalous dispersion in an atomic medium gives rise to a giant nonlinearity of the atomic susceptibility, in a similar manner to the dark coherence responsible for the well-known electromagnetically induced transparency. The intensity dependent refractive index of Cs vapour with a ground state Zeeman coherence in the vicinity of the D2 resonance line has been measured at low light intensity. The Kerr nonlinearity in the bright coherent state (n2 approx 1.0 × 10-6 cm2 mW-1) is higher than that in a dark state under the same experimental conditions. Higher order nonlinear components of the refractive index have also been estimated for both coherent states.
Large Faraday rotations can be generated by circular birefringence of atomic samples in an axial magnetic field in the vicinity of atomic resonance lines. More generally, magneto-optical effects in atomic samples include circular dichroism in addition to birefringence, resulting in a modification of the ellipticity as well as the polarization alignment. Usually such effects are investigated for homogeneous linear polarizations, but the mechanisms apply also to polarization structures such as vector vortices. We investigate the effect of optical activity of a rubidium vapor in the hyperfine Paschen–Back regime along the D2 line, for the example of azimuthally polarized input light. We show that for low atomic densities, circular birefringence dominates over dichroism, and azimuthal polarization is rotated toward radial polarization. The rotation angle increases with increasing optical densities. At high vapor temperatures, dichroism becomes more and more relevant, leading to intricate variations of both alignment and ellipticity. Our results shine new light on the interplay between different magneto-optic effects at strong magnetic fields. Their highly sensitive response to detuning may find applications in spectroscopy and quantum sensing.
We study numerically the nonlinear magneto-optical rotation of polarization (NMOR) of the laser pulse during its propagation through a cold Rb cloud with induced Zeeman coherences and electromagnetically induced transparency. Evolution of NMOR is calculated by solving the Maxwell–Bloch equations. We consider a linearly polarized Gaussian pulse with different pulse peak amplitudes and widths. For an intensity peak of 5 mW cm−2 and full-width at half-maximum of 10 μs, transient behaviour of NMOR does not follow the pulse intensity variation: NMOR begins to decrease as the pulse's intensity nears its peak value. When the pulse has a smaller peak intensity, NMOR behaves qualitatively differently: the angle of rotation constantly increases during the pulse propagation. Observed differences are explained by the optical pumping into the dark state and the behaviour of the ground-state coherences subjected to coherent population trapping. The same pulse intensity, from different sides of the pulse, during rising and falling sides, produces qualitatively different NMOR shapes, its amplitudes and widths which result can be explained by the successive excitation of atoms during the pulse propagation. It was shown that increasing the relaxation rates of the ground-state coherences, shifts the maximum of the NMOR to higher magnetic field, while the atomic density strongly influences the magnitude of the NMOR.
In the present communication we report on the investigation of the effect of elliptically polarized laser light exciting the Fg=3 Cs D2 absorption line. Coherent resonances in Cs have been studied, obtained in Hanle configuration by scanning of magnetic field parallel to the light propagation direction. The resonances were investigated depending on the polarization of the irradiating light field. It has been observed that for linear polarization dark resonances in the fluorescence are registered, while for circularly polarized light, bright resonances are obtained, probably due to stray orthogonal magnetic field. For elliptical polarization a narrow peak appears superimposed on a broader dip. Theoretical description has been made, which shows that at elliptical polarization and orthogonal magnetic field in the case of weak light fields, a single peak in the excited state population is observed, while strong fields lead to the splitting of this peak into two peaks. The presence of both weak and strong light fields, probably due to reflection of the light beam on the cell walls, could lead to the experimentally observed fluorescence behaviour.