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Molecular Physics

Kerr dispersion of atomic sodium and lithium

Martin P. Bogaard, A. David Buckingham, Brian J. Orr

Published Jan 1, 1967• 24 citations
Publisher

Abstract

A detailed theory of the frequency dependence of the electro-optical Kerr effect of an atom in the region of absorption lines is presented and applied to the particular case of 2 P←2 S doublets of sodium and lithium vapours. Doppler broadening is taken into account. With electric dipole matrix elements derived from the Coulomb approximation for both discrete and continuum states, the molar Kerr constant, m K(32 P←32 S), of atomic sodium vapour in the D-line absorption region is calculated to ±30 per cent; the calculations indicate that m K in the vicinity of the D2 line (32 P 3/2←32 S 1/2) should be very much greater than near the D1 line (32 P 1/2←32 S 1/2) in qualitative agreement with the experiments of Kopfermann and Ladenburg Qualitative consideration is also given to dispersion of magnetic birefringence; in contrast with electric birefringence strong dispersion is expected near both lines of alkali metal 2 P←2 S doublets.

DOI
10.1080/00268976700101461

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A detailed theory of the frequency dependence of the electro-optical Kerr effect of an atom in the region of absorption lines is presented and applied to the particular case of 2 P←2 S doublets of sodium and lithium vapours. Doppler broadening is taken into account. With electric dipole matrix elements derived from the Coulomb approximation for both discrete and continuum states, the molar Kerr constant, m K(32 P←32 S), of atomic sodium vapour in the D-line absorption region is calculated to ±30 per cent; the calculations indicate that m K in the vicinity of the D2 line (32 P 3/2←32 S 1/2) should be very much greater than near the D1 line (32 P 1/2←32 S 1/2) in qualitative agreement with the experiments of Kopfermann and Ladenburg Qualitative consideration is also given to dispersion of magnetic birefringence; in contrast with electric birefringence strong dispersion is expected near both lines of alkali metal 2 P←2 S doublets.
Using a three-level model and semiclassical density matrix formalism, we show that optical pumping influences both line positions and amplitudes in Doppler-broadened alkali-atom D1 and D2 spectra for intensities much lower than the two-level atom saturation intensity. The influence on the D2 spectrum is particularly interesting due to the presence of closed hyperfine transitions unaffected by optical pumping. This effect is of importance for example when lasers are frequency stabilized using linear absorption or when the alkali-atom vapour pressure is determined using absorption measurements.
We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom-light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data, showing the validity of the approximations.
Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.
We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.
Abstract We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.
Abstract Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of 87Rb in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.