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arXiv:1107.1212 · Journal of Physics B Atomic Molecular and Optical Physics

An analytical model of off-resonant Faraday rotation in hot alkali metal vapours

Stefan L Kemp, Ifan G. Hughes, Simon L. Cornish

Published Nov 18, 2011• 23 citations
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Abstract

We report a thorough investigation of the Faraday effect on the 852 nm D 2 transition in a hot caesium vapour, culminating in the development of a simple analytical model for off-resonant Faraday rotation. The model, applicable to all hot alkali metal vapours, is seen to predict the rotation observed in caesium, at temperatures as high as 115 °C, to within 1% accuracy for probe light detuned by greater than 2 GHz from the D 2 lines.

DOI
10.1088/0953-4075/44/23/235004

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Optics and Spectroscopy•Apr 1, 2002•1 citation
We report a thorough investigation of the Faraday effect on the 852 nm D 2 transition in a hot caesium vapour, culminating in the development of a simple analytical model for off-resonant Faraday rotation. The model, applicable to all hot alkali metal vapours, is seen to predict the rotation observed in caesium, at temperatures as high as 115 °C, to within 1% accuracy for probe light detuned by greater than 2 GHz from the D 2 lines.
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.
New results demonstrating the dramatic changes to the form and magnitude of the resonant Faraday rotation with laser intensity, buffer gas pressure and magnetic field strength are presented for the transitions 4f 6 6s 2 7 F 0 -4f 6 6s6p 5 D 1 at 621 nm and 4f 6 6s 2 7 F 1 -4f 6 6s6p 5 D 0 at 654 nm. For both transitions, exact analytical solutions to the steady-state density matrix equations are possible and have been used. The experimental results show good qualitative agreement with the theoretical predictions. In the case of the 654 nm line Zeeman coherence occurs in the ground state and can be achieved at lower laser intensities than for the 621 nm line under comparable conditions.
Theoretical studies of the Faraday rotation (FR) effect in alkali vapors contained in extremely thin cells are presented. It is shown that the spectra of the FR signal are well frequency resolved despite the huge number of atomic transitions. This allows one to study the evolution of the Cs D 1 (λ = 895 nm) line hyperfine structure of F g = 4 → F e = 3, 4 atomic transitions in magnetic fields. The presented theoretical model predicts the coherent Dicke narrowing effect and its revival with a periodicity Δ L = λ. The practical applications of the FR are noted.
This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D1_11​ line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of 10−410^{-4}10−4. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.
Results of a numerical study of the Faraday effect arising upon propagation of the light beams with the frequencies ω L1 (resonant to the nS 1/2-nP 1/2, 3/2 transitions) and ω L2 (resonant to the nP 1/2, 3/2-(n+2)S 1/2 transitions) through alkali-metal vapors are presented. Characteristics of the magneto-optical rotation spectra at each of the frequencies are strongly affected by the second intense radiation field resonant to the adjacent transition. When the atoms interact with two strong light waves, resonant to adjacent transitions, and with a magnetic field, the shape of the Faraday rotation spectra depends on the energy shifts of the atomic states that arise due to the dynamic Stark effect and the Zeeman effect (the Paschen-Back or an intermediate-type effect), as well as due to the difference of populations of these states caused by the interaction of the atoms with the fields. The results obtained show that in the frequency selection method, based on the resonance Faraday effect, the frequency of the generated narrow-band beam can be tuned by the intensity of the strong wave, resonant to the transition between the excited states.