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Journal of Physics B Atomic and Molecular Physics

Doppler-free Faraday effect

B. Glushko

Published Sep 28, 1981• 0 citations
Publisher

Abstract

It is shown that the dispersion dependence of the rotation of the plane of polarisation of weak radiation passing through a three-level atomic medium may be free of Doppler broadening, on the account of a velocity-dependent Stark-shift which is created by saturating the wave on an adjacent transition. In the case of two-photon resonance the use of opposing light beams with different frequencies gives the possibility for an essential increase of the signal on account of the resonance gain on an intermediate transition, without additional Doppler broadening.

DOI
10.1088/0022-3700/14/18/009

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It is shown that the dispersion dependence of the rotation of the plane of polarisation of weak radiation passing through a three-level atomic medium may be free of Doppler broadening, on the account of a velocity-dependent Stark-shift which is created by saturating the wave on an adjacent transition. In the case of two-photon resonance the use of opposing light beams with different frequencies gives the possibility for an essential increase of the signal on account of the resonance gain on an intermediate transition, without additional Doppler broadening.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
Discusses the theory of Doppler-free two-photon transitions. The theory is worked out for the case of one arbitrarily strong field and one weak field. The Doppler limit is assumed. These simplifications allow the authors to discuss the experimental manifestations of various parameters. They consider power shifts and broadening the number of resonant peaks and their positions. The general case of an off-resonant intermediate state and the single-frequency case with a resonant intermediate state are discussed. The former is found to lead to a power shift, whereas the latter is unshifted in a certain region. In addition the resonant case gives an enhancement without an appreciable increase in width.
We describe the influence of the intensity variation of the light in a standing wave on the lineshape of a Doppler-free multi-photon transition. We show that as long as the light shifts and the saturation are small compared to the Doppler width, a motional narrowing effect occurs and the line remains Lorentzian, the centre being shifted by an amount equal to the mean value of the dynamic Stark effect. We consider also the case of transients. We show that at resonance, it is possible to observe different responses according to the light intensity. In particular, it is possible to observe Rabi oscillations only if the Rabi frequency is larger than the natural width and smaller than the Doppler width of the transition.
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.
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.
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.