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Journal of the Physical Society of Japan

Inverted Signals in Polarization Spectroscopy of Sodium Vapour

Shigeru Nakayama

Published Feb 1, 1981• 7 citations
Publisher

Abstract

The purpose of this paper is to interpret inverted signals in polarization spectroscopy of sodium vapour by using a model of four-level system. It is shown that the inverted rotation of polarization stems from the occurrence of cross-over resonances because of the high multiplicity of Zeeman sublevels.
DOI
10.1143/jpsj.50.606

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The aim of this paper is to present detailed theory of polarization spectroscopy of Na in the case of a slow relaxation rate of a lower state involved in a resonant transition. An interpretation of the signal in such a polarization spectroscopy is given by combining the theory of birefringence and dichroism with a first-order theory of velocity-selective optical pumping in a four-level system. Because of the high multiplicity of Zeeman levels, the signal is complicated by the occurrence of cross-over resonances in addition to the principal resonances. This interpretation is in good agreement with the experimental results which have been already published about the Na D 1 line.
A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.
Theoretical analyses have been made of polarization-and angular momentum-dependences of backward four-wave mixing in atomic lines. These results were also applied to the problem of "vectorial" phase-conjugation in atomic vapours. Experimental demonstration of the vectorial phase-conjugation was carried out in D2 resonance line of sodium. Concerning the phase-conjugation spectroscopy in condensed matter, it has been proposed to detect X(3)1221 component to eliminate thermal grating effect.
The relative intensities of the Doppler-free signals in the transition from polarized and dispersive signals to absorptive signals of the Na D1 line are calculated theoretically from the approximation of a single cycle of opticalpumping in a four-level system. The transition from polarized signals to saturated signals is made by varying the angle of an analyzer. Since the signal in polarization spectroscopy is mixed with the signal in saturation spectroscopy during the transition, spurious signals due to saturation and polarization effects should be taken into account in the signal analysis of polarization and saturation spectroscopies, respectively. Both theories, of polarization spectroscopy and saturation spectroscopy are unified and applied to the Doppler-free signals of the Na D1 line. The results obtained from the four-level optical pumping theory which mixes polarization spectroscopy with saturation spectroscopy are in good agreement with experimental reports.
Abstract Polarization rotation in electromagnetically induced transparency (PREIT) in rubidium vapour at room temperature has been studied experimentally as well as theoretically in the absence of any magnetic field. PREIT is observed for both 85 Rb and 87 Rb combining the D 1 and the D 2 transitions with a V-type configuration. For 85 Rb, two EIT peaks and for 87 Rb, one EIT peak were observed. Nonlinear characteristics of the variations of the angle of rotation corresponding to the EIT position were observed for both the isotopes of Rb. We have modelled a four level system to explain the occurrence of the double EIT in case of the 85 Rb and the occurrence of one EIT peak for 87 Rb. The rotation of plane of polarization of the probe beam can be further explained with this model. The characteristic behaviour of the variation of rotation corresponding to the EIT position from theoretical analysis has matched well with the experimental observations. A sharp rotation with a high signal to noise ratio in the vicinity of the EIT can be used as a modulation free and noise insensitive signal for the frequency stabilization.