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Journal of the Physical Society of Japan

Optical Pumping Theory in Polarization Spectroscopy of Na

Shigeru Nakayama

Published Feb 1, 1981• 31 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.50.609

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Journal of the Physical Society of Japan•Feb 1, 1981•7 citations
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.
Theoretical analysis of D 1 lines of most stable alkali atoms in velocity selective optical pumping (VSOP) spectroscopy is presented by using the approximation of a single cycle of optical pumping in a four-level system. VSOP spectroscopy is clearly compared with polarization spectroscopy and then it is shown that the results obtained for polarization spectroscopy can be applied to the theory in VSOP spectroscopy. The relative signal intensities of Na D 1 line in polarization spectroscopy have been theoretically calculated and experimentally confirmed to be in good agreement with those in VSOP spectroscopy. The first-order theory in VSOP spectroscopy can be applied to the cases of the D 1 lines of the other alkali atoms. It is expected that the theoretical analysis can be useful for future experiments of the Doppler-free D lines in the alkali atoms.
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.
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.
Doppler-free spectra of linear and circular dichroisms for the hyperfine structures of Na D1{D}_{1}D1​ and D2{D}_{2}D2​ lines have been obtained by means of polarization-modulated optical pumping spectroscopy. The experimental results are compared with recent theoretical calculations based on velocity-selective optical pumping in a four-level atomic system.