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Journal of Applied Physics

Electronic Raman scattering from Al, Ga, In, and Tl atoms

L. Vriens, M. Adriaansz

Published Jul 1, 1975• 17 citations
Publisher

Abstract

An experimental and theoretical study is made of Stokes and anti-Stokes Raman scattering from Al, Ga, In, and Tl atoms. Relative phases of 2P01/2,3/2→2D3/2 dipole matrix elements are obtained from the polarization properties of the scattered radiation. For Ga these phases are different from those obtained for Al, In, and Tl, and they are in contrast to what is expected on the basis of single configuration approximations. The experimentally determined phases are used to calculate the Raman cross sections.

DOI
10.1063/1.321962

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An experimental and theoretical study is made of Stokes and anti-Stokes Raman scattering from Al, Ga, In, and Tl atoms. Relative phases of 2P01/2,3/2→2D3/2 dipole matrix elements are obtained from the polarization properties of the scattered radiation. For Ga these phases are different from those obtained for Al, In, and Tl, and they are in contrast to what is expected on the basis of single configuration approximations. The experimentally determined phases are used to calculate the Raman cross sections.
Polarization nondegenerate nonstationary coherent anti-Stokes Raman spectroscopy was used in measurements of pulse responses for separate electronic multipole moments. The 6P(1/2)-6P(3/2) transition of Tl atoms was investigated. Doppler dephasing conditions, quantum beats of the hyperfine components of this transition are clearly seen when pure anisotropic scattering is registered, but they are small in the case of purely antisymmetric scattering. Under collisional dephasing conditions the relaxation rates of anisotropic and antisymmetric scattering agree with existing theory within +/-5%.
An inhomogeneous differential equation method is used to calculate the Rayleigh and Raman scattering cross sections for atomic hydrogen and atomic caesium as functions of wavelengths below and above the ionization limits. The profile of the scattering cross section near the 6s-6p resonance of atomic caesium is determined by including an energy-independent radiative width in the scattering formula. The effect of replacing the electric dipole operation by a modified form that takes account of the polarization of the core by the valence electron is explored.
A report is given of the first quantitative study of the spontaneous and stimulated electronic Raman scattering by a resonance doublet of the sodium atom excited resonantly at the D 1 and D 2 lines by a tunable dye laser. Theoretical and experimental analyses of the differential scattering cross section and polarization properties at the Stokes and anti-Stokes frequencies show that the observed scattering is due to a nearly resonant process involving the ground state 3 S 1/2 as the dominant intermediate state. The stimulated Stokes and anti-Stokes scattering lines, which are shifted from the D 1 and D 2 lines by an amount corresponding to the frequency separation between lowest-lying excited doublets 3 P 1/2 and 3 P 3/2 , are observed by exciting a sodium vapor cell with a passively mode-locked dye laser.
Quantum-mechanical expressions for nonresonance-dipole light-scattering cross sections are related to corresponding expressions for oscillator strengths and refractive indices. In particular, Rayleigh and Raman cross sections for atoms are expressed in terms of oscillator strengths and vector-coupling coefficients. Several of our results, including the relationship between Rayleigh scattering and refractive index, differ in general from the corresponding results of classical dispersion theory. We show that these differences arise from antisymmetric components Ckja = (Ckj − Cjk)/2 of the polarizability tensor, which have been neglected in the classical analyses. Calculated Rayleigh cross sections for cesium and aluminum atoms, and Raman cross sections for aluminum atoms are presented to illustrate our results. The antisymmetric contribution is found to be substantial in all of these cross sections; its most obvious effect is to cause the depolarization (for linearly polarized incident light) to exceed 34 over extended wavelength ranges away from resonance. On the other hand, for atoms initially in states of zero angular momentum, and molecules under conditions which allow the use of Placzek’s polarizability approximation, our results agree with those of classical dispersion theory.
Early theoretical works on coherent anti-Stokes Raman scattering in optically active medium consider only heterodyne signal and subsequently, fourth- and fifth-rank tensor averages have been used. In this work, we presented a full signal expression of coherent anti-Stokes Raman scattering in optically active medium with the help of eighth- and ninth-rank tensor averaging for simplest experimental configuration namely, measurements of post-selected circularly polarized components of scattered anti-Stokes field in the presence of three incident laser beams all linearly polarized along the same axis.