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Journal of Physics B Atomic and Molecular Physics

A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light

Wojciech Gawlik, J. Kowalski, Ronny Neumann, H. B. Wiegemann

Published Dec 14, 1979• 43 citations
Publisher

Abstract

A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light, i.e. the effect of rotation of the polarisation plane of resonance monochromatic radiation in atomic media, is suggested. As well as discussing the general principles of the method, an experimental test with sodium D 1 and D 2 lines is described. This test yields the most accurately known value of relative oscillator strength f D2 /f D1 =1.985+or-0.004.

DOI
10.1088/0022-3700/12/23/014

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Theory of the inverse hook method for measuring oscillator strengths

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The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix \ensuremath{\rho} of state a initially has only diagonal elements given by 〈m\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}m〉=C+${\mathrm{Dm}}^{2}$ where C and D\ensuremath{\ne}0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ``depolarization curve,'' the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\ensuremath{\omega}}_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.

Physical Review A•Aug 1, 1987•3 citations
A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light, i.e. the effect of rotation of the polarisation plane of resonance monochromatic radiation in atomic media, is suggested. As well as discussing the general principles of the method, an experimental test with sodium D 1 and D 2 lines is described. This test yields the most accurately known value of relative oscillator strength f D2 /f D1 =1.985+or-0.004.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.
Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance
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.
The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix \ensuremath{\rho} of state a initially has only diagonal elements given by 〈m\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}m〉=C+Dm2{\mathrm{Dm}}^{2}Dm2 where C and D\ensuremath{\ne}0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ``depolarization curve,'' the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\ensuremath{\omega}}_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.