The forward scattering of a resonant intense and broad-band (of the order of 1 GHz) laser light on sodium atoms is described. The experimental results for the D 1 and D 2 sodium lines (the 3 2 S 1/2 -3 2 P 1/2 and 3 2 S 1/2 -3 2 P 3/2 transitions) are compared with those of the scattering of the light from a conventional spectral lamp and from a monochromatic laser. The observed differences are explained by taking into account the Zeeman coherences created in the irradiated atoms and the concept of the 'hyperfine uncoupling' is proposed for describing the interaction of atoms with the broad-band laser light.
The forward scattering of a resonant intense and broad-band (of the order of 1 GHz) laser light on sodium atoms is described. The experimental results for the D 1 and D 2 sodium lines (the 3 2 S 1/2 -3 2 P 1/2 and 3 2 S 1/2 -3 2 P 3/2 transitions) are compared with those of the scattering of the light from a conventional spectral lamp and from a monochromatic laser. The observed differences are explained by taking into account the Zeeman coherences created in the irradiated atoms and the concept of the 'hyperfine uncoupling' is proposed for describing the interaction of atoms with the broad-band laser light.
A quantum-electrodynamic (QED) description of the resonant interaction of monochromatic light with the 32S1/2(F'=2)\ensuremath{\rightarrow}32P3/2(F=3,2,1) hyperfine transitions of the sodium D2 line is formulated in terms of the Heisenberg atomic operator. Off-diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences, and certain state coherences form a closed subset of the total system of equations. This subset is small enough to be computed numerically. The results of calculations with this model are compared with three previously developed semiclassical descriptions using the density operator. One of the semiclassical models was developed to describe the interaction of weak light with the atomic transition while another is suitable in the case of high-intensity light. For both \ensuremath{\pi} and \ensuremath{\sigma} excitation it is shown that the QED calculated values for the time-averaged, excited-level population probability converge to those of each of the semiclassical models in the appropriate limit of light intensity. For homogeneous broadening, results show that the optimum light intensity to obtain the largest fraction of atoms in the 32P3/2 level after transversing a 1-mm-diam laser beam is 1.15 mW/mm2 for \ensuremath{\pi} excitation and 1.43 mW/mm2 for \ensuremath{\sigma} excitation.
We present experimental and theoretical investigations of a Gaussian laser beam interacting with Zeeman-tuned J=1\ensuremath{\rightarrow}J=0 atomic systems. In our experiment a single-mode cw dye-laser beam traverses a neon discharge in a longitudinal magnetic field. The excited neon transitions used for these studies are 1s4(J=1,g=1.464)\ensuremath{\rightarrow}2p3(J=0) and 1s2(J=1,g=1.034)\ensuremath{\rightarrow}2p1(J=0). In the laser-induced forward-scattered light, dark and bright ring-shaped structures are observed. The ring structures are investigated as a function of the magnetic detuning of the m=\ifmmode\pm\else\textpm\fi{}1 sublevels and as a function of the laser-beam power. We find that the line shapes of the spectra, i.e., the forward-scattered light intensities as a function of the magnetic detuning, are sensitive to the transverse intensity distribution of the laser beam. Analytical expressions based on a semiclassical theory are derived and the calculated results on the ring structures and the spectra are compared with the experimental results. Good agreement between the calculated and the experimental results are obtained only when the transverse effects are taken into account.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
The effects of magnetic optical activity in the sodium D1 line are investigated in detail both theoretically and experimentally. Particular consideration is given to the ultra-narrow Hanle-type features that are produced by the crossing of ground state Zeeman sub-levels and which although strongly exhibited by the F g =2 to F e =1, 2 doublet, are apparently absent from the F g =1 to F e =1,2 doublet. We demonstrate, quantitatively for the first time, that these features are principally a manifestation of Delta M=2 (quadrupole) coherences and are therefore not evidence for the existence of Delta M=4 (hexadecapole) coherences as originally proposed by Gawlik and co-workers (1987). Indeed the latter is shown to have little influence on these features even at light field intensities for which significant power broadening is observed. We also show explicitly that the width of these narrow crossing features is, for the typical vapour pressures used to give an optically thin sample, a function of the average time of transit through the light field. Using a simple phenomenological model we predict numerically both the absolute width of these coherence features and the rate at which they power broaden. Finally a brief consideration of the same coherence effects within the D2 line is presented.
The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.