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Journal of Physics B Atomic and Molecular Physics

Theory of electron scattering from laser excited atoms

J. H. Macek, Ingolf Volker Hertel

Published Nov 11, 1974• 99 citations
Publisher

Abstract

An expression is derived for the intensity of electrons inelastically scattered from an atomic state prepared by optical pumping. The expression is a sum of state multipoles, the coefficient of each multipole being a spherical harmonic in the polar coordinates of the light direction for circularly polarized light, or the direction of the electric vector for linearly polarized light times a weight function depending on the population of the initial state. These weight functions are given in closed form for both linearly and circularly polarized light.

DOI
10.1088/0022-3700/7/16/016

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Physical Review A•Aug 1, 1991•28 citations
An expression is derived for the intensity of electrons inelastically scattered from an atomic state prepared by optical pumping. The expression is a sum of state multipoles, the coefficient of each multipole being a spherical harmonic in the polar coordinates of the light direction for circularly polarized light, or the direction of the electric vector for linearly polarized light times a weight function depending on the population of the initial state. These weight functions are given in closed form for both linearly and circularly polarized light.
The formalism applied to superelastic electron scattering from laser-excited atoms has to date assumed perfect polarization of the laser light. We consider the effects of imperfect polarization, deriving an expression for the superelastic scattering rate from target atoms optically pumped with elliptically polarized light, and show how imperfect polarization effects can be measured and minimized under experimental conditions. In particular, we find that in measuring the scattering for linearly polarized light with a small circular component, the errors are proportional to the undesired circular polarization component and to P3{P}_{3}P3​, the scattering sensitivity to circular light. We also present in detail a polarizer design which generates both linear and circular polarizations, allowing measurement of all scattering polarization sensitivities without requiring interchange of optical elements.
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. 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Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. 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By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.
The development of the theory of the effect of a laser on electron-atom scattering is continued by the derivation of explicit relations between the observed electron-atom scattering cross sections in the presence of a laser and exact electron-atom scattering cross sections with no laser present. No approximation concerning the scattering interaction is made. The only approximations concerning the laser are that (1) the laser-atom interaction energy is small compared to atomic energies, (2) the Rabi frequency times the collision time is small, and (3) the laser intensity in appropriate units is small.
We investigate the early stages of superfluorescent emission from a large spherical volume containing atoms all initially in the same excited state. The electric polarization fluctuations that characterize a fully inverted atomic system, and which trigger superfluorescence, are found to cause field amplification only in vector spherical-harmonic multipole modes of limited order. The field and polarization fluctuations obey Gaussian statistics, a result that has been used to calculate the angular correlation of intensities radiated in any two directions. Components of the electric field radiated in two arbitrary directions and circularly polarized in opposite senses are found to be uncorrelated. They thus have no intensity-intensity or higher-order correlations. Field components which are circularly polarized in the same sense, however, are shown to be correlated over an angular range that is proportional to the ratio of the wavelength to the radius of the sphere.
The optical pumping parameters that modify the pure-state pseudo-Stokes parameters in an electron-superelastic-scattering experiment are calculated for the 3 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​(F=2)--32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(F) transitions of Na. A QED model is used to describe the laser excitation. It is found, that while the magnitude of the pumping parameter K' associated with circularly polarized excitation is close to unity for other than weak laser intensities, the value of the parameter K, associated with linearly polarized light, differs significantly from unity and is dependent on such experimental conditions as laser intensity, laser detuning, laser beam profile, and the Doppler width of the atomic transition. Methods for measuring K are suggested.