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Physical Review

Scattering of Intense Light

Walter C. Henneberger

Published Dec 13, 1965• 0 citations
Publisher

Abstract

The variation of scattering cross section with beam intensity is computed for the scattering of ruby-laser light on atomic hydrogen. The result contradicts that of an earlier calculation which omits the contribution of some important intermediate states. The scattering cross section is found to increase very slightly as the intensity of the incident light is increased.

DOI
10.1103/physrev.140.a1864

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The variation of scattering cross section with beam intensity is computed for the scattering of ruby-laser light on atomic hydrogen. The result contradicts that of an earlier calculation which omits the contribution of some important intermediate states. The scattering cross section is found to increase very slightly as the intensity of the incident light is increased.
This paper is an extension of a previous one and discusses the theory of the quenching of the metastable 2S2S2S state of atomic hydrogen by means of optical radiation, for example by the light from a ruby laser. The case discussed is that for which the incident intensity is sufficiently weak for the usual quantum-electrodynamical perturbation theory to be valid. A procedure developed by Schwartz and others is used to carry out the sum over intermediate states without explicit enumeration. The results are given for a range of incident wavelengths from 5000 \AA{} to 5\ensuremath{\mu}. For unpolarized light from a ruby laser (6934 \AA{}), the total cross section for quenching is found to be ${\ensuremath{\sigma}}_{Q}=1.27\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ cm2{\mathrm{cm}}^{2}cm2. The cross section for coherent scattering has also been calculated for the same range of wavelengths; for ruby laser light, the total cross section for scattering is found to be ${\ensuremath{\sigma}}_{S}=1.03\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ cm2{\mathrm{cm}}^{2}cm2.
The angular distribution of scattered Lyman-$\ensuremath{\alpha}$ photons from atomic hydrogen is calculated as a function of an applied magnetic field. The intensity of the scattered radiation is a function of the energy difference of the excited-2P2P2P levels and shows an extremum at the point where two levels cross. Neglecting hyperfine structure, there are two level crossings of interest: one at 3484 G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\frac{1}{2}}$), and the other 5223G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$), respectively. The coher$\stackrel{\mathrm{\ifmmode \breve{}\else \u{}\fi{}}}{\mathrm{e}}$nt and incoherent resonance scattering is determined near these crossing points by using a Hamiltonian that includes hyperfine structure and higher-order radiative effects. In the low-field region (3484 G), the hyperfine crossings that contribute to the coherent signal are at 3476.06 and 3491.93 G, respectively. The radiative width of the levels is considerably larger than the hyperfine splittings, and the total scattering intensity has a single peak at 3483.97 G. In the high-field region (5223 G), two hyperfine levels with ${m}_{F}=\ensuremath{-}1$ repel each other (anticross) with a minimum energy separation of 15.3 Mc/sec at 5200.1 G. Resonances occur at 5220.6 and 5223.9 G, and the maximum of the total signal is at 5222.6 G.
We have calculated the cross section for Raman scattering of light from a hydrogenic atom, for a wide range of photon energies. The calculation assumes the photon encounters the atom in its ground state and excites it to the 2s2s2s state. Since various contributions to the matrix element may be isolated in the computation, the calculation allows one to obtain a notion of the relative importance of various classes of intermediate states in a given frequency range. We also point out that the Raman efficiency SSS may be expressed in terms of the derivative of the electronic polarizability tensor with respect to a parameter that measures the degree of excitation of the atom. Thus, the formal expression for SSS assumes an appearance identical to the expression encountered in the phenomenological theory of the first-order Raman effect in solids.
The problem of resonance Rayleigh scattering by an atom in an intense laser beam, whose bare spectrum consists of one discrete fundamental state and an excited continuum of states, is studied with the use of the density-matrix formalism. Evolution equations for the density-matrix elements are solved, leading to the determination of the populations of the atom in the discrete state ∣g〉|g〉∣g〉 in the presence of nnn laser photons, and to the calculation of the dipole-moment correlation function. The importance of cascade effects is discussed. The emitted spectrum is calculated and its dependence on the intensity of the laser beam and on the frequency of the incident photons is studied.
The effect of mixing two high-power ruby-laser beams in several gases has been investigated by means of light scattering. Coherently scattered light has been observed with intensities of up to three orders of magnitude, exceeding that of incoherent Rayleigh scattered light. The dependence of the effect on laser power, gas density, and refractive index is described. It is shown that for higher pressures (\ensuremath{\sim} 100 Torr) a threshold power exists for the effect, and that saturation is observed with increasing pressure as well as increasing mixing beam power.
Light scattering of monochromatic radiation by atoms and dilute vapours is reviewed. The relative contributions of incoherent and coherent scattering are calculated for weak incident fields. It is shown that, to lowest order in the intensity of the driving field, there can be several inelastic components in the scattered spectrum. The positions and widths of these components are related to light shifts and optical pumping of the atoms in the field. The complications that one encounters in scattering by two atoms, moving atoms, and atomic ensembles are discussed in qualitative terms.