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Canadian Journal of Physics

Coherent Radiation Damping

Haider R. Zaidi

Published Jul 1, 1972• 3 citations
Publisher

Abstract

The frequency spectrum of the resonant scattering cross section is calculated from a boundary value solution of Maxwell's equation. The spectral width of the cross section gives the coherent radiation damping rate for the resonant medium. For a large sphere, the coherent width is found to be proportional to the radius, and is much larger than the collision and the Doppler widths in a gas. It is proposed that this effect may also be observable in some absorption experiments.

DOI
10.1139/p72-196

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The frequency spectrum of the resonant scattering cross section is calculated from a boundary value solution of Maxwell's equation. The spectral width of the cross section gives the coherent radiation damping rate for the resonant medium. For a large sphere, the coherent width is found to be proportional to the radius, and is much larger than the collision and the Doppler widths in a gas. It is proposed that this effect may also be observable in some absorption experiments.
The resonant scattering of monochromatic light in gases is analyzed. Explicit expressions for the differential cross section are obtained in the limits (Doppler width) \ensuremath{\gg} (natural width) \ensuremath{\gg} (collision width) and (collision width) \ensuremath{\gg} (natural width) \ensuremath{\gg} (Doppler width). In the former limit, the frequency distribution of scattered light is narrowed in the forward and backward directions, and has the full absorption width for right-angle scattering. In the collision-dominated limit, the cross section separates into a coherent and a fluorescent component. The motion of the atoms broadens the $\ensuremath{\delta}$ function distribution characterizing coherent scattering from a stationary target. The interference between light scattered by different atoms is assessed.
Imprisonment of resonant radiation in gases on the basis of the numerical solution of the rate balance equation for the excited atoms and the transfer resonant radiation equation is investigated. Calculations of the escape factor for the slab, cylinder and sphere at Doppler and Lorentz forms of absorption and scattering profiles are executed. Calculation results of the escape factor for the cylinder and slab are compared with Holsten's asymptotical solutions. The numerical data for time dependence of a spectrum, the intensity of resonant radiation and the spatial distribution of the excited atomic concentration in a regime of afterglow are also considered.
The frequency dependence of the differential cross section characterizing the resonant scattering of photons by the atoms of a dilute gas has been investigated. It is supposed that the scatterers are sufficiently dispersed so that interference between different scatterers may be neglected. Elastic collisions between the scatterers and the atoms of a buffer gas are treated in the impact approximation. A Maxwell-Boltzmann distribution of velocities is assumed. Analytic expressions for the cross section are obtained in the limits natural width\ggcollision width\ggDoppler width, Doppler width\ggnatural width\ggcollision width, and collision width\ggnatural width\ggDoppler width. The significance of these results is discussed.
The coherent radiation of N atoms that are excited by an external field is studied close to a resonant transition. The resonant atoms are uniformly distributed over a sphere and the external field is a pulse that propagates in a fixed direction. The linear classical continuum theory is used for the above configuration. Exact expressions are obtained for the polarization, for the fields everywhere in space, and for the energy radiated and absorbed by the resonant atoms. Two equivalent methods for the derivation of the exact expression of the polarization are given, i.e., either by solving Maxwell’s equations and boundary conditions, or by solving an integral equation inside the sample. The equivalence of the two methods, in the general case of an arbitrary external field, has been proved elsewhere. Approximate expressions are also obtained for the physical quantities mentioned above in the extreme cases of a dilute and a dense resonant sample with radius much smaller than the radiation wavelength. Inside the dense small sample the polarization depends on position, and this space dependence is expressed in terms of spherical Bessel functions and vector spherical harmonics. It is shown that outside the dense small sample, a broadening of the original resonant line and a shift of the resonance frequency occur in the radiation spectrum of the atoms.
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 response of a medium to radiation with a complex frequency corresponding to an exponential time decrease in the radiation amplitude has been analyzed. The effect of complex resonance has been demonstrated when the real and imaginary parts of the complex radiation frequency approach the real and imaginary parts of the complex frequency of damping natural oscillations of medium oscillators. In resonance itself, the absolute value of the refractive index is divergent and radiation is completely reflected from the medium boundary. It has been shown that scanning of not only the real part, but also the imaginary part of the probe radiation frequency expands the capabilities of spectroscopy and makes it possible to, e.g., distinguish resonances even with coinciding (real) frequencies and close (of the same order of magnitude) widths.