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Physical Review A

Total fluorescent scattering cross sections

Herman W. Chew

Published Jun 1, 1988• 18 citations
Publisher

Abstract

The total cross section for fluorescent scattering by a spherical particle uniformly filled with fluorescent scatters is computed using a model for fluorescent scattering formulated earlier. Results are given for an arbitrary incident beam and for a linearly polarized plane wave normalized to the cross section for the same number of scatterers in bulk medium. The cross section has a form which clearly shows the possibility of resonance peaks when either the incident or the fluorescent frequency (or both) coincides with eigenfrequencies of the particle.

DOI
10.1103/physreva.37.4107

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The total cross section for fluorescent scattering by a spherical particle uniformly filled with fluorescent scatters is computed using a model for fluorescent scattering formulated earlier. Results are given for an arbitrary incident beam and for a linearly polarized plane wave normalized to the cross section for the same number of scatterers in bulk medium. The cross section has a form which clearly shows the possibility of resonance peaks when either the incident or the fluorescent frequency (or both) coincides with eigenfrequencies of the particle.
A theory appropriate for investigating the angular spectra of atoms scattered out of an atomic beam by resonance fluorescence due to interactions with an orthogonal uniform light beam is presented. Particular emphasis is made on the scattering in the plane containing the two beams. The atomic distribution is shown to be intimately related to the angular distribution of the spontaneously emitted photons. Both distributions show marked variations with the detuning and field intensity parameters, leading to the possibility of maximum scattering of atoms to occur on either side of the atomic beam, while the accompanying photons are always emitted on one particular side of the light beam. Since the angular distributions reflect the momentum changes suffered by both the atoms and the electromagnetic field, this lends insight into the basic mechanisms involved in resonance fluorescence.
A theory for the resonance light scattering in a molecular system interacting with the heat bath is developed, taking into account the multilevel structure of the molecular system. An expression for the cross section of the resonance light scattering process is derived by using the Liouville operator method in the Markoff approximation; the cross section consists of three terms: resonance Raman scattering, resonance fluorescence, and their mixing. The mixing term vanishes in the limit of the zero vibrational dephasing constant. Analytical expressions for the resonance Raman scattering and resonance fluorescence cross sections are derived in the displaced harmonic oscillator model. Model calculations of the vibrational band structure in the resonance light scattering cross section are performed by using the expressions derived. Differences of the band intensity distribution in the resonance fluorescence from that in the resonance Raman scattering are illustrated.
Stationary states are unavoidable from the practical viewpoint, since all the computations of observables, such as cross sections and other experimentally measurable physical quantities, are carried out within timeindependent scattering theory. In a scattering experiment, one attempts to determine the momentum of the impact projectile as precisely as possible. However, in the standard formulation of scattering theory, one tries to reach the same ideal goal by identifying the initial state in the remote past with the plane wave. The problem of the asymptotic convergence of scattering states cannot be formulated in the same way for both proper and improper state vectors. The optical theorem is a convenient way of computing the total cross section Q, when one knows the value of the imaginary part of the scattering amplitude in the forward direction. The scattered particles are moved away from the incident beam for a certain amount which is proportional to the value of the total cross section Q.
A treatment of resonance fluorescence is given in which the properties of the incident and scattered light are expressed in terms of coherency matrices. Calculations are made for two successive scattering processes corresponding to the experiments described in an accompanying paper. For the first process the scattering atoms are subjected to a magnetic field consisting of parallel static and oscillating components. The fluorescent light is frequency-modulated and may also be polarization-modulated. This light excites fluorescence in a second cell in which the atoms are subjected to a static magnetic field. The equations show under what conditions the second fluorescence is intensity-modulated and describe the resonances in the amplitude of modulation which occur when the modulation frequency matches a Zeeman interval of the excited atoms.