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Physical Review

Polarization and Direction of Propagation of Successive Quanta

Donald R. Hamilton

Published Oct 1, 1948• 36 citations
Publisher

Abstract

The correlation between the direction of propagation of one quantum and the polarization of another quantum, when the two are emitted successively (in any order) by a radiating system, is investigated theoretically. This direction-polarization correlation is found to be capable of determining the relative parities of all three levels of the radiating system. The correlation is simply related to the already investigated correlation between the directions of propagation of two successive quanta. Results are given explicitly for the possible combinations of dipole and quadrupole radiation. The discussion applies also to certain types of resonance radiation.

DOI
10.1103/physrev.74.782

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•Jan 1, 2019•0 citations
The correlation between the direction of propagation of one quantum and the polarization of another quantum, when the two are emitted successively (in any order) by a radiating system, is investigated theoretically. This direction-polarization correlation is found to be capable of determining the relative parities of all three levels of the radiating system. The correlation is simply related to the already investigated correlation between the directions of propagation of two successive quanta. Results are given explicitly for the possible combinations of dipole and quadrupole radiation. The discussion applies also to certain types of resonance radiation.
The angular distribution and polarization of the resonance radiation are deduced for elliptically polar- ized light incident on an atomic system of arbitrary initial and intermediate total angular momenta. The incident and re-radiated light are characterized by Stokes's representation, which allows an immediate generalization to partially polarized incident radiation. The results follow closely in form those deduced for free electron (Rayleigh) scattering but give, in general, a rather smaller degree of anisotropy for the resonance radiation. The results also determine the complete correlation, in polarization and direction of propagation, of two successive quanta emitted by a radiating system
It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties. The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive. Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified. The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.
Measurements have been made of the polarization properties of the two photons emitted in the decay of metastable atomic deuterium in an experiment in which three linear polarizers, instead of the normal two, are used. The quantum-mechanical predictions for these imperfect polarizers have been calculated and shown to be in good agreement with the experimental results. The results have also been used to test local realistic models which are capable of explaining all existing two-polarizer-type experiments, and have provided conclusive evidence against these theories.
The admixture effect of dipole and quadrupole type atomic transitions on the Stokes parameters characterizing the emitted radiation in the presence of an external magnetic field is studied. The transition from an upper level with angular momentum Ju = 3/2 to a lower level with angular momentum Jl = 1/2 is considered to take account of the admixture effect. The analytical expressions showing the emitted Stokes parameters for the case of upper and lower levels having same parities are derived. It is shown that the radiative transition probabilities of magnetic dipole (M1) and electric quadrupole transition (E2) are more intense than those of electric dipole transition (E1) and magnetic quadrupole transition (M2). The polarization components that are not usually seen in the Stokes I; Q and V profiles appear due to the admixture effect. The interference of the polarization components with opposite signs is responsible for the smaller strength of Stokes I; Q; V in admixture transition compared to those observed in pure transition. In pure dipole transition case, U Stokes profile is always zero for all emitted radiation directions. However, the Stokes U profile arises only due to the admixture effect.