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A Generalized Extinction Theorem and Its Role in Scattering Theory

  • Emil Wolf

Abstract

When an electromagnetic wave is incident on a homogeneous medium with a sharp boundary, it is extinguished inside the medium in the process of interaction and is replaced by a wave propagated in the medium with a velocity different from that of the incident wave. A classic theorem of molecular optics due to P.P. Ewald (1912) and C.W. Oseen (1915) expresses the extinction of the incident wave in terms of an integral relation, that involves the induced field on the boundary of the medium. Various generalizations of this theorem have recently been proposed and it was also shown that the customary physical interpretation of the theorem is incorrect.

Keywords

Sharp Boundary Schrodinger Equation Incident Field True Meaning Incident Electric Field 
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References

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    Preliminary results of this investigation were presented in a lecture at the annual meeting of the Optical Society of America held in Ottawa in October 1971 (Abstr. WC16, J.Opt.Soc.Amer., 61, 1560 (1971)) and in a note published in Optics Commun. 6, 217 (1972).Google Scholar
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    A slightly different argument to that given below is needed if the incident field is a plane wave (i. e. if the source is at infinity), but the final formulae remain the same. The case of plane wave incidence is discussed explicitly in connection with the quantum mechanical extinction theorem, in the last part of this paper.Google Scholar
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    That this is so follows at once from the Maxwell equation V.D = 0. For this implies that 0 = ∇.(ɛ E) = ɛ ∇.E (ɛ = dielectric constant), so that ∇.E = 0 and hence also ∇.P = 0 (because of the linearity of the medium), unless ɛ = 0.Google Scholar
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Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Emil Wolf
    • 1
  1. 1.University of RochesterRochesterUSA

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