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.
Research supported by the Air Force Office of Scientific Research and the Army Research Office (Durham).
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References
P.P. Ewald, Dissertation, Univ. of Munich, 1912;
P.P. Ewald, Ann. Phys. 49, 1 (1915).
C.W. Oseen, Ann. Phys. 48, 1 (1915).
For a detailed account of the theorem see M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford and New York, 1970) 4th ed., §2.4,
L. Rosenfeld, Theory of Electrons (North-Holland Publishing Co., Amsterdam, 1951) Chapt. VI, §4.
J.J. Sein, An Integral-Equation Formulation of the Optics of Spatially-Dispersive Media, Ph.D. Dissertation, New York University, 1969, Appendix III.
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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).
While this manuscript was being prepared for publication a paper reporting some closely related results was published by J. de Goede and P. Mazur, Physica 58, 568 (1972). This paper also contains some additional references to publications concerning the extinction theorem.
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.
See, for example, Chen-To Tai, Dyadic Green’s Functions in Electromagnetic Theory (In-text Educational Publishers, Scranton and San Francisco, 1971).
One of them was presented in reference 5j.
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.
M. Lax, Phys. Rev. 85, 646 (1952).
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Wolf, E. (1973). A Generalized Extinction Theorem and Its Role in Scattering Theory. In: Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2034-0_22
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DOI: https://doi.org/10.1007/978-1-4684-2034-0_22
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