The Ewald-Oseen Extinction Theorem

摘要

When a beam of light enters a material medium, it sets in motion the residentelectrons, whether these electrons are free or bound. The electronicoscillations in turn give rise to electromagnetic radiation which, in the caseof linear media, possess the frequency of the exciting beam. Because Maxwell'sequations are linear, one expects the total field at any point in space to bethe sum of the original (exciting) field and the radiation produced by all theoscillating electrons. However, in practice the original beam appears to beabsent within the medium, as though it had been replaced by a different beam,one having a shorter wavelength and propagating in a different direction. TheEwald-Oseen theorem resolves this paradox by showing how the oscillatingelectrons conspire to produce a field that exactly cancels out the originalbeam everywhere inside the medium. The net field is indeed the sum of theincident beam and the radiated field of the oscillating electrons, but thelatter field completely masks the former. Although the proof of the Ewald-Oseentheorem is fairly straightforward, it involves complicated integrations overdipolar fields in three-dimensional space, making it a brute-force drill incalculus and devoid of physical insight. It is possible, however, to prove thetheorem using plane-waves interacting with thin slabs of material, whileinvoking no physics beyond Fresnel's reflection coefficients. The thin slabsrepresent sheets of electric dipoles, and the use of Fresnel's coefficientsallows one to derive exact expressions for the electromagnetic field radiatedby these dipolar sheets. The goal of the present article is to outline a proofof the Ewald-Oseen theorem using arguments that are based primarily onthin-film optics.