Some may find this interesting. complete paper here. http://pubs.nrc-cnrc.gc.ca/rp-ps/inDetail.jsp?jcode=cjp&lang=eng&vol=87&is=4
Fresnel’s formulae and the Minkowski momentum A. Hirose and R. Dick Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, SK S7N 5E2, Canada. Received 3 March 2009. Accepted 19 March 2009. Published on the NRC Research Press Web site at http://cjp.nrc.ca on 22 June 2009. Abstract: It is shown that the momentum of an electromagnetic wave in a dielectric medium can be uniquely determined to be the Minkowski momentum by considering oblique incidence of electromagnetic wave on a flat dielectric boundary. The Minkowski momentum is consistent with the Fresnel’s formulae and satifies the energy and momentum conservation laws. In classical electrodynamics, the momentum of an electromagnetic wave in a dielectric medium continues to be as unsettled a problem ever since the proposals of the two well known, but conflicting definitions by Minkowski [1] and Abraham [2] a century ago. For an electric field wave amplitude E in a medium having an index of refraction n, the Minkowski momentum flux density is (1) while the definition proposed by Abraham is (2) The difference has important implications for the understanding of the direction and magnitude of the radiation pressure exerted by electromagnetic waves on dielectric bodies and is by no means of mere academic interest. For example, in as early as 1905, Poynting [3] predicted an outward pressure at an air-dielectric boundary (3) regardless of the direction of wave propagation where is the tangential electric field at a boundary. (The tangential field is continuous.) The outward force is consistent with the Maxwell’s stress and Minkowski momentum, but not with the Abraham momentum, which predicts inward force [4]. Most experimental observations [3, 5–7] support the Minkowski momentum. However, recently, She et al. [8] reported an observation of the deflection of optical fibers that appeared to be consistent with the prediction by Loudon. For the Minkowski–Abraham controversy, see the reviews by Brevik [9] and Peierls [10]. In this paper, we show that the Fresnel’s formulae for reflection and transmission of light wave obliquely incident on a dielectric surface uniquely determine the amount of momentum transmitted into the dielectric medium. The momentum turns out to be the Minkowski momentum. The Fresnel’s formulae evidently satisfy energy conservation. However, to our knowledge, the aspect of momentum conservation contained in the formulae has not been exploited to “derive” the momentum of electromagnetic wave in a dielectric medium...
