Energy-momentum quanta in Fresnel's evanescent wave

Abstract

Fresnel's theory of the evanescent wave in total reflection entails that the propagation vectork and the momentum quantaħ k have an imaginary component and, thus, a projection on the reflecting plane that is larger (in units such thatc=1) than the angular frequencyω and the energy quantaħω. We discuss the ‘tachyon properties’ of these energy-momentum quanta and propose an experimental test using absorption or stimulated emission by an atomic or ionic beam. We then show that the Maxwell-Minkowski tensor (although certainly appropriate to discuss the macroscopic energy-momentum exchange between wave and diopter) does not describe adequately the energy-momentum density of the quanta in the evanescent wave, this stemming from its too remote connection with the generator ∂_i of space-time displacements. On the other hand de Broglie's energy-momentum tensorA _k[∂ⁱ]B ^jk is the density canonically associated with the generator of space-time displacements; we show that it describes quite satisfactorily both the energy fluxes (as measured through the longitudinal Goos-Hänchen and our new transverse shifts of the reflected beam in total reflection) and the momentum densities of the quanta inside the evanescent wave. Finally, we show that it is the gauge which is transverse in the diopter's rest frame that directly yields the physically measured energy fluxes. We take this fact as a new argument, strongly supported by experimental evidence, in favour of the physical reality of electromagnetic potentials.