The Refractive Index in Electron Optics and the Principles of Dynamics

Abstract

In view of mis-statements made in the literature, the origin of the refractive index in electron optics is discussed in some detail, and the uniqueness of an expression previously given is demonstrated. On this basis, some general properties of electron optics are investigated. A relation between ray direction and wave normal is obtained. Whereas the refractive index is unique in terms of the magnetic vector potential A, this itself is arbitrary to some extent. It is shown that A must, for purposes of electron optics, be chosen so as to satisfy Stokes' theorem and that, if it does, no observable effects result from the arbitrariness of A. An expression for the optical path difference is given in terms of the magnetic flux enclosed. The results are applied to a number of questions, viz. the differential equations for trajectories, the focusing properties of an axially symmetric field and the interference pattern produced by two converging bundles of rays which enclose a magnetic flux.