Theory of Refraction, Ray-Wave Tilt, Hidden Momentum, and Apparent Topological Phases in Isotropy-Broken Materials based on Electromagnetism of Moving Media

Abstract

One of the problems of physics arguably greater in stature than even mathematical Hilberts problems is the mysterious nature of electromagnetic momentum in materials. In this paper we show that the difference between the Minkowski and Abraham momenta, which is composed of the Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We demonstrate that individual electromagnetic waves with non-unit indices of refraction n appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames these high-k waves are Fresnel-Fizeau dragged from rest to their phase velocities and acquire longitudinal hidden momentum and related refractive properties. On the material level all electromagnetic waves belong to Fresnel wave surfaces topologically classified according to hyperbolic phases by Durach and determined from the electromagnetic material parameters. To moving observers, material parameters appear modified, which leads not only to the alterations of Fresnel wave surfaces, but even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of the electromagnetic momentum tilt, defined as non-zero angle between Abraham and Minkowski momenta or equivalently between the rays and the wavefront propagation direction. We show that momentum tilt is only possible in isotropy-broken media, where E and H fields can be longitudinally polarized in presence of electric and magnetic bound charge waves. The momentum tilt can be understood as differential aberration of rays and waves when observed in material rest frame.