Electromagnetic momenta at wave refraction into dispersive medium

Background and Objectives: There are two types of a field momentum in the classical electrodynamics, namely, the Abraham momentum, and the Minkowski momentum. The question arises how these momenta are conserved in the refraction on the boundary surface of a medium. Methods: The electromagnetic stress tensor and momentum density in a dispersive medium, including the case of negative permittivity and negative permeability, are derived and used in this paper. Results and Conclusion: It is shown that the momentum of an incidence wave is conserved as the sum of the Abraham momentum, the Abraham force momentum, and the momentum of the electromagnetic pressure on the boundary surface of the medium. In the same time, the tangential component of the incidence momentum is conserved as the Minkowski momentum. The reason is that there is an invariance of the "vacuum–plane–matter" system in the transfer along the boundary surface of the medium. Consequently, a quasi-momentum should be conserved in this direction. On the other hand, there is no such symmetry in the direction perpendicular to the boundary surface of the medium. Consequently, any quasi-momentum in this direction does not exist. This shows that the Abraham momentum and the Minkowski momentum can work together, although these quantities corresponds to the different expansions of the total momentum into field and media parts.