Electromagnetic energy–momentum tensors in general dispersive bianisotropic media

Abstract

The macroscopic electromagnetic (EM) energy–momentum tensor is one of the most important quantities characterizing the propagation and interaction of light in materials. In recent years, while exotic optical effects in various kinds of bianisotropic materials have been discovered, there still lacks a rigorous analysis of the energy and momentum of EM fields in such general cases. In this paper, using Noether’s theorem and the “Abrahamization” procedure, we obtain generalized Minkowski and Abraham EM energy–momentum tensors, applicable for both arbitrary time-dependent real EM fields and complex-valued analytic signals, in generic lossless bianisotropic media with frequency dispersion. The frequency dispersion of the materials modifies the expressions of EM energy density and Minkowski momentum, making them different from their familiar forms in nondispersive media. Our results reveal that the generalized Minkowski momenta for both real fields and analytic signals are conserved in source-free homogeneous media, while the Abraham momenta, characterizing the centroid motion of light, can change over time, which leads to the counterintuitive phenomenon that wave packets can travel along curved trajectories even in homogeneous bianisotropic media. We also show that the energy–momentum tensor for analytic signals derived from the action principle directly gives the conservation law of time-averaged fields and hence can describe the envelope evolution of waves in quasi-monochromatic approximation.