Continuity equation for momentum of the electromagnetic wave in a lossy dispersive magnetoelectric medium

Abstract

Continuity equation for the canonical pseudomomentum density in a magnetoelectric medium with dispersive losses is examined using consistent microscopic description of the electromagnetic wave energy. Accordingly, the canonical pseudomomentum is presented by the kinetic momentum of the electromagnetic field and pseudomomentum of oscillating bound charges, which is identified as a combination of the medium and electromagnetic pseudomomenta in contrast with previous quasi-static approaches. The ponderomotive and reaction forces are defined by the time derivatives of the medium and electromagnetic pseudomomenta, which depend on the “hidden momentum” in the case of a magnetoelectric medium. Properties of medium-field interaction are connected with translational invariance of the pseudomomentum in relation to a homogeneous lossless medium. Transport of the canonical pseudomomentum is explained by the kinetic momentum flux corresponding to the energy flux as well as translational invariance of the pseudomomentum, which are illustrated using the relativistic and effective mass densities of the electromagnetic wave. The optical pseudomomentum of the electromagnetic wave is defined in accordance with conducted analysis of energy and momentum transport while fallacies of approaches based on the Abraham, Minkowski, and total momenta are specified. Structure of the full momentum density of a closed medium-field system comprised of the densities of the optical pseudomomentum of the electromagnetic wave as well as the mechanical momentum and pseudomomentum of a host medium is expounded using description of medium-field interaction.

Keywords:

• energy density of the electromagnetic field
• canonical pseudomomentum
• kinetic momentum
• Abraham–Minkowski controversy
• ponderomotive and reaction forces

Disclosure statement

No potential conflict of interest was reported by the author.