Abstract

For over eighty years the momentum density of an electromagnetic wave in a material medium has been in dispute. Minkowski proposed that it was DxB while Abraham proposed that it was ϵ_o E x μ_oH. In recent years opinion has tended, though not unanimously, toward resolution based on the Abraham result being (true) momentum density and the Minkowski result being pseudomomentum density. We differ with both of these conclusions: we find the (true) momentum density to be ϵ_o ExB and the pseudomomentum density to be PxB. Our results are obtained from derivations of the momentum and pseudomomentum conservation laws, the latter resulting from homogeneity of the material medium. The derivations follow from a Lagrangian formulation of an arbitrary dielectric crystal, treated non-relativistically, in Interaction with the electromagnetic field. The formulation produces all the modes of motion of the system, acoustic, optic (both Ionic and electronic), and electromagnetic, and allows for arbitrary interactions between them. This permits a physical interpretation of the difference between ϵ_oExB and ϵ_oExμ_oH. By obtaining the conservation laws both from the equations of motion and from the Lagrangian by Noether's theorem we are able also to interpret the difference between PxB and DxB.

© 1990 Optical Society of America