Electromagnetic momentum and radiation pressure derived from the Fresnel relations

Using the Fresnel relations as axioms, we derive a generalized electromagnetic momentum for a piecewise homogeneous medium and a different generalized momentum for a medium with a spatially varying refractive index in the Wentzel-Kramers-Brillouin (WKB) limit. Both generalized momenta depend linearly on the field, but the refractive index appears to different powers due to the difference in translational symmetry. For the case of the slowly varying index, it is demonstrated that there is negligible transfer of momentum from the electromagnetic field to the material. Such a transfer occurs at the interface between the vacuum and a homogeneous material allowing us to derive the radiation pressure from the Fresnel reflection formula. The Lorentz volume force is shown to be nil.