Counterposition and negative phase velocity in uniformly moving dissipative materials

Abstract

We considered the phenomena of counterposition and negative phase velocity, which are relevant to certain metamaterials and certain astrophysical scenarios. The Lorentz transformations of electric and magnetic fields were implemented to study (i) the refraction of linearly polarized plane waves into a half-space occupied by a uniformly moving material and (ii) the traversal of linearly polarized Gaussian beams through a uniformly moving slab. Motion was taken to occur tangentially to the interface(s) and in the plane of incidence. The moving materials were assumed to be isotropic, homogeneous and dissipative dielectric materials from the perspective of a co-moving observer. Two different moving materials were considered: from the perspective of a co-moving observer, material A supports planewave propagation with only positive phase velocity, whereas material B supports planewave propagation with both positive and negative phase velocity, depending on the polarization state. For both materials A and B, the sense of the phase velocity and whether or not counterposition occurred, as perceived by a non-co-moving observer, could be altered by varying the observer's velocity. Furthermore, the lateral position of a beam upon propagating through a uniformly moving slab made of material A, as perceived by a non-co-moving observer, could be controlled by varying the observer's velocity. In particular, at certain velocities, the transmitted beam emerged from the slab laterally displaced in the direction opposite to the direction of incident beam. The transmittances of a uniformly moving slab made of material B were very small and the energy density of the transmitted beam was largely concentrated in the direction normal to the slab, regardless of the observer's velocity.