Potential relativistic dispersion in material medium

Abstract

Lorentz space-time transformation has been applied to the phase factor of a plane electromagnetic wave in linear material medium. The derivation shows in the limiting case for v = c, the phase velocity converges to its monochromatic value implying no such dispersion effect can exist in free space. However in linear material medium, wave speed may exceed the monochromatic phase velocity by a factor purely due to the relativistic consideration of the phase factor invariant under Lorentz transformation. The equation suggests such speed dispersion factor will be higher in the denser medium to its monochromatic material phase velocity. A critical cut-off number for the refractive index may exist to excite such mode in the material. The results can be interesting particularly for materials with high refractive index as well as for anisotropic space-time metric formulations in Transformation Optics. Keywords: Lorentz transformation, Phase factor, Refractive index, Dispersion factor