Relativistic finite-difference time-domain analysis of high-speed moving metamaterials

In this paper, we apply a relativistic finite-difference time-domain (FDTD) method by using the Lorentz transformation to analyze metamaterials moving at a high speed. As an example, we consider a slab of left-handed metmaterial (LHM) with both relative permittivity and permeability equal to -1. Simulation results show that when the LHM slab moves at a high speed, its electromagnetic responses are drastically different from the static case. Specifically, when the LHM slab moves toward the source, for the case of normal incidence, there exists a special velocity at which fields experience a zero spatial phase delay through the LHM slab; while for the oblique incidence, above a certain velocity fields inside the LHM become evanescent. On the other hand, when the LHM slab moves away from the source, for the case of normal incidence, at the same special velocity the magnitudes of both electric and magnetic fields inside the LHM slab reach their minimum values; for the oblique incidence, the slab functions as a field converter. Besides, the transmitted waves through the LHM slab experience a red-shift (to a lower frequency) and the shift is proportional to the velocity of the LHM slab regardless of the moving direction.