Some aspects of mass-energy equivalence which appears in left-handed metamaterials

In this work, the concept of mass-energy equivalence in left-handed metamaterials is discussed by following Einstein's box thought experiment. Left-handed metamaterials are artificial composite structures that exhibit unusual properties, especially negative refractive index, in which phase and group velocities are directed oppositely. Equation E=mc(2) assumes that, in vacuum, the propagation of an electromagnetic radiation from emitter to receiver is accompanied by the transfer of mass. It was hypothesized previously that if the space between emitter and receiver is medium with a negative refractive index, then radiation transfers the mass not from the emitter to receiver as expected, but rather from the receiver to the emitter due to the opposite directions of phase and group velocities. In this paper, it is shown that even though one radiating atom is taken, the negative mass transferring must be in force. In particular, it means that, if the atom radiates a photon in a medium with negative refractive index, photon transfers the mass not from the atom, but to the atom.