Photon conservation in trans-luminal metamaterials
J. B. Pendry, E. Galiffi, Paloma A. Huidobro
Abstract
Structures that appear to move at or near the velocity of light contain singular points. Energy generated by motion accumulates at these points into ever-narrowing peaks. In this paper, we show that energy is generated by a curious process that conserves the number of photons, adding energy by forcing photons already present to climb a ladder of increasing frequency. We present both a classical proof based on conservation of lines of force, and a more formal quantum electrodynamics proof demonstrating the absence of unpaired creation and annihilation operators. Exceptions to this rule are found when negative frequencies make an appearance. Finally, we make a connection to laboratory-based models of black holes and Hawking radiation.