Photon conservation in trans-luminal metamaterials

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.