Analysis of motion-induced radiation of charged particles

Čerenkov radiation has hinted people to unfold energy transfer from kinetic energy of moving electrons to electromagnetic waves, evanescent or traveling. However, such dissipative motion-induced radiations require particles to move faster than light in medium or to encounter velocity transition to pump energy. An emergent Transformation Optics strategy provides possibility to manipulate light flow almost arbitrarily. Therefore such a curved electromagnetic space becomes an energy-pumping candidate from motion-induced radiation of particles. Inspired by a method to detect cloak by observing radiation of a fast-moving electron bunch going through it by Zhang et al., we attempt to derive another transition radiation of moving electron bunch going through a differently curved geometry of light: Maxwell's fish-eye, which in principle provides unlimited resolution as a perfect imaging lens. Our calculation may pave the way to investigate new scheme of transferring energy from electron to radiation.