Coherent Cherenkov radiation and laser oscillation in a photonic crystal

We demonstrate that photonic crystals can be used to generate powerful and highly coherent Cherenkov radiation that is excited by the injection of a beam of free electrons. Using theoretical and numerical investigations we present the startup dynamics and coherence properties of such a laser, in which gain is provided by matching the optical phase velocity in the photonic crystal to the velocity of the electron beam. The operating frequency can be varied by changing the electron beam energy and scaled to different ranges by varying the lattice constant of the photonic crystal