Coherent Cerenkov emission from electrons streaming through a photonic crystal

Cerenkov radiation is usually incoherent radiation emitted by charged particles when they pass through a medium with sufficiently high, usually relativistic velocity. It has recently been shown that in photonic crystals Cerenkov emission is possible without a velocity threshold, however emission from electrons streaming through the crystal typically remains incoherent. Here we show that sufficiently strong feedback between the electrons and the Cherenkov radiation results in coherent emission. The coherent amplification results in a growth of the power by many orders of magnitude, from incoherent emission to saturation in the kW-range. This concept to directly generate coherent radiation with free-electrons in a photonic crystal forms a novel type of coherent radiation source, which can be termed a photonic free-electron laser. The required increase in feedback is obtained via properly designing the photonic crystal. Specifically, the structure is chosen to strongly reduce the phase velocity of a low order spatial harmonic of the radiation field to match it to the electron velocity. Additionally, the structure is chosen to maximize the electric field component in the propagation direction, to provide maximum bunching of the electrons and thereby generate strong stimulated emission. This laser has several unique properties. First, the laser output frequency can be continuously tuned by varying the electron velocity. Second, as the photonic crystal has many natural channels for the electron beam in parallel, adding more electron beams increases the output power while still maintaining full transverse coherence. Finally, due to the scale invariance of Maxwell’s equations, downsizing the photonic crystal structure by a certain factor scales up the frequency of the laser by the same factor, without requiring a change in velocity of the electrons. Here we demonstrate, the principle physics behind this device and illustrate this with numeric results obtained with a so-called particle-in-cell simulation code for a device working in the microwave spectral region