Photonic crystals versus diffraction gratings in Smith-Purcell radiation

The emission cross section of Smith-Purcell radiation is calculated for a charged particle running near the surface of a photonic crystal. The cross section of a photonic crystal of arrayed dielectric spheres and that of a diffraction grating are compared. It is shown that well-defined photonic bands of the photonic crystal bring about a spectrum full of resonant structures of enhanced intensity, whose peak heights are an order of magnitude larger than the emission intensity of the diffraction grating. The results of calculations thus show a possible advantage of photonic crystals over diffraction gratings as a converter of the evanescent field from a running charge into propagating waves.