  We report the observation of an exotic radiation (unconventional
Smith-Purcell radiation) from a one-dimensional photonic crystal. The physical
origin of the exotic radiation is direct excitation of the photonic bands by an
ultra-relativistic electron beam. The spectrum of the exotic radiation follows
photonic bands of a certain parity, in striking contrast to the conventional
Smith-Purcell radiation, which shows solely a linear dispersion. Key
ingredients for the observation are the facts that the electron beam is in an
ultra-relativistic region and that the photonic crystal is finite. The origin
of the radiation was identified by comparison of experimental and theoretical
results.
