  Unusual emission of light, called the unconventional Smith-Purcell radiation
(uSPR) in this paper, was demonstrated from an electron traveling near a finite
photonic crystal (PhC) at an ultra-relativistic velocity. This phenomenon is
not related to the accepted mechanism of the conventional SPR and arises
because the evanescent light from the electron has such a small decay constant
in the ultra-relativistic regime that it works practically as a plane-wave
probe entering the PhC from one end. We analyze the dependence of the SPR
spectrum on the velocity of electron and on the parity of excited photonic
bands and show, for PhCs made up of a finite number of cylinders, that uSPR
probes the photonic band structure very faithfully.
