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.

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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 ultrarelativistic 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 ultrarelativistic region and that the photonic crystal is finite. The origin of the radiation was identified by comparison of experimental and theoretical results.

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This paper presents the formula for the density of states ͑DOS͒ of photonic bands (PB's) in the leaky region of the phase space of a slab-type photonic crystal. It is expressed by the eigenphase shifts of the scattering matrix defined in terms of the complex transmission and reflection amplitudes of plane wave external incident light. The derivation is given for the general case in which a number of diffracted plane wave lights are produced by the incident lights. The DOS profile calculated as a function of frequency and wave vector enables us to obtain the dispersion relation and lifetime of leaky PB's. The usefulness of the derived formula is demonstrated by applying it to the PB structure of dielectric spheres, arrayed periodically to form a photonic crystal of finite thickness. PACS number(s): 42.70.Qs II. SCATTERING MATRIX AND ITS EIGENVALUES A. Definition of scattering channelsWe consider a slab PC extending in the x , y direction with the origin of coordinates r = 0 taken at its center. The period- PHYSICAL REVIEW B 70, 035109 (2004)