Time Dependence of the Intensity of Diffracted Radiation Produced by a   Relativistic Particle Passing through a Natural or Photonic Crystal
  The formulas which describe the time evolution of radiation produced by a relativistic particle moving in a crystal are derived. It is shown that the conditions are realizable under which parametric (quasi-Cherenkov) radiation, transition radiation, diffracted radiation of the oscillator, surface quasi-Cherenkov and Smith-Purcell radiation last considerably longer than the time of the particle flight through the crystal. The results of carried out experiments demonstrate the presence of additional radiation peak appearing after the electron beam has left the photonic crystal. 
V.G. Baryshevsky, A.A. Gurinovich
physics.acc-ph physics.optics