  The nontrivial dispersion relation of a periodic medium affects both the
spectral and the spatial distribution of Cherenkov radiation. We present a
theory of the spatial distribution of Cherenkov radiation in the far-field zone
inside arbitrary three- and two-dimensional dielectric media. Simple analytical
expressions for the far-field are obtained in terms of the Bloch mode
expansion. Numerical examples of the Cherenkov radiation in a two-dimensional
photonic crystal is presented. The developed analytical theory demonstrates
good agreement with numerically rigorous finite-difference time-domain
calculations.
