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The asymptotic analysis of the radiation pattern of a classical dipole in aphotonic crystal possessing an incomplete photonic bandgap is presented. Thefar-field radiation pattern demonstrates a strong modification with respect tothe dipole radiation pattern in vacuum. Radiated power is suppressed in thedirection of the spatial stopband and strongly enhanced in the direction of thegroup velocity, which is stationary with respect to a small variation of thewave vector. An effect of radiated power enhancement is explained in terms of\emph{photon focusing}. Numerical example is given for a square-latticetwo-dimensional photonic crystal. Predictions of asymptotic analysis aresubstantiated with finite-difference time-domain calculations, revealing areasonable agreement.Comment: Submitted to Phys. Rev.

Radiation pattern of a classical dipole in a photonic crystal: Photon focusing