Radiation pattern of a classical dipole in a photonic crystal: photon focusing.
An asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stop band and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of photon focusing. A numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.
Chigrin
Dmitry N
DN
Institute of Materials Science and Department of Electrical and Information Engineering, University of Wuppertal, Gauss-strasse 20, 42097 Wuppertal, Germany. chigrin@th.physik.uni-bonn.de