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Photon emission rates in photonic band-gap materials

A photonic crystal efficiently controls the radiation rate of an embedded dipolar emitter. The influence of the periodic refractive index patterning on the emitter characteristics is assessed and the efficiency of a dipolar photonic source is calculated for a realistic, three-dimensional photonic crystal. Taking as a starting point the photonic band structure, it is shown that the emission rate is strongly correlated with the density of modes. For an infinite crystal, the computation of the field propagator confirms, in particular, that the emission rate falls to zero in the frequency range defined by the photonic band gap. We specifically consider a photonic crystal with a woodpile structure, offering a wide gap, with a monochromatic oscillating dipole at specific points (in or outside the rods) and orientations in the structure, and compute the emitted fields, expanded in terms of the photonic crystal eigenmodes. Radiation rate enhancements or inhibitions are predicted, according to the frequency and to the direction of the emission.