Mie resonances of dielectric spheres in face-centered cubic photonic crystals

With use of plane waves as a basis for the band-structure calculation of a periodic assembly of highly refringent microspheres, it can be shown that resonance-mode frequencies of isolated dielectric spheres show up in the band structures. The strongly localized bands provided by the photonic-crystal analysis is compared with exact calculations made in spherical symmetry for an isolated microsphere. This comparison sheds some light on the effectiveness of the methods based on the description of mode coupling and, in particular, on the validity of tight-binding approaches of the description of photonic band structures. In addition, examining the effect of modifying the distance separating the spheres in the lattice, makes it easy to visualize the overlap between the modes of individual spheres. Thus quantitative information is provided on the geometry needed to feed energy into low-angular-momentum morphology-dependent resonances from a sharp source of the evanescent field and on the lifetime of these modes, when the resonances are disturbed by the proximity of a dielectric object of similar radius.