  We study the formation of the photonic band structure in small clusters of
dielectric spheres. The first signs of the band structure, an attribute of an
infinite crystal, can appear for clusters of 5 particles. Density of resonant
states of a cluster of 32 spheres may exhibit a well defined structure similar
to the density of electromagnetic states of the infinite photonic crystal. The
resonant mode structure of finite-size aggregates is shown to be insensitive to
random displacements of particles off the perfect lattice positions as large as
half-radius of the particle. The results were obtained by an efficient
numerical method, which relates the density of resonant states to the the
scattering coefficients of the electromagnetic scattering problem. Generalized
multisphere Mie (GMM) solution was used to obtain scattering matrix elements.
These results are important to miniature photonic crystal design as well as
understanding of light localization in dense random media.
