  A finite length linear chain of dielectric loss-less identical spheres is
considered. A propagation of dipole radiation in the chain of particles induced
by the point dipole source placed near one end of the chain is investigated. It
is found that at sufficiently large refractive index there exist frequency pass
bands around every low frequency Mie resonance. In particular, if the dipole
oscillates across the chain axis, one can reveal a longitudinal mode frequency
pass band if refractive index of the spheres exceeds 1.9. Then, if the dipole
oscillates transversely to the chain axis, the transverse frequencies pass
bands show up depending on the chain length. In this case, the pass band is
formed if the length chain is large enough. Three dielectric materials ZnO,
rutile and GaAs are considered. It is found that the top of the frequency pass
band corresponds to the top of the Brillouin band edge in the quasi-momentum
space. On the order hand, the bottom of the frequency pass band corresponds to
the guiding wave criterion. This explains the remarkable feature of the band
picture established for infinite chain: the band structure breaks down as the
wavevector becomes small enough. The multisphere Mie scattering formalism is
used to calculate how the amplitude of the radiation changes along the chain.
