  A propagation of dipolar radiation in a finite length linear chain of
identical dielectric spheres is investigated using the multisphere Mie
scattering formalism (MSMS). A frequency pass band is shown to be formed near
every Mie resonances inherent in the spheres. The manifestation of the pass
band depends on the polarization of the travelling radiation. To prove this
effect, a point dipole placed by the end of the chain is used as an external
source of radiation. It is found that, if this dipole is directed parallel to
the to the chain axis, the frequency pass bands exist if the refractive index
of dielectric spheres is sufficiently large. For the dipole normal to the chain
axis, the pass band can always be formed if the chain is sufficiently long.
Such a distinction is due to different behavior of the far-field dipolar
interaction between the spheres induced by the external source. The edges of
the pass bands are defined by the guiding wave criterion based on the
light-cone constraint. The criterion of creation of the pass bands correlate
with condition of formation of high quality factor modes in these systems found
in our previous papers. A comparison with the results available for infinite
chains is made. In particular, we clarify the nature of braking down the band
structure for small enough wavevectors.
