  Low-dimensional ordered arrays of optical elements can possess bound modes
having an extremely high quality factor. Typically, these arrays consist of
metal elements which have significantly high light absorption thus restricting
performance. In this paper we address the following question: can bound modes
be formed in dielectric systems where the absorption of light is negligible?
Our investigation of circular arrays of spherical particles shows that (1) high
quality modes in an array of 10 or more particles can be attained at least for
a refractive index $n_{r}>2$, so optical materials like TiO$_{2}$ or GaAs can
be used; (2) the most bound modes have nearly transverse polarization
perpendicular to the circular plane; (3) in a particularly interesting case of
TiO$_{2}$ particles (rutile phase, $n_{r}=2.7$), the quality factor of the most
bound mode increases almost by an order of magnitude with the addition of 10
extra particles, while for particles made of GaAs the quality factor increases
by almost two orders of magnitude with the addition of ten extra particles. We
hope that this preliminary study will stimulate experimental investigations of
bound modes in low-dimensional arrays of dielectric particles.
