Bound Whispering Gallery Modes in Circular Arrays of Dielectric Spherical Particles

Low-dimensional ordered arrays of dielectric particles can possess bound optical modes having an extremely high quality factor depending on the material used. 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 within the framework of the multisphere Mie scattering theory using the simplest dipolar-like approach shows that high quality modes in an array of 10 or more particles can be attained at least for a refractive index n_r > 2; the most bound modes have nearly transverse polarization perpendicular to the circular plane; and in a particularly interesting case (TiO₂ particles, 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 of GaAs the quality factor increases by almost two orders of magnitude. The error of the dipolar approach does not exceed one percent if n_r >2. Minimum acceptable disordering not affecting the quality factor is also investigated.