Bound whispering gallery modes in circular arrays of dielectric spherical particles

Abstract

Low-dimensional ordered arrays of dielectric particles can possess bound optical modes having an extremely high quality factor depending on the material used. If these arrays consist of metal particles, then they cannot have a high quality factor because their light absorption restricts 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 within the framework of the multisphere Mie scattering theory using the simplest dipolar-like approach shows that (1) high quality modes in an array of <i>10</i> or more particles can be attained at least for a refractive index <i>n</i>_r > 2, so optical materials like TiO₂ 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 TiO₂ particles (rutile phase, n_r = <i>2.7</i>), 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. The consideration of higher multipole contributions has demonstrated that the error of the dipolar approach does not exceed one percent if the refractive index <i>n</i>_r is greater than 2. Minimum acceptable disordering not affecting the quality factor is studied.