Features of propagation of light in the linear array of dielectric spheres

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 n_r 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 with n_r = 1.9, n_r = 2.7, n_r = 3.5 are considered what corresponds to ZnO, TiO₂, GaAs. 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 [2, 3]. This explains the remarkable feature of the band picture established for infinite chain in Ref. [1]: 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.