Features of Propagation of Light in the Linear Array of Dielectric Spheres

TL;DR

This paper investigates how light propagates in a finite chain of dielectric spheres, revealing frequency pass bands related to Mie resonances and the influence of chain length and material properties on these bands.

Contribution

It introduces a detailed analysis of frequency pass bands in dielectric sphere chains, highlighting the effects of refractive index, chain length, and oscillation direction on light propagation.

Findings

Frequency pass bands exist around Mie resonances at high refractive indices.

Longitudinal and transverse mode pass bands depend on refractive index and chain length.

The band structure breaks down at small wavevectors, explained by guiding wave criteria.

Abstract

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 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 ZnO, rutile and GaAs are considered. 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. This explains the remarkable feature of the band picture established for infinite chain: 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.