Light Propagation in Linear Arrays of Spherical Particles

TL;DR

This paper investigates how dipolar radiation propagates in finite chains of dielectric spheres, revealing frequency pass bands near Mie resonances that depend on polarization and chain length, with implications for waveguiding.

Contribution

It demonstrates the formation of frequency pass bands in finite dielectric sphere chains using multisphere Mie scattering, highlighting polarization-dependent effects and boundary conditions.

Findings

Pass bands form near Mie resonances in dielectric sphere chains.

Pass band existence depends on polarization and chain length.

Edges of pass bands are defined by light-cone guided wave criteria.

Abstract

A propagation of dipolar radiation in a finite length linear chain of identical dielectric spheres is investigated using the multisphere Mie scattering formalism (MSMS). A frequency pass band is shown to be formed near every Mie resonances inherent in the spheres. The manifestation of the pass band depends on the polarization of the travelling radiation. To prove this effect, a point dipole placed by the end of the chain is used as an external source of radiation. It is found that, if this dipole is directed parallel to the to the chain axis, the frequency pass bands exist if the refractive index of dielectric spheres is sufficiently large. For the dipole normal to the chain axis, the pass band can always be formed if the chain is sufficiently long. Such a distinction is due to different behavior of the far-field dipolar interaction between the spheres induced by the external source. The edges of the pass bands are defined by the guiding wave criterion based on the light-cone constraint. The criterion of creation of the pass bands correlate with condition of formation of high quality factor modes in these systems found in our previous papers. A comparison with the results available for infinite chains is made. In particular, we clarify the nature of braking down the band structure for small enough wavevectors.