Manifestation of photonic band structure in small clusters of spherical particles

TL;DR

This paper demonstrates that small clusters of dielectric spheres can exhibit photonic band structure characteristics similar to infinite crystals, with implications for photonic device design and light localization understanding.

Contribution

It shows that finite clusters of dielectric spheres can display photonic band structure features, using an efficient numerical method based on GMM scattering matrices.

Findings

Band structure signs appear in clusters of 5 particles.

Density of resonant states in 32-sphere clusters resembles infinite crystal states.

Resonant mode structure is insensitive to particle displacements.

Abstract

We study the formation of the photonic band structure in small clusters of dielectric spheres. The first signs of the band structure, an attribute of an infinite crystal, can appear for clusters of 5 particles. Density of resonant states of a cluster of 32 spheres may exhibit a well defined structure similar to the density of electromagnetic states of the infinite photonic crystal. The resonant mode structure of finite-size aggregates is shown to be insensitive to random displacements of particles off the perfect lattice positions as large as half-radius of the particle. The results were obtained by an efficient numerical method, which relates the density of resonant states to the the scattering coefficients of the electromagnetic scattering problem. Generalized multisphere Mie (GMM) solution was used to obtain scattering matrix elements. These results are important to miniature photonic crystal design as well as understanding of light localization in dense random media.