Light propagation from a fluorescent particle embedded in a photonic cluster of micrometer-sized dielectric spheres

In self-assembled multilayer arrays of micrometer-sized spheres that include small amounts of fluorescent particles, unique six-dot-triangular and seven-dot-hexagonal patterns have been known to appear in the fluorescence microscopic images. Although it has been suggested that these two types of patterns correspond to local domain structures, i.e., face centered cubic (fcc) or hexagonal closed packed (hcp), no conclusive evidence has been provided to support this claim. In this study, we systematically investigated the relationship between the propagation patterns and the arrangement of the particles. Through a cross-check between an experiment using well-defined clusters fabricated by a micromanipulation technique and a rigorous calculation based on the expansion of vector spherical harmonics, we confirmed that the six-dot-triangular and seven-dot-hexagonal patterns correspond to the fcc and hcp domains, respectively. Further, we also found that the propagation patterns depend on the size of the clusters. As a result of a quantitative discussion on the light propagation in clusters with various sizes, it was clarified that a sufficient domain size is necessary for the appearance of clear triangular or hexagonal patterns.