Optical origins of central circular reflections in spherical colloidal clusters

Spherical colloidal clusters composed of submicron particles often exhibit vivid structural colors due to optical interference. When they are observed under an optical microscope, a circular reflection spot clearly appears at the center of the spherical clusters. For clusters with an onion-like structure, this spot is well explained by the stacking of periodic particle layers. However, it is intriguing that a similar spot appears even in clusters with other structural types. This paper reports that two circular spots with different radii can generally be observed in spherical colloidal clusters. We clarify their optical mechanisms by combining optical microscopy, geometrical analysis, and numerical simulations. We conclude that two distinct optical processes are responsible for these spots: one is reflection at the cluster surface, and the other is the combination of spectral filtering during transmission through the cluster and reflection at the substrate surface. In the second process, Bragg diffraction from the (111) planes of a face-centered cubic lattice causes the spectral filtering effect, resulting in particle-size-dependent coloration. These findings provide new insights into the structure-optics relationship in colloidal clusters and highlight design principles for spherical structural color materials.