Numerical study of light scattering in a hollow sphere using Mie theory

Optical characterization of sub-micron to micron-scale particles is essential in various fields. Hollow particles with a two-layer structure and internal voids present challenges for light scattering analysis due to their complex geometry. In this study, we extend Sorensen’s Q-space formalism, originally developed for homogeneous spheres, to quantitatively investigate the light scattering behavior of hollow spheres. Using rigorous Mie theory implemented, we computed angle-resolved scattering phase functions for hollow spheres with core radii of 0.8, 1.5, and 2.2 μm, as well as for a homogeneous solid sphere. The shell radius and refractive index were fixed at 2.5 μm and 1.5, respectively, the core refractive index was set to 1.0, and the incident wavelength was set to 654.5 nm. Scattering intensity was analyzed as a function of the dimensionless parameter qR, defined by the scattering vector q and shell radius R. As a result, hollow spheres with small and moderate void fractions closely matched the master curve of the homogeneous sphere. In contrast, for large void fractions, the typical (qR)⁻⁴ decay associated with surface scattering was weakened, suggesting the presence of a new scattering feature where surface contributions no longer dominate the far-field pattern. These results clarify how differences in void fraction affect the light scattering properties of hollow particles.