Cluster of homogeneous spheres (well, almost like on the picture, but they have to be homogeneous) can be solved analytically in terms of infinite series. Such solution are based on Mie solution for individual spheres and subsequent expansion of these solutions to account for boundary conditions. Spheres can not intersect.

Name Author Type Language Description
GMM, GMM papers, GMM description Xu multispheres, Mie Fortran Codes which calculate (exactly) electromagnetic scattering by an aggregate of spheres in a single orientation or at an average over individual orientations (these codes were previously available on There are 3 files: code, description, and relevant papers.
Mackowski Dan Mackowski multisphere, Mie Fortran Codes for calculation of the scattering matrix and cross sections of neighboring, non-intersecting spheres. Dan Mackowski's papers on multisphere are one of the most comprehensive. Older local version.
MSTM Dan Mackowski (2013) multisphere, Mie Fortran MSTM (Multiple Sphere T Matrix) is a fortran-90 code for calculation of the electromagnetic scattering and absorption properties of a system of spherical surfaces. The code is designed to run either on serial platforms or distributed—memory compute clusters.

Other papers

Features of Propagation of Light in the Linear Array of Dielectric Spheres

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