Forming of three-dimensional optical fields consistent with the superposition of scalar spherical harmonics

Abstract Spherical functions are the angular part of the family of orthogonal solutions of the Laplace equation written in spherical coordinates. They are widely used to study physical phenomena in spatial domains bounded by spherical surfaces and in solving physical problems with spherical symmetry. In this paper, the superposition equation of spherical harmonics satisfying the Helmholtz equation was obtained. Modelling and visualization of three-dimensional fields, coordinated with separate spherical harmonics and their superpositions, was carried out.