Semi-analytical solution to arbitrarily shaped beam scattering

•An exact semi-analytical solution is presented in a spherical coordinate system.•This solution is applicable to an arbitrarily shaped beam and object.•Numerical results for three shaped beams are provided as examples.

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.