Scattering of Mathieu beams by a rigid sphere

Based on the recent results on the scattering of Bessel beams by a sphere and using the Whittaker integral, the scattering by a rigid sphere centred on a Mathieu beam is derived. The scattering field is expressed as a partial wave series involving the scattering angles relative to the beam axis and Mathieu beam parameters. Some numerical calculations are performed and it is shown that the illumination of a rigid sphere by a Mathieu beam produces asymmetrical scattering as a function of scattering angles θ and ϕ. The geometrical properties of the scattering Mathieu beam are noted.

Research Highlights
► The representation of Mathieu beams in terms of plane waves is used to derive an analytical formulation of the scattered field in our study.
► The expression of the far-field optical scattering is evaluated by using of a partial wave series.
► Numerical calculations show that the scattering field depends on: spatial propreties of Mathieu beams, radius of sphere and scattering angles.