Scattering of Ince-Gaussian beams by a homogeneous isotropic dielectric sphere

Scattering of Ince-Gaussian (IG) beams by a homogeneous dielectric sphere is investigated using a volume integral equation formulation solved numerically using the method of moments. The incident IG beams are characterized by their mode indices, parity, beam waist, semi-focal distance, and polarization state. The scattering characteristics are analyzed in terms of directivity, normalized total scattered power, and normalized absorbed power. Validation of the formulation is established through comparisons with limiting cases, including plane-wave and Laguerre-Gaussian-beam incidences. Numerical results reveal that the directivity patterns strongly depend on the beam mode indices, namely the order and degree, as well as the beam parity. Odd-order modes exhibit zero directivity in the forward and backward directions, consistent with a symmetry property of the incident field. The dependence of the directivity on the semi-focal distance is shown to be linked directly to the sensitivity of the corresponding Ince polynomials. Furthermore, the effect of the beam waist on the directivity depends on the mode, with changes in the maximum directivity and the depths and positions of the minima. The normalized total scattered and absorbed powers increase with the electrical size of the sphere, while their magnitudes depend strongly on the beam mode, with considerably lower values observed for some higher-order modes. However, the modes with the highest normalized total scattered power do not necessarily have the highest normalized absorbed power. The influence of polarization is found to be weak for the fundamental mode and IG_2,0 ^e , but more pronounced for some other modes, with absorption generally showing a stronger dependence on the polarization state than scattering.