van de Hulst essay: Geometric-phase portrayal of electromagnetic scattering by a three-dimensional object in free space

Quantifying the dissimilarity in the locations of two plane waves on the Poincaré sphere by using spinor algebra, the concept of geometric phase was applied to initiate a novel portrayal of electromagnetic scattering by a three-dimensional object in free space. Whereas the incident electromagnetic field is that of an arbitrarily polarized plane wave, the direction-dependent far-zone scattering amplitude was used to define direction-dependent Stokes parameters for the scattered field. Both symmetric and asymmetric Poincaré spinors were formulated to characterize the polarization states of incident plane wave and the far-zone scattering amplitude, and two different geometric phases were defined therefrom. Density plots of both geometric phases were calculated for six different homogeneous isotropic spheres with different linear constitutive properties and boundary conditions: dielectric–magnetic spheres (non-dissipative and dissipative), impedance spheres, perfect electrically conducting spheres, charged dielectric–magnetic spheres, dielectric–magnetic spheres with topologically insulating surface states, isotropic chiral spheres, and isotropic chiral spheres with topologically insulating surface states. The incident plane waves were taken to be linearly and circularly polarized, for the sake of illustration. Numerical results revealed that geometric-phase density plots possess significantly richer features than their counterparts for the differential scattering efficiency. The geometric-phase portrayals exhibit enhanced sensitivity to changes in the size and composition of the scatterer, the boundary conditions, and the incident polarization state, suggesting promise for inverse-scattering problems.