Poynting vector singularities in scattering from cylinders with curl-free gauge fields

We study Mie scattering from a cylinder comprised of engineered refractive index mimicking a free vortex leading to a magneto-electric coupling for stationary material. We find Poynting vector singularities in the near field distribution and predict an additional phase change in the far-field for magneto-electric-cylinder compared to conventional Mie scattering. We show that the magnitude of the artificial curl-free gauge fields can be used to control the angular position of the phase change in the far-field and the position of the Poynting vector singularities. Furthermore, we investigate the space-time reversal symmetry of material containing artificial curl-free gauge fields and dispersion relation for such spatially dispersive medium. The high k-vector region around the singularity can be exploited for near-field superresolution imaging and the far-field phase for scattered field holography.