Polarization evolution on the higher-order Poincare sphere via photonic Dirac points

In this work, we report a general reflection model to describe the reflected behaviors of a Gaussian beam near photonic Dirac point at the optical interface. With spin polarized electromagnetic waves strikes near the single Dirac point on Dirac material interface, vortical phase distribution and spin inversion are demonstrated for reflected state, and we further develop a higher-order Poincare sphere to describe the evolution of polarization states. It is possible to generate any desired Poincare vortex beam on the sphere by modulating the incident polarization state of light. Moreover, we discuss the case of normal incidence around two adjacent Dirac points, reflection spectrum involves a couple of spin flip vortices corresponding to two points with the corresponding topological invariants, which are consistent with the Berry curvature and topological charge. These results can be extended to similar hyperbolic metamaterials with degenerate point, and inspire a different perspective for manipulating polarized vortex beam with photonic Dirac point.