Analysis of the Pancharatnam-Berry phase of vector vortex states using   the Hamiltonian based on the Maxwell-Schr\"odinger equation
  We derived the Berry connection of vector vortex states (VVSs) from the "true" Hamiltonian obtained through the Maxwell--Schr\"odinger equation for an inhomogeneous anisotropic (IA) medium, and we experimentally demonstrated measurement of the corresponding Pancharatnam--Berry (PB) geometrical phase of VVSs. The PB phase (PBP) of VVSs can be divided into two phases: homogeneous and inhomogeneous PBPs. Homogeneous and inhomogeneous PBPs are related to the conventional PBP and the spatially-dependent geometric phase given by an IA medium such as a polarization converter, respectively. We theoretically detected that inhomogeneous PBP accumulation originates from the gauge dependence of the index of the hybrid-order Poincar\'e sphere, which provides an alternate method for understanding optical spin--orbital angular momentum conversion. The homogeneous PBP, which is explicitly observed for the first time, has implications for quantum state manipulation and information processing. 
Masato Suzuki, Keisaku Yamane, Kazuhiko Oka, Yasunori Toda, and Ryuji   Morita
physics.optics