Higher Order Pancharatnam-Berry Phase and the Angular Momentum of Light

The first experimental demonstration of a new Pancharatnam-Berry phase for light beams with spatially inhomogeneous, or vector, states of polarization referred to as the higher-order Pancharatnam-Berry phase is presented. This new geometric phase is proportional to light's total angular momentum, a sum of spin and higher dimensional orbital angular momentum, sharply contrasting the well-known Pancharatnam-Berry phase associated with the plane wave state of polarization of a spatially homogeneous light beam. The higher-order Pancharatnam-Berry phase is directly related to the rotational symmetry of a vortex-bearing electromagnetic field, associated with the rotational frequency shift of a light beam, and has implications in quantum information science as well as other physical systems such as electron vortex beams.