Ladder operators formalism for optical angular momentum transfer and space-variant Pancharatnam-Berry phase

Ladder operators are introduced in SU(2) parameter space to analyze the space-variant Pancharatnam-Berry (PB) phase. The spin and orbital angular momentum transfers to a wave passing through the PB phase optical elements are understood in terms of the PB phase. Space-variant PB phase structures are identified in polarization grating and cholesteric liquid crystal, providing an explanation for the beam propagation direction alteration. A simultaneous occurrence of the wavefront shaping and the beam propagation direction alteration is demonstrated experimentally.