Geometric phase associated with transformations of cylindrical vector beams

We present a geometric phase arising from transformations along the surface of a Poincare sphere representation for cylindrical vector beams. Cylindrical vector beams are expressed as the superposition of orthogonal circular polarized Laguerre-Gaussian modes of opposite topological charge. Two spheres are described where the poles of each sphere are circular polarized Laguerre-Gaussian modes, and points along the equator are cylindrical vector beams. A closed loop transformation on the sphere's surface is carried out using combinations of wave plates and cylindrical lens mode converters, and an acquired geometric phase is experimentally measured interferometrically.