Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum

We present an easy, efficient, and fast method to generate arbitrary linear combinations of light orbital angular-momentumeigenstates � =± 2startingfromalinearlypolarizedTEM00 laserbeam.Themethodexploits the spin-to-orbital angular-momentum conversion capability of a liquid-crystal-based q plate and a Dove prism inserted into a Sagnac polarizing interferometer. The nominal generation efficiency is 100%, being limited only by reflection and scattering losses in the optical components. When closed paths are followed on the polarization Poincar´ e sphere of the input beam, the associated Pancharatnam geometric phase is transferred unchanged to the orbital angular momentum state of the output beam.