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We present an easy, efficient and fast method to generate arbitrary linearcombinations of light orbital angular momentum eigenstates $\ell=\pm 2$starting from a linearly polarized TEM$_{00}$ laser beam. The method exploitsthe spin-to-orbital angular momentum conversion capability of aliquid-crystal-based $q$-plate and a Dove prism inserted in a Sagnac polarizinginterferometer. The nominal generation efficiency is 100\%, being limited onlyby reflection and scattering losses in the optical components. When closedpaths are followed on the polarization Poincar\'{e} sphere of the input beam,the associated Pancharatnam geometric phase is transferred unchanged to theorbital angular momentum state of the output beam.

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