We present an easy, efficient, and fast method to generate arbitrary linear combinations of light orbital angular-momentum eigenstates =±2 starting from a linearly polarized TEM₀₀ laser beam. The method exploits 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.
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Karimi et al. (2010) studied this question.
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