A unified SU(2) framework treats vector beam transformations as spatially varying polarization operations and gives an explicit construction for doubly inhomogeneous waveplates that implement exact mappings including global phase.
Zhan, Cylindrical vector beams: from mathematical concepts to applications, Advances in Optics and Pho- tonics1, 1 (2009)
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A Unified SU(2) Framework for Vector Beam Transformations and Complex Beam Shaping
A unified SU(2) framework treats vector beam transformations as spatially varying polarization operations and gives an explicit construction for doubly inhomogeneous waveplates that implement exact mappings including global phase.