A novel polarimetric method of generating a variety of Poincaré beams such as half Poincaré beams and full Poincaré beams using doubly inhomogeneous wave plates (-plates) is proposed. In this method, every input state of polarization (SoP) through such a -plate generates a unique Poincaré beam, thereby giving access to a potentially infinite number of them. Furthermore, the generation of full Poincaré beams is presented here as an instance of the geometrical problem of mapping the surface of a sphere onto a plane, and this insight allows one to design -plates that convert the input SoP to every possible SoP, within a finite region of the beam. A gadget composed of three singly inhomogeneous wave plates for an equivalent realization of these -plates is also presented.
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