Wave retarders having spatially varying optical axes orientations, called q-plates are extremely efficient devices for converting spin to orbital angular momentum of light and for the generation of optical vortices. Most often, these plates are designed for a specific wavelength and have a homogeneous constant retardance. The present work provides a polarimetric approach for overcoming both these limitations. We theoretically propose and experimentally demonstrate q-plates with tunable retardance, employing a combination of only standard q-plates and waveplates. A clear prescription is provided for realizing wavelength indepedent q-plates for a desired retardance, with a potential for ultrafast switching. Apart from the potential commercial value of the proposed devices, our results may find applications in quantum communication protocols, astronomical coronography, angular momentum sorting and in schemes that leverage optical vortices and spin to orbital angular momentum conversion.
Waveplates having spatially varying fast-axis orientation and retardance provide an elegant and easy way to locally manipulate different attributes of light beams, namely, polarization, amplitude, and phase, leading to the generation of exotic structured light beams. The fabrication of such doubly inhomogeneous waveplates (d-plates) is more complex, compared with that of singly inhomogeneous waveplates (s-plates) having uniform retardance, which can be easily fabricated by different means such as photoalignment of liquid crystals, metasurfaces, etc. Here, exploiting the SU(2) formalism, we establish analytically that any d-plate can be equivalently implemented using a pair of quarter-wave s-plates and a half-wave s-plate. To underline the scope of this method, we propose novel d-plates toward complex amplitude shaping and also for imparting a polarization-dependent phase profile to a scalar light beam. For these two illustrations, the corresponding three-s-plate gadget is constructed, and its functioning is validated with extensive numerical simulations. The main result and its illustrations are generic and agnostic to the way the s-plates are fabricated, and we believe they carry the potential to push the current state of the art in interdisciplinary applications involving structured light beams.
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 (
d
-plates) is proposed. In this method, every input state of polarization (SoP) through such a
d
-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
d
-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
d
-plates is also presented.
It is well known that state transformation from one polarization state to another can be achieved with a minimal gadget consisting of two quarter waveplates. A constructive, geometric approach is presented, which provides a direct prescription for the fast axis setting of the waveplates to transform any completely polarized states of light to any other, including orthogonal ones.
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