SU(2) gadget for higher-order Poincar\'e sphere
Abstract
The combination of two quarter-wave plates and one half-wave plate, regardless of their sequential arrangement, constitutes a well-established universal SU(2) gadget capable of implementing all polarization transformations on the standard Poincar\'e sphere. However, there is no analogous system for realizing all polarization transformations on the higher-order Poincar\'e sphere, a member of a higher topological index space. This work demonstrates that an optical gadget, comprising two quarter-wave q-plates and one half-wave q-plate, arranged in any order, is an SU(2) gadget to realize arbitrary polarization evolution on the higher-order Poincar\'e sphere.
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