SU(2) gadget for higher-order Poincar\'{e} sphere

TL;DR

This paper introduces an optical gadget using q-plates that can perform all polarization transformations on the higher-order Poincaré sphere, extending the universal SU(2) gadget concept to higher topological index spaces.

Contribution

It demonstrates that a combination of two quarter-wave and one half-wave q-plates, in any order, forms a universal SU(2) gadget for the higher-order Poincaré sphere.

Findings

The gadget can realize arbitrary polarization transformations on the higher-order Poincaré sphere.

The arrangement of q-plates is flexible, maintaining universality.

This extends the SU(2) gadget concept to higher topological index spaces.

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.