Geometric Representation of Vector Vortex Beams: The Total Angular Momentum-Conserving Poincaré Sphere and Its Braid Clusters

This paper presents the total angular momentum-conserving Poincare sphere (TAM-C PS), which offers a novel framework for efficiently characterizing a wide range of vector vortex beams. Unlike other types of Poincare spheres, the TAM-C PS achieves a better balance between generality and validity, while also providing clearer physical interpretation. By linking the poles of different spheres, the study also introduces two distinct categories of TAM-C PS braid clusters, enabling the representation of various Poincare spheres within a unified framework. The Poincare spheres include classical, higher-order, hybrid-order, Poincare sphere with orbital angular momentum, and TAM-C PS. This is the first clear and unified approach to express multiple Poincare spheres within a single framework. The TAM-C PS and its braid cluster can be employed to guide the creation of targeted vector vortex light beams, offer a geometric description of optical field evolution, and calculate the geometric phase of optical cyclic evolution.

Automated summary

This paper introduces the total angular momentum-conserving Poincare sphere (TAM-C PS) as a novel framework for characterizing vector vortex beams. The TAM-C PS achieves a better balance between generality and validity compared to other types of Poincare spheres, and also provides clearer physical interpretation. By connecting the poles of different spheres, the study introduces two distinct categories of TAM-C PS braid clusters, which allows for the representation of various Poincare spheres within a unified framework. The TAM-C PS can be used to guide the creation of targeted vector vortex light beams, provide a geometric description of optical field evolution, and calculate the geometric phase of optical cyclic evolution.