Flexibly modulated Poincaré sphere vector optical field in input and focal planes.

We theoretically design and experimentally generate the flexibly modulated Poincare sphere vector optical field (PS-VOF), which can be constructed by flattening the Poincare sphere surface. This new kind of PS-VOF provides additional degrees of freedom to modulate the spatial structure of polarization based on Poincare sphere. The focal property of the PS-VOF is further studied, and we focus on studying the polarization coverage of the Poincare sphere in the focal plane. In focusing process, the conversion and annihilation of spin angular momentum are presented. In addition, when the proportion of right-handed polarizations from the northern hemisphere of the Poincare sphere satisfies Golden ratio (0.618) in the input plane, a full PS-VOF with high quality can be achieved in the focal plane. We hope this study of PS-VOF in both input and focal planes can enrich the family of VOFs, provide a new avenue in studying VOFs based on the Poincare sphere, and can be potentially applied in the regions with sensitivity to polarizations.