Spin-orbit optical Hall effect in π-vector fields

Given the tremendous increase of data in digital era, vector vortex light with strongly coupled spin and orbital angular momenta of photons have attracted great attention for high-capacity optical applications. To fully utilize such rich degrees of freedom of light, it is highly anticipated to separate the coupled angular momentum with a simple but powerful method, and the optical Hall effect becomes a promising scheme. Recently, the spin-orbit optical Hall effect has been proposed in terms of general vector vortex light using two anisotropic crystals. However, angular momentum separation for π-vector vortex modes, another important part in vector optical fields, have not been explored and it remains challenging to realize broadband response. Here, the wavelength-independent spin-orbit optical Hall effect in π-vector fields has been analyzed based on Jones matrices and verified experimentally using a single-layer liquid-crystalline film with designed holographic structures. Every π-vector vortex mode can be decoupled into spin and orbital components with equal magnitude but opposite signs. Our work could enrich the fields of high-dimensional optics.