Topological Differential Microscopy Based on the Spin–Orbit Interaction of Light in a Natural Crystal

We experimentally demonstrate a two-dimensional topological differential microscopy based on the spin–orbit interaction of light through a thin uniaxial crystal slab. First, a three-dimensional propagation theory is established for the light propagating through a uniaxial material. Then it is found that, due to the spin–orbit interaction, the two circularly polarized components of incident light are imposed with opposite topological charges, leading to the azimuthal splitting of spin states. Consequently, the cross-polarized field approximately amounts to the second-order spatial differentiation of the incident field. Finally, such an optical differentiation performed by a lithium niobate crystal is successfully applied to edge detection in microscopy. Further experiments validate its good performance in edge enhancement of both amplitude and phase objects. The results provide an economic, simple but robust approach to real-time, colorful, and high-contrast biological imaging in living systems.