Topological spatial differentiators upon reflection of the normally incident light

We theoretically propose topological spatial differentiators by the normal-incidence reflection of light. Firstly, a three-dimensional propagation model is established for the light normally incident on the interface between two media. It is found that due to the spin-orbit interaction of light, a given circularly polarized light always induces oppositely polarized light carrying a topological charge, so the two intrinsic spin components are separated radially or azimuthally. Moreover, the normally reflected fields are approximately proportional to two kinds of second-order spatial differentiations of the input circularly and linearly polarized fields. Further results applying to the two-dimensional image processing for edge detection validate the two topological spatial differentiators.