  The Chern number has been widely used to describe the topological properties
of periodic structures in the momentum space. Here, we introduce a real-space
spin Chern number for the optical near fields of finite-sized structures. This
new spin Chern number is intrinsically quantized and equal to the structure's
Euler characteristic. The relationship is robust against continuous deformation
of the structure's geometry and is irrelevant to the specific material
constituents or external excitation. Our work enriches topological physics by
extending the concept of Chern number to the real space, opening exciting
possibilities for exploring the real-space topological properties of light.
