Optical spatial differentiation enabled layer sensing of two-dimensional atomic crystals.

Zero-thickness model and slab model are two important models in the description of optical behaviors in two-dimensional atomic crystals. The predicted difference in optical behaviors between the two models is very small, which is difficult to distinguish by established measurement methods. Here, we present an optical spatial differentiation method to examine the difference in edge images of different graphene layers. The theoretical results show that the edge imaging is significantly different between the two different models. When the beam reflection is at the Brewster angle, different graphene layers are used to adjust the spatial differentiation. It is shown that the slab model is more sensitive to the number of graphene layers. The zero-thickness model is more suitable for one-dimensional optical differential operation. Moreover, the spatial differentiation plays the role of a band-pass filter. The high-frequency edge information components will pass through the filter, thus realizing layer-sensitive edge-enhanced imaging. In addition, we do not focus on the verification of the exact model, but only provide an alternative method to characterize the number of graphene layers based on two models, and also provide possibilities for achieving imaging edge detection by graphene differential operators. This study may provide a possible method for the optical characterization of two-dimensional atomic crystals.