Abnormal Spatial Shifts in Graphene Measured via the Beam Displacement Amplification Technique: Implications for Sensors Based on the Goos–Hänchen Effect

The Goos–Hänchen (GH) shift and Imbert–Fedorov (IF) shift caused by light–matter and spin–orbit interactions can reveal the intrinsic properties of nanomaterials. We propose a beam displacement amplification technique (BDAT) that can break the optical diffraction limit in beam displacement measurements. The displacement resolution of the BDAT is 4 nm, and the detection size is 5 μm, which is very suitable for the displacement measurement of mechanically exfoliated two-dimensional (2D) materials with a thickness on the scale of nanometers. With the help of the BDAT, we measured the GH shift and IF shift of graphene with different thicknesses. We found that the s-polarized light has a strong absorption effect in graphene with a thickness of approximately 15 nm, causing abnormal GH and IF shifts. This abnormal GH shift combined with the BDAT can be applied to detect changes in the refractive index, with a sensitivity of up to 9.5 × 10^–8 per reflective index unit. The BDAT holds promise as the most widespread means of displacement measurement, uncovering the properties of 2D materials and enhancing their application potential.