Positive and negative Goos–Hänchen shifts in anisotropic two-dimensional atomic crystals

In this paper, the positive and negative Goos–Hänchen (GH) shifts in anisotropic two-dimensional atomic crystals are systematically investigated. As an example, the GH shifts including the spatial GH shift and the angular GH shift in the black phosphorus-substrate are studied. It is found that the spatial GH shift and the angular GH shift are sensitive to the incident angle, photon energy, optical axis angle and doping concentration. Further studies have shown that the signs variations of the spatial GH shift stem from a phase mutation of the reflection coefficients, and the angular GH shift is proportional to the angular derivative of the modulus of the reflection coefficients. Based on the above results, a systematic method of positive and negative regulations of GH shifts is explored, and it is found that the positive and negative of spatial GH shift can be flexibly controlled by altering the photon energy or rotating the optical axis angle, and the signs of angular GH shift can be easily regulated by changing the incident angle. Finally, combined with weak measurement techniques, an application scheme for accurately sensing the optical axis angle of black phosphorus based on the amplified GH shifts is proposed. These results can be extensively extended to other anisotropic two-dimensional atomic crystals.