Spatial Goos–Hänchen Shifts of Airy Vortex Beams Impinging on Graphene/hBN Heterostructure

Based on the angular spectrum expansion, the spatial Goos–Hänchen (GH) shift of an Airy vortex beam reflected from the graphene/hexagonal boron nitride (hBN) heterostructure is investigated analytically. The influences of graphene/hBN heterostructure parameters and incident Airy vortex beam parameters on the spatial GH shifts are analyzed in detail. It is found that the position of the Brewster angle mainly depends on the relaxation time and hBN thickness of the heterostructure, and the magnitude and sign of GH shifts at a certain Brewster angle can be controlled effectively by tuning the Fermi energy and layer numbers of graphene. Moreover, the variation in the GH shifts with the Fermi energy and hBN thickness exhibits hyperbolicity at the Brewster angle, similar to the variation in the permittivity of hBN. For the incident beam, the vortex position and the decay factor in the x direction have a great effect on the GH shifts. The influence of the vortex position on the GH shift is related to the distance of the vortex position from the origin point. The magnitude of the GH shift decreases as the decay factor in the x direction increases, and a large GH shift can be obtained by adjusting the decay factor in the x direction. Finally, the application of spatial GH shift in sensing is discussed. The results presented here may provide some supports to the design of optical switch and optical sensor.