Spatial shifts of the reflective light beam off the metasurface of hyperbolic crystals

We investigated Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts of the reflective beam from a uniaxial hyperbolic crystal (HC) with a metasurface (MS) that is a subwavelength rectangular-grating layer. Due to the optical axis of this MS normal to that of the HC, this structure is similar to a biaxial HC for the reflective beam. We obtained analytical expressions of reflective beam for any polarized incident light beam and then derived the GH and IF shifts of the relevant reflective beam. Based on the hexagonal boron nitride crystal (hBN), we numerically simulated shift spectra of the reflective beam for differently polarized incident beams. We compared the results obtained from this structure with those for the bulk hBN or MS layer with infinite thickness. We found that the shift spectra from this structure resemble neither those from the bulk hBN nor those from the MS layer so that they are much more complicated than those in the two extreme cases. The effect of the MS coupling with the hBN substrate is very remarkable. First, both the GH and IF shifts are evidently enlarged, especially the IF shift. Second, the shift spectra exhibit oscillation behavior and sharp shift peaks or dips. Finally, the MS brings out the nonreciprocity of the two shifts for the circularly polarized incident beams.