Precise control of positive and negative Goos-Hänchen shifts in graphene

We study the Goos-Hanchen (GH) effect in a graphene-substrate system comprehensively by using the transfer matrix method. It is revealed that the magnitude and sign of GH shifts are closely related to the imaginary part of graphene conductivity in the case of the fixed refractive index of substrate, while the Brewster angle position is largely influenced by the real part of conductivity. Further studies show that the position of Brewster angle keeps invariable when the Fermi energy exceeds 0.4 eV, and the magnitude and sign of GH shifts at a certain Brewster angle are changed only by Fermi energy. On the basis of these findings, a scheme to control the positive and negative GH shifts precisely is proposed and demonstrated by instances. We first adjust the refractive index of substrate to control the Brewster angle position under the condition of the Fermi energy exceeding 0.4 eV, and then adjust the Fermi energy to make the GH shift approach target value. Finally, we apply these precise control properties of GH shift to design a refractive index detector with adjustable sensitivity coefficient. These researches may have potential applications in refractive index sensor with high sensitivity and precise measurement of graphene parameters.