Electrically tunable Goos–Hänchen shift from epsilon-near-zero (ENZ) structure with graphene

In this paper, we have studied electrically tunable Goos–Hänchen shift (GHS) for TM/ p polarized light wave incident on a multilayered epsilon-near-zero (ENZ) structure containing graphene. Transfer matrix method has been used to obtain GHS for the multilayered structure composed of three slabs. We have studied the impact of changing Fermi energy, incident angle and graphene layer position on the obtained GHS. We observed that by adjusting the Fermi energy, the direction of GHS in the multilayered structure can be changed. Moreover, the imaginary part of graphene conductivity affects the magnitude and sign of GHS while real part of conductivity is closely linked with Brewster angle position. Besides, we have discussed the effect of changing permittivity of slabs and number of graphene layers on the obtained GHS. Published results for single epsilon-near-zero (ENZ) slab were recovered by using equal slab permittivity and zero conductivity for graphene. The results presented in this work will help in designing optical sensors using multilayered ENZ medium. Graphical abstract