We assess the controllable Goos–Hänchen (GH) shift of Airy light beams reflected from a graphene-ENZ hybrid photonic structure. We comprehensively analyze the influence of key material and structural parameters, namely Fermi energy, carrier relaxation time, and the layer count of graphene, on the GH shift for both Gaussian and Airy beam profiles. Our results demonstrate that Fermi energy serves as the most effective control parameter, enabling significant tuning of the GH shift, including a reversal from positive to negative values, by modulating graphene’s optical conductivity and the reflection phase. Notably, the enhanced lateral displacement provided by Airy beams becomes even more pronounced at higher values. A crucial finding is that the relative advantage of Airy beams over Gaussian beams, representing their differential lateral displacement, remains robust and largely independent of the number of graphene layers (N). Conversely, the carrier relaxation time plays a less dominant role in tuning the GH shift. The high sensitivity of the GH shift to Fermi energy and incident angle suggests the potential for applications in optical sensors and tunable optical devices.
