Advancing the shielding effectiveness through a graphene-perturbed slab characterized by a Gaussian rough profile

This work analytically and numerically investigates the effect of a slightly rough surface with a Gaussian profile on the scattering coefficients and corresponding shielding effectiveness (SE) for a finite-width slab immersed in air. The Gaussian profile is modeled using the Small Perturbation Method, which is employed to calculate the bistatic scattering and transmission coefficients, along with the SE, for both parallel and perpendicular polarizations. Initially, the considered framework is modeled for a conventional copper slab, yielding an analysis in the radio frequency range. To explore higher-frequency regimes, the investigation is extended into the far-infrared and near-infrared regions by incorporating graphene, which exhibits an exceptionally adjustable optical response. To this end, a finite number of graphene sheets are integrated – modeling it as a homogeneous, isotropic slab with a complex permittivity that is implicitly dependent on the incident frequency, chemical potential, temperature, and number of graphene sheets. Additionally, the effects of variation in roughness parameters, namely height h, correlation length 𝑙𝑐, and scattering angles, are examined for both cases: with and without graphene integration. Furthermore, the proposed methodology is numerically validated against previously published results, demonstrating strong agreement with established findings. The results reveal how graphene's tunable properties and surface roughness collectively influence scattering behavior, offering design guidelines for graphene-based optical devices and temperature-sensing applications across extended frequency ranges.