Advancing the shielding effectiveness through a graphene-perturbed slab

This study examines the impact of a slightly rough surface with a Gaussian profile on the scattering coefficients and shielding effectiveness (SE) of a finite-width slab in air. The Gaussian profile is modeled using the Small Perturbation Method to calculate bistatic scattering and transmission coefficients, along with SE, for both parallel and perpendicular polarizations. Initially, a conventional copper slab is analyzed in the radio frequency range. The study extends to the far-infrared and near-infrared regions by incorporating graphene, known for its adjustable optical response. Graphene sheets are integrated, modeled as a homogeneous, isotropic slab with complex permittivity dependent on incident frequency, chemical potential, temperature, and number of graphene sheets. The effects of roughness parameters, including height, correlation length, and scattering angles, are examined with and without graphene. The methodology is numerically validated against previous results, showing strong agreement. Results indicate how graphene's tunable properties and surface roughness influence scattering behavior, providing design guidelines for graphene-based optical devices and temperature-sensing applications.

Natural surfaces in electromagnetic (EM) environments are inherently rough, leading to specular reflection and scattering in multiple directions. EM scattering from rough surfaces is relevant in applications like remote sensing, civil infrastructure analysis, optical systems, and plasma diagnostics. The analysis of scattered fields is challenging due to the lack of precise analytical solutions, leading to the use of approximate techniques like the small perturbation method (SPM). SPM is effective when surface height variations and slopes are small compared to the wavelength of incident fields. It simplifies the scattering problem by relating statistical properties of the rough interface with scattered fields in terms of correlation functions, yielding the bistatic scattering coefficient (BSC) for either polarization.

This work provides a detailed analysis of the BSC and bistatic transmission coefficient (BTC) for a Gaussian rough surface, exploring roughness impact on these quantities and corresponding SE. The SE concept for flat surfaces remains applicable for slightly rough surfaces. In environments with multiple electronic devices, unwanted EM emissions can interfere with neighboring equipment, necessitating effective shielding. SE has been widely investigated for flat surfaces across radio-frequency to microwave-frequency regimes. The presence of slight roughness alters transmitted fields due to scattering effects, but the overall formulation of SE as a measure of attenuation remains valid.

EM shielding is influenced by material properties and geometric configuration. Shielding enclosures are constructed from materials like mu-metal, silver, brass, aluminum, stainless steel, nickel, and conductive composites. Copper, with high electrical conductivity and excellent shielding performance across the RF regime, serves as a reference material for shielding studies. The study incorporates copper to compute BSC, BTC, and SE, establishing a reference model to assess material properties and configuration. To examine these quantities across a broader frequency range, the approach is extended to graphene.

Graphene, a two-dimensional carbon sheet, exhibits exceptional electrical conductivity, high carrier mobility, and mechanical strength. Its conductivity, described by Kubo's model, depends on frequency, temperature, and chemical potential, controllable through chemical doping or electrical gating. Graphene's ability to manipulate EM light in the optical frequency range makes it attractive for next-generation communication. Recent studies highlight graphene's potential in transparent EM shields, terahertz and infrared modulators, photonic and optoelectronic devices, and high-performance sensors. However, earlier analyses were limited to monolayer graphene at fixed temperatures and narrow frequency ranges. This study models graphene as a finite-thickness slab, extending its applicability over a broader frequency range.

The analysis extends in several directions: applying SPM to compute BTC/BSC and SE for a slab in air with a Gaussian rough upper interface, investigating surface roughness impact on SE beyond the flat-surface assumption, using copper as a baseline shielding material, and integrating graphene sheets to achieve BSC, BTC, and SE across a broader frequency range. BSC and SE are controlled by tuning graphene's parameters, such as chemical potential, temperature, and number of layers, as well as roughness parameters.

The paper is structured as follows: Section 2 formulates the theoretical model, deriving Fresnel coefficients along with BTC/BSC and outlining the SE framework for transverse electric and transverse magnetic polarizations. Section 3 presents numerical analysis for copper and graphene-based slabs across different frequency regimes. Section 4 concludes the study.