A Proposal of a Laminated Versatile Sensor for Refractive Index and Displacement With Variable Quality Factor Influenced by the Graphene Based on the Reflected Goos–Hänchenn Effect

Abstract

In this study, an innovative multifunctional sensor with variable quality factor influenced by graphene for refractive index (RI) and displacement in the terahertz (THz) regime founded on the reflected Goos–Hänchen (GH) effect is proffered. Under a laminated 1-D photonic crystals (PCs) structure comprising graphene sheets in a specific periodic arrangement, the enhanced GH phenomenon is discerned to occur at the specific frequency point, which is utilized as the probe of the proposed sensor due to the considerable sensitivity of the frequency of the peak GH shift to the alternations of the RIs and the thicknesses of the certain dielectric layers. Manipulating the transfer matrix and the stationary phase approaches, the performance indicators of the proposed sensor are calculated embodying the quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> ), the figure of merit (FOM), and the detection limit (DL). Compared to conventional single-function sensor devices, the proposed structure via the modulation of the chemical potential of the graphene sheet achieves adjustable characteristics of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> within the specific range on top of versatile sensing of the displacement and the RI, which likewise implies variable FOM with DL, but the sensitivity is relatively stable for both sensing modes. Additionally, the impacts of the thickness of the silicon layers as well as the number of cycles of the 1-D PC are discussed. The mixture of characteristics of the multifunctional sensing and the variable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> furnishes a significant reference to the GH sensor design.