Graphene oxide nanoparticle-infused metamaterial sensor for low permittivity characterization

Accurate characterization of low-permittivity materials is essential for advancing high-frequency electronics, novel substrates, and microwave sensing systems. However, conventional methods often suffer from bulkiness, limited sensitivity, or complex measurement processes. To overcome these limitations, an innovative graphene oxide nanoparticle-infused metamaterial sensor specifically engineered for low-permittivity detection. The sensor comprises a hybrid circular and square split-ring resonator (SRRs) fabricated using 0.035 mm conductive copper tape on a graphene oxide substrate, enabling tunable resistive properties and enhanced electromagnetic confinement. The sensor is experimentally measured in an X-band waveguide system with TRL calibration from 8 to 10 GHz. The sensor exhibits a strong agreement between simulated and measured S 21 responses, with a resonance shift from 8.592 GHz (ε=1 ) to 8.36 GHz ( ε = 3.66 ), and a relative error consistently below 1%. Effective medium analysis reveals that the metamaterial exhibits negative permittivity ( ε < 0 ) and permeability ( μ< 0 ) at resonance, confirming its left-handed metamaterial behavior. The surface current, electric field, and magnetic field distributions show strong localization at the resonator gaps contributing to enhanced sensing performance. A linear regression model between dielectric constant and resonance frequency shift ( Δf ) is developed with a coefficient of determination R 2 = 0.908, and the derived model exhibits a maximum absolute error under 2%. The measured sensitivity reached up to 140.3 MHz/Δε for ε = 1.57, demonstrating superior performance in low-ε characterization compared to traditional sensors. The combination of metamaterial-inspired resonance behavior, tunable graphene conductivity, and analytical modeling enables this sensor to serve as an efficient, low-cost, and highly sensitive platform for dielectric characterization.