Metamaterials based on hyperbolic-graphene composite: A pathway from positive to negative refractive index at terahertz

This work presents a novel metamaterial based on a hyperbolic-graphene composite (MMHGC) designed for operation in the terahertz frequency range. Our research advances the field of metamaterials through multiple significant contributions. We demonstrate a breakthrough in metamaterial design through simulation: a duallayered graphene composite with a dishnet pattern structure. This innovative design enables dynamic control of the refractive index, allowing switching between positive and negative values across the 1.8-2.7 THz frequency range through electrostatic biasing. Increasing the Fermi level from 0.0 to 0.6 eV enhances magnetic resonance and achieves remarkable transmission rates of 85 % for positive refractive index (PRI) and 70 % for double-negative refractive index (D-NRI). Additionally, we develop a comprehensive theoretical framework based on an equivalent LC circuit model. This model provides precise magnetic resonance and plasma frequency predictions, with its accuracy validated through detailed numerical simulations. Our investigation also extended to studying the impact of varying graphene layers in the MMHGC's unit cell. The numerical analysis reveals that increasing graphene layers from 10 to 30 strengthens the magnetic resonance, with the 30-layer configuration achieving switching between 80 % reflection at 0.0 eV and 70 % D-NRI transmission at 0.6 eV across 2.1-2.9 THz. These results demonstrate the significant potential of graphene-based hyperbolic metamaterials for developing dynamically controllable THz devices.