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Terahertz (THz) wave interaction from graphene coated metamaterial cylinder has been investigated analytically and numerically. The analytical formulation of electromagnetic fields is being modeled in the frame work of Mie theory while the modeling of the graphene is done by random phase approximation method. The causality principle based Kramer-Kroing relations are used to simulate the DNG metamaterial, while the DPS metamaterial is modeled by the Drude relations of SiO2. The analytical formulation is developed for both parallel and perpendicular polarized waves. The impedance boundary conditions (IBC) approach is used to model the infinitely thin graphene coating on metamaterial cylinder. Further the IBC at the interface of graphene layer and metamaterial cylinder are applied to compute the unknown scattering coefficients. The efficiency factors i.e., scattering efficiency (Qsca), extinction efficiency (Qexc) & absorption efficiency (Qabs) and bistatic radar cross section (RCS) have been computed analytically as well as numerically for both micro and nano cores. The influence of graphene parameters i.e., chemical potential (μc) & scattering rate (τ1) and size of metamaterial cylinder (R) on the scattering efficiency (Qsca) and extinction efficiency (Qexc) has been analyzed for DPS and DNG cores. It is observed that the in the nano regime, for perpendicularly polarized wave, graphene coated metamaterial cylinder supports the localized surface plasmon resonance (LSPR) modes and LSPR is found sensitive to the change in the graphene parameters and core size. However, it is reported that the parallel polarized wave has same response towards the DPS and DNG cores in the nano regime. It is concluded that under suitable parameters the graphene coating may provide extraordinary degree of freedom to actively control the THz interactions i.e., scattering efficiency, extinction efficiency and bistatic RCS. The present work may have potential applications in designing and manufacturing of Electromagnetic invisibility, cloaking and target protection devices for THz region. Keywords: Scattering, Absorption, Metamaterials, Graphene, Cylinder, Eco width, Radar Cross Section (RCS), Efficiency Factors, Surface Plasmon Resonance

A theoretical analysis on the propagation of hybrid surface waves supported by the chiral metamaterial-graphene-metamaterial planar structures has been carried out. The constitutive relations are used to simulate the different types of metamaterials while the electromagnetic response of the graphene is modeled in the framework of Kubo’s formulation. The characteristics of surface waves for different configurations of chiral metamaterial-graphene-metamaterial planar structure (Chiral DNG–graphene–DNG and chiral DPS–graphene–DPS) are studied. The dispersion relation for each configuration is computed by implementing the impedance boundary conditions at the interface. The influence of chemical potential (μ) of graphene and chirality (ξ) of chiral material on the dispersion curves, fields distributions, effective mode index (Neff), and phase speed (vp) are presented for the both configurations. It is concluded that presence of graphene layer between the metamaterial structures may provide an additional degree of freedom to manipulate and tune the characteristics of surface waves. The results also found in accordance with the published literature. Moreover, these results may have potential applications in wave-guiding technology, controlling, slow-speed wave guides, and plasmonic technology.