Cross-correlated Tensor Surface Impedance Characterization of Orthogonally Discrete IMU & CMU for Impedance Modulated Metasurface

In this article, a detailed characterization of Tensor Surface Impedance Matrix (TSIM) for orthogonally discrete inductive and capacitive meta unit-cell has been performed. Four orthogonally distributed digitally coded (i.e ${\bf 0 0},{\bf 0 1},{\bf 1 0},11)$ states have been assigned for both orthogonally discretized inductive and capacitive meta unit-cell. Tensor Surface Impedance Matrix (TSIM) is implemented for each unit cell to characterize the isotropic, non-homogeneous nature of $\overline{\overline{Z_{\text{surf}}}}$. From dispersion relation, the variation of phase velocity has been characterized for both Inductive Meta unit-cell (IMU) as well as Capacitive Meta unit-cell (CMU). Further, Cross Correlation between similar coded IMU and CMU has been performed to extract the linear dependency of those complementary structures. Also, the Cross correlation between the proposed orthogonally discrete unit-cells have been performed to extract the equivalent impedance coupling factor $(\ddot{}{Z}_{c})$. Effective $\overline{\overline{Z_{\text{surf}}}}$ vs direction of surface wave propagation $(\theta_{k})$ is characterized for each orthogonally discrete unit cell for both proposed IMU and CMU.