High Efficient Impedance Tensor Extraction Method for Arbitrarily Shaped Metasurface Elements

Advances in metasurface design have significantly developed high-performance antennas. This work presents a novel method for extracting the anisotropic surface impedance tensor of a pixel geometry within an arbitrarily shaped unit cell. The eigenvectors of the purely isotropic tensor are modified using the rotation matrix to obtain the anisotropic impedance tensor. This creates a 3D-tensor database to assign the analytical impedance tensors to physical pixel geometries. Furthermore, evaluation metrics for anisotropy degree and impedance modulation are introduced to enable a comprehensive metasurface elements characterization. The proposed eigenvector rotation method enables an extremely fast and highly accurate anisotropic tensor extraction and evaluation process. Based on the characterization, an anisotropic holographic-based leaky wave antenna consisting of hexagonal unit cells is fabricated on a fused silica wafer. The far field measurements show a gain of 34.4 dBi, an aperture efficiency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$49 \,\%$</tex-math></inline-formula>, polarization purity of 40 dB, and a side-lobe level of 27 dB at 160 GHz.