Calibration and Cross-Polarization Measurement Standard Requirements for Focus Beam Material Characterization Systems

Novel metamaterial and metasurface realizations provide unique control of the wave dispersion but present many challenges for accurate constitutive parameter extraction. Practical material measurement approaches for characterizing complex materials, such as biaxial anisotropic and gyrotropic media, rely on either waveguide or focus beam techniques with trade-offs in sample size and bandwidth. Multi-static focus beam setups offer many advantages for complex material measurements by enabling wider sampling bandwidths, measurement degrees of freedom and larger sample sizes. However, rotational misalignment of the principal crystal and measurement coordinates of the biaxial anisotropic media sample results in cross-polarized scattered field contributions. Likewise, interrogating gyrotropic or general bianisotropic media with a dual-polarized focus beam measurement setup produces cross-polarized scattering matrix components. These non-diagonalized S-parameters for the complex sample under test must be measured to successfully extract the constitutive parameters. A time-domain gated response isolation calibration scheme is one common approach to establish the measurement reference plane and minimize fixture uncertainties for samples with limited cross-polarization. This paper extends the time-domain gated response isolation methodology for free-space focus beam systems to account for cross-polarization terms present in both the sample under test as well as the measurement setup. The featured analysis leverages a 4x4 S-parameter matrix notation to capture the polarimetric scattering at each cascaded stage. An equivalent line standard procedure is developed where four unique, linearly independent calibration standard measurements are shown to account for all unknown terms.