A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials

A rectangular waveguide-based two-step approach for measuring the complex permittivity tensor of uniaxial highly lossy nonmagnetic composite materials in the S-band is presented. In the proposed scheme, two independent sets of reflection and transmission coefficient data for each material-under-test (MUT) are measured by aligning the electric field vector of the dominant TE₁₀ mode in the rectangular waveguide parallel and perpendicular to the fiber orientation of the uniaxial sample, respectively. The complex permittivity tensor of the MUT is determined from these measured scattering data in two successive steps. The first step uses the newly proposed analytical approach, which can resolve the ambiguity problem, commonly encountered with samples of electrical length larger than a wavelength. In the second step, nonlinear least square optimization algorithms are employed, where the material parameters using the first step are now used as the initial guess. The proposed two-step approach is valid for multilayered structures, and the local minima problem commonly encountered with optimization routines are also avoided. A number of carbon-fiber composite materials along and, transverse to the fiber orientation are measured using the proposed method. Finally, a brief uncertainty analysis, to study the effect of air-gaps on waveguide measurements, is carried out.