Engineered materials with special electromagnetic properties are gaining an interest for applications where tailored material parameters are needed to meet stringent requirements. As the number of applications and the complexity of the engineered materials increase, there is a growing need for characterization methods that can accurately predict the constitutive parameters of these materials. Rectangular waveguide methods are popular in characterizing isotropic and anisotropic materials for many reasons, such as ease of sample preparation, high signal strength due to field confinement, the ability to control the polarization of the applied electric field, and high transmission efficiency over a broad frequency band. However, most characterization techniques based on rectangular waveguides are implemented by placing the sample against various metallic objects such as irises or posts, or by confining samples in sample holders, which increases the measurement complexity and the extraction uncertainties. In this work, a partially-filled waveguide technique that overcomes the drawbacks of the traditional methods is investigated for the characterization two types of anisotropic materials: biaxial and gyromagnetic. The first group of materials considered for this characterization method are biaxial materials, which have three nonzero entries in each material tensor, corresponding to six complex material parameters that must be extracted. Typically three different samples are manufactured from the same material and placed into the rectangular waveguide in three orientations in order to interrogate the material along three orthogonal axes. Instead of using three samples, this technique uses a single cubical sample of biaxial material which is placed at the center of a guide and measured under three different rotations, providing the required number of reflection and transmission measurements to determine the six unique constitutive parameters. The theoretical reflection and transmission coefficients are determined using a modal analysis. The desired complex constitutive parameters can be obtained by minimizing the difference between theoretical and measured data.The second type of materials considered in this work are gyromagnetic. Gyromagnetic materials have scalar permittivity and anisotropic permeability which can be described by a tensor with three diagonal entries and two off-diagonal entries. Since the cross-sectional dimensions of waveguides become large at low frequencies where the gyromagnetic properties are most pronounced, and sufficiently large samples that can fill the cross-section of the waveguide are typically unavailable, a technique overcomes the limitation of sample size and only requires the sample to fill part of the guide is beneficial. The measured refection and transmission coefficients can be obtained from a gyromagnetic sample under various experimental configurations. The theoretical refection and transmission coefficients are determined using a mode matching technique. A nonlinear least squares method is employed to extract the gyromagnetic material parameters using optimization algorithms in Matlab.
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