Rectangular waveguide methods are appealing for measuring isotropic and anisotropic materials because of high signal strength due to field confinement, and the ability to control the polarization of the applied electric field. As a stepping stone to developing methods for characterizing materials with fully-populated anisotropic tensor characteristics, techniques are presented in this dissertation to characterize isotropic, biaxially anisotropic, and gyromagnetic materials. Two characterization techniques are investigated for each material, and thus six different techniques are described. Additionally, a waveguide standard is introduced which may be used to validate the measurement of the permittivity and permeability of materials at microwave frequencies. The first characterization method examined is the Nicolson-Ross-Weir (NRW) technique for the extraction of isotropic parameters of a sample completely filling the cross-section of a rectangular waveguide. A second technique is proposed for the characterization of an isotropic conductor-backed sample filling the cross-section of a waveguide. If the sample is conductor-backed, and occupies the entire cross-section, a transmission measurement is not available, and thus a method must be found for providing two sufficiently different reflection measurements.The technique proposed here is to place a waveguide iris in front of the sample, exposing the sample to a spectrum of evanescent modes. By measuring the reflection coefficient with and without an iris, the necessary two data may be obtained to determine the material parameters. A mode-matching approach is used to determine the theoretical response of a sample placed behind the waveguide iris. This response is used in a root-searching algorithm to determine permittivity and permeability by comparing to measurements of the reflection coefficient.For the characterization of biaxially anisotropic materials, the first method considers an extension of the NRW technique for characterization of a sample filling the cross-section of a waveguide. Due to the rectangular nature of the waveguide, typically three different samples are manufactured from the same material in order to characterize the six complex material parameters. The second technique for measuring the electromagnetic properties of a biaxially anisotropic material sample uses a reduced-aperture waveguide sample holder designed to accommodate a cubical sample. All the tensor material parameters can then be determined by measuring the reflection and transmission coefficients of a single sample placed into several orientations. The parameters are obtained using a root-searching algorithm by comparing theoretically computed and measured reflection and transmission coefficients. The theoretical coefficients are determined using a mode matching technique. The first technique for characterizing the electromagnetic properties of gyromagnetic materials considers requires filling the cross-section of a waveguide. The material parameters are extracted from the measured reflection and transmission coefficients. Since the cross-sectional dimensions of waveguides become prohibitively large at low frequencies, and it is at these frequencies that the gyromagnetic properties are most pronounced, sufficiently large samples may not be available. Therefore, the second technique uses a reduced-aperture sample holder that does not require the sample to fill the entire cross section of the guide. The theoretical reflection and transmission coefficients for both methods are determined using a mode matching technique. A nonlinear least squares method is employed to extract the gyromagnetic material parameters. Finally, this dissertation introduces a waveguide standard that acts as a surrogate material with both electric and magnetic properties and is useful for verifying systems designed to characterize engineered materials using the NRW technique. A genetic algorithm is used to optimize the all-metallic structure to produce a surrogate with both relative permittivity and permeability near six across S-band, and with low sensitivity to changes in geometry to reduce the effects of fabrication errors.
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