Determining the electrical permittivity and magnetic permeability of materials is an important task in electromagnetics research. The method using reflection and transmission scattering parameters to determine these constants has been widely employed for many years, ever since the work of Nicolson, Ross, and Weir in the 1970's. For general materials that are homogeneous, linear, and isotropic, the method they developed (the NRW method) works very well and provides an analytical solution.For materials which possess a metal backing or are applied as a coating to a metal surface, it can be difficult or even impossible to obtain a transmission measurement, especially when the coating is thin. In such a circumstance, it is common to resort to a method which uses two reflection type measurements. There are several such methods for free-space measurements, using multiple angles or polarizations for example. For waveguide measurements, obtaining two independent sources of information from which to extract two complex parameters can be a challenge.This dissertation covers three different topics. Two of these involve different techniques to characterize conductor-backed materials, and the third proposes a method for designing synthetic validation standards for use with standard NRW measurements. All three of these topics utilize modal expansions of electric and magnetic fields to analyze propagation in stepped rectangular waveguides. Two of the projects utilize evolutionary algorithms (EA) to design waveguide structures. These algorithms were developed specifically for these projects and utilize fairly recent innovations within the optimization community.The first characterization technique uses two different versions of a single vertical step in the waveguide. Samples to be tested lie inside the steps with the conductor reflection plane behind them. If the two reflection measurements are truly independent it should be possible to recover the values of two complex parameters, but success of the technique ultimately depends upon how independent the measurements actually are.Next, a method is demonstrated for developing synthetic verification standards. These standards are created from combinations of vertical steps formed from a single piece of metal or metal coated plastic. These fully insertable structures mimic some of the measurement characteristics of typical lab specimens and thus provide a useful tool for verifying the proper calibration and function of the experimental setup used for NRW characterization. These standards are designed with the use an EA, which compares possible designs based on the quality of the match with target parameter values. Several examples have been fabricated and tested, and the design specifications and results are presented.Finally, a second characterization technique is considered. This method uses multiple vertical steps to construct an error reducing structure within the waveguide, which allows parameters to be reliably extracted using both reflection and transmission measurements. These structures are designed with an EA, measuring fitness by the reduction of error in the extracted parameters. An additional EA is used to assist in the extraction of the material parameters supplying better initial guesses to a secant method solver. This hybrid approach greatly increases the stability of the solver and increases the speed of parameter extractions. Several designs have been identified and are analyzed.
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