This dissertation investigates the design of a quarter-wave polarization transformer and presents some options for a high-performance polarizer in both normally incident and obliquely incident cases. Then, a novel concept for investigating polarization transformation is presented. Based on this concept, the broad axial ratio bandwidth polarizer, composed by anisotropic and chiral media, is accomplished using genetic algorithm. For the normally incident case, we present some methods to eliminate the reflection for designing novel high-performance polarizer in two situations. The polarizers provide perfect linear-to-circular polarization transformation without insertion loss at the center frequency. Then, two novel designs are presented for a high-performance quarter-wave polarizer in the obliquely incident case. In these designs, the material parameters of uniaxial media can be arbitrary. The polarizer is achieved by using only one layer of the uniaxial anisotropic medium without conventional anti-reflection coatings because of the unique property of the oblique incidence. The polarizer can produce a perfect linear-to-circular polarization transformation without any insertion loss at the center frequency. The equivalent circuit concept is presented to study polarization transformations. This concept is more convenient when dealing with polarization transformation problems in multiple layers. The anisotropic medium and the chiral medium can be regarded as circuit elements. Specifically, we show that anisotropic media can be seen as transformers and chiral media as transmission lines. Once the equivalent circuits are determined, the microwave network theory can be used to investigate the polarization transformation. An example is used to demonstrate the transformation from the horizontally polarized wave to the circularly polarized wave employing the equivalent circuit concept. Based on the equivalents concept, we present broad axial ratio bandwidth quarter-wave polarizer composed of mutilayered uniaxial anisotropic media and chiral media using genetic algorithm. In our design, the constitutive parameters of materials can be arbitrary. This broadband polarizer can be realized through the adjustment of the thickness of materials. The nearly optimal and suitable thickness of each cell is determined by using a genetic algorithm. Two numerical examples with three and five cells are presented to validate the design. The axial ratio bandwidths of about 84.1% and 92.8% can be achieved, more than double the maximum theoretical bandwidth for the case of the single uniaxial anisotropic slab.

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