| Summary: | Photonic bandgap materials are periodic structures that exclude electromagnetic field propagation over frequency intervals known as bandgaps. These materials exhibit remarkable wave dispersion and have found use in many applications that require control over dynamic electromagnetic fields, as their properties can be tailored by design. The two principal objectives of this thesis are the development of a liquid crystal-based microwave photonic bandgap device whose bandgap could be tuned during operation and the design and implementation of a spectral transmission-line modeling method for band structure calculations.
The description of computational methods comprises an overview of the implemented numerical routines, a derivation of the spectral properties of the transmission-line modeling method in periodic domains, and the development of an efficient sparse matrix eigenvalue algorithm that formed the basis of the spectral transmission-line modeling method. The discussion of experimental methods considers the use of liquid crystals in microwave applications and details the design and fabrication of several devices. These include a series of modified twisted nematic cells that were used to evaluate liquid crystal alignment and switching, a patch resonator that was used to measure liquid crystal permittivity, and the liquid crystal photonic bandgap device itself.
Numerical experiments showed that the spectral transmission-line modeling method is accurate and substantially faster and less memory intensive than the reference plane wave method for problems of high dielectric contrast or rapidly varying spatial detail. Physical experiments successfully realized a microwave photonic bandgap structure whose bandgap could be continuously tuned with a bias voltage. The very good agreement between simulated and measured results validate the computational and experimental methods used, particularly the resonance-based technique for permittivity measurement. This work's results may be applied to many applications, including microwave filters, negative group velocity/negative refraction materials, and microwave permittivity measurement of liquid crystals.
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