Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Jay K. Lee


Anisotropic Media, Biaxial Media, Method of Moments, Microstrip Antennas, Reflection and Transmission

Subject Categories

Electrical and Computer Engineering


This dissertation explores the electromagnetic behavior of arbitrarily oriented biaxially anisotropic media. An overview of wave behavior in biaxially anisotropic (or simply biaxial) media is presented. The reflection and transmission behaviors of electromagnetic waves from half-space and two-layer isotropic-biaxial interfaces are studied. The reflection and transmission coefficients are used in the formulation of eigenvector dyadic Green's functions. These Green's functions are employed in full-wave analyses of rectangular microstrip antennas printed on biaxial substrates.

The general characteristics of electrically biaxially anisotropic (biaxial) media are presented including permittivity tensors, optic axes, orientation of the medium, and birefringence. After a detailed discussion of wave propagation, wave behavior at isotropic-biaxial interfaces is investigated. The reflection and transmission of electromagnetic waves incident upon half-space and two-layer interfaces, at which the waves may be incident from either the isotropic region or the biaxial region, are investigated. The biaxial medium considered may be aligned with the principal coordinate system or may be arbitrarily oriented. Critical angle and Brewster angle effects are analyzed for the half-space case. Once the wave behavior is well understood, the eigenvector dyadic Green's function is presented for two-layer geometries involving isotropic and biaxially anisotropic media. The symmetrical property of the dyadic Green's function is derived and used to generate an unknown Green's function from a known Green's function for the two-layer geometry of interest. This new Green's function is used to model rectangular microstrip antennas.

Following the investigation of reflection and transmission, rectangular microstrip antennas are analyzed using the eigenvector dyadic Green's function and the method of moments. Galerkin's method is used to evaluate current distributions on gap-fed dipole antennas and probe-fed patch antennas. The resulting current distributions are used to compute antenna parameters such as input impedance, resonant length and principal polarization radiation patterns. For the patch antennas, impedance bandwidth and cross-polarization patterns are also investigated. Results are presented for biaxially anisotropic substrates of varying thickness, permittivities, and orientations, providing the understanding of the complex behaviors of microstrip antennas printed on biaxially anisotropic substrates.


Open Access