Date of Award

May 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Jay K. Lee

Second Advisor

Thong Q. Dang


anisotropic, dyadic Green's function, Hertzian dipole, method of moment, microstrip dipole, radiation

Subject Categories



In this dissertation, the dyadic Green‟s functions (DGFs) for unbounded and layered anisotropic media, with no restriction imposed on the medium property, are derived. Utilizing the obtained DGFs, the radiation problems of a Hertzian dipole and a microstrip antenna in the presence of an anisotropic substrate are solved.

After a brief introduction, the eigenvector dyadic Green‟s functions (E-DGFs) for an unbounded general anisotropic medium through the eigen-decomposition method are derived. The E-DGFs of a layered anisotropic geometry are then constructed based on the derivation of the unbounded E-DGFs using two different approaches. One is through the symmetrical property of the DGFs and the other is through the direct construction method. Rigorous proof and detailed derivation of the formulation for the E-DGFs are presented. The usage and limitation of each approach as well as the relationships between the corresponding E-DGFs are discussed.

Applying the method of stationary phase to the associated E-DGFs, we formulate the radiation fields of an arbitrarily oriented Hertzian dipole located either above or inside the layered anisotropic medium. The important new findings include the analysis of the radiation field in terms of the reflection coefficients as a function of incidence angle, and the use of the biasing magnetic field to improve the broadside directivity for a z-directed source when a gyroelectric medium is involved.

In addition to solving the radiation of a Hertzian dipole in the presence of a layered anisotropic medium, the layered E-DGFs derived here are also utilized to solve the more practical problem of a microstrip dipole printed on an anisotropic substrate. A method of

moment solution is formulated with the E-DGF in the spectral domain. To demonstrate the feasibility of this method applicable to a general anisotropic medium, the current distribution, input impedances, and radiation patterns are numerically calculated for a microstrip dipole printed on various anisotropic substrates. Furthermore, a detailed parametric study of the effect of frequency, and direction and magnitude of the biasing magnetic field is provided for a dipole printed on a gyroelectric substrate. The parametric analysis in this dissertation may lead to a method whereby the additional freedom introduced by the gyroelectric medium can be utilized effectively to adjust the resonant length and radiation pattern of a printed dipole antenna.


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