Theoretical and Analytical Investigation of Electromagnetic Problems Using Dispersive Material and the Kramers-Kronig Transformations

In reality, there is no material with constant permittivity, permeability, and conductivity values over the entire frequency spectrum. The variation in these parameters is well-known as the dispersion phenomenon, which can be analytically interpreted using the Kramers-Kronig relations. Through this thesis, we extensively explain how to take advantage of the dispersion in these parameters to numerically investigate some electromagnetic problems. Among these is a practical problem of separating the electric conductive losses from the dielectric losses of any dispersive lossy material. On the other hand, the performance of particular electrically small antennas is improved by exploiting the frequency dispersion in the dielectric and magnetic material. Electrically small antennas have great attention in many applications due to their drastically reduced size. However, the size reduction comes at the expense of performance degradation, such as increasing the internally stored electromagnetic energy, narrowing the operating bandwidth, decreasing radiation efficiency, and poor matching to surrounding media, particularly when the antenna element has direct contact with a lossy medium like biomedical tissues. Therefore, we try to numerically investigate the performance of these antennas by coating them with dispersive dielectric or magnetic material. In this thesis, some artificially synthesized material with frequency-dependent permittivity, permeability, and electric conductivity values over a wide range of frequencies are suggested to represent the dispersive lossy material. The Kramers-Kronig (KK) relations are employed as a mathematical solution to interrelate the real and imaginary parts of the suggested frequency-dependent relative permittivity and permeability values of the artificial material. Finally, the solution methods are verified by applying them to real-world material found in the literature.


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