Information and Communication Engineering Programme

Abstract

In this thesis, investigated the scattering of an H-polarized electromagnetic line source from circular strip structures within an analytical-numerical framework. The first stage of the study considers circular strip geometries with classical impedance boundary conditions; this formulation is then generalized using fractional boundary conditions. The aim is to define a continuous transition between ideal boundary behavior and impedance-controlled surfaces. The theoretical formulation is developed in a cylindrical coordinate system, and the incident and scattered magnetic fields are explicitly expressed. The induced current densities on the scattering surface are represented using orthogonal polynomial expansions, primarily Chebyshev and Gegenbauer polynomials. This approach allows for the accurate fulfillment of the edge conditions required by the circular geometry, while also offering high numerical stability and fast convergence. Fractional boundary conditions are applied through a generalized Leontovich relation where the fractional order parameter determines the relationship between the tangential electric and magnetic field components. Because of this, we can correctly model the surface behaviours whih cannot be efficiently described like a classical integer order models. Numerical analyses were performed to investigate the effects of parameters such as fractional order, surface impedance, aperture size, and the location of the line source on the scattering response. Evaluations were made considering the total radar cross section (TRCS) and near-field distributions. The results show that the resonance behavior is depend on the fractional order and the difference between the internal and external surface impedances. As the fractional order increases, shifts occur in the resonance characteristics, and significant changes are observed in the field's localization behavior. These effects do not appear in the results obtained with classical perfect electrical or magnetic conduction boundary conditions. The accuracy and reliability of the proposed method were verified through comparisons with analytical results in the literature for limit cases representing ideal boundary conditions. The observed agreement and limited numerical deviations demonstrate the effectiveness of the orthogonal polynomial-based fractional formulation in terms of convergence and accuracy. Consequently, the analytical-numerical approach developed in this study offers a flexible and physically meaningful tool for investigating electromagnetic scattering from circular ribbon structures; it also provides a solid foundation for the analysis and design of resonance-controlled and impedance-based electromagnetic structures.