Scattering from Different Geometries in the Presence of Topological Insulator and Metamaterials

Abstract

Kobayashi potential is a semi-analytical method frequently used to solve scattering problems mainly related to geometries containing strip, grating, aperture, disk. Kobayashi potential method has been applied in this dissertation for solving scattering problems. According to Kobayashi potential method, longitudinal component of the unknown scattered field is assumed in terms of unknown weighting functions. Moreover, use of the relevant boundary conditions of discussed problems leads to the formation of algebraic equations and dual integral equations. Further, Integrands of the dual integral equations are expanded in terms of the characteristic functions with unknown expansion coefficients which must satisfy, simultaneously, the required edge and boundary conditions. The expressions derived from expansion of the integrands are combined with algebraic equations in order to express the unknown weighting function in terms of unknown expansion coefficients. The weighting functions, in terms of expansion coefficients, are then substituted in the dual integral equations. Moreover, the projection treatment is applied using properties of the Jacobi polynomials which yields matrix equation being solved numerically for unknown expansion coefficients. The far-zone field expressions have been derived using Saddle point method of integration. Finally, the scattered field has been calculated with aid of matrix equation. In this dissertation, scattering from a canonical object has been investigated by using Kobayashi potential method. Different geometries have been considered in this aspect. In the start of this dissertation, perfectly conducting strip has been placed inside of unbounded topological insulator medium. Additionally, an impedance strip has been taken as canonical object surrounded with topological insulator medium. Furthermore, a planar interface of topological insulator and chiral medium has been examined with presence of perfectly conducting strip. Finally, another planar interface with different non-integer dimensional dielectric media has been observed. These different geometries have been worked out analytically by using Kobayashi potential method. The geometries have been ex- 6 cited by plane wave. The numerical results have been plotted by applying Matlab software and subsequent discussion has also been made in this regard. Different parameters have been considered as special parameters for different geometries namely topological, impedance, chirality, non-integer dimensional parameters. In the end of the dissertation, conclusions along with directions for future researchers have been discussed.