A STUDY OF SOME ELECTROMAGNETIC SCATTERING PROBLEMS USING VECTOR ELGENFUNCTION EXPANSION

Abstract

The scattering of electromagnetic waves by an object is a classical topic in the electromagnetic research area. Once a scatterer is introduced into the radiation space, the scattering effect will cause a lot of changes to the EM field distribution in that space, and make the system much more complicated. The scattering characteristics are also very useful in radar systems, in which the RCS's can be used to detect and recognize the unknown scatterers. In this thesis, three different methods are utilized to analyze the scattering problem of three different geometries. Throughout the analysis, the vector eigenfunction expansion technique is applied together with different numerical methods. Firstly, the scattering effects of a spherical chiral radome on the radiation of dipoles and TE11 mode excited open ended circular waveguide will be analyzed. The unknown coefficients of the expanded eigenfunctions of the radiation fields with consideration of the scattering effects due to the multilayered chiral radome are derived. The Huygen's equivalence principle is next utilized to simplify the problem. The electric- and magnetic-type dyadic Green's function for the three-layer geometry are formulated and applied to analyze the radiated electromagnetic fields outside the chiral radome. Both the exact and approximate expressions of the electric fields valid for the corresponding Fresnel and Fraunhofer zones are obtained using the spherical vector wave functions and their approximations in the far-zone. Various chiral material parameters are assumed and computations of the antenna parameters are carried out. The effects of the dielectric chiral radome on the radiation resistance, radiation power patterns, sidelobe levels, and 3-dB beamwidths are also discussed numerically. Following this, a novel method is presented for solving the classical electromagnetic scattering from a perfectly electrical conducting (PEC) circular disk. A hybrid method, which combines the vector wave eigenfunction expansion technique, the least-squares fitting method, and the dyadic Green's function, is used to derive the unknown scattering coefficients of the expanded eigenfunctions of the scattered fields. Orthogonality of the vector wave functions together with the Cauchy's residue theorem for the closed contour integral is also utilized. The scattering coefficients, which are coupled with each other, are obtained in a closed form and expressed in terms of compact matrices. Numerical computation of the radar cross sections (RCS's) of the perfectly conducting disk is carried out. Experimental data published elsewhere are also used to confirm the applicability of the hybrid method developed in this work. Finally, a radially layered geometry in which a PEC circular patch located in the incident EM plane waves is analyzed. The iteration method is adopted to derive the unknown scattering coefficients in the eigenfunction expansions of the scattered fields. The magnetic dyadic Green's function in spherically multilayered media is utilized. The radiated field distribution in the whole space with the presence of the multilayered media is also formulated. Orthogonality of the vector wave functions is again used in the derivation of the coupled scattering coefficients.