The theory of electromagnetic characteristic modes was published roughly forty years ago, for both conducting and penetrable objects. However, while the characteristic mode analysis of conducting objects has found renewed interest as a tool for antenna designers, computed results for the characteristic mode eigenvalues, eigencurrents and eigenfields for penetrable objects have not appeared, not even in the seminal papers on the subject. In this thesis both volume and surface integral equation formulations are used to compute the characteristic modes of penetrable objects for what appears to be the first time. This opens the way for the use of characteristic mode theory in the design of antennas made of penetrable material whose polarization current densities constitute the main radiating mechanism of the antenna. Volume formulations are shown to be reliable but computationally burdensome. It is demonstrated that surface formulations are computationally more efficient, but obtrude some non-physical modes in addition to the physical ones. Fortunately, certain field orthogonality checklists can be used to provide a straightforward means of unambiguously selecting only the physical modes. The sub-structure characteristic mode concept is extended to problems involving both perfectly conducting and penetrable materials. It is also argued that sub-structure modes can be viewed as characteristic modes that implicitly use modified Green’s functions, but without such Green’s functions being needed explicitly. This makes the concept really practical, since the desired modified Green’s functions are not known explicitly in most cases.

The theory of electromagnetic characteristic modes was published roughly forty years ago, for both conducting and penetrable objects. However, while the characteristic mode analysis of conducting objects has found renewed interest as a tool for antenna designers, computed results for the characteristic mode eigenvalues, eigencurrents and eigenfields for penetrable objects have not appeared, not even in the seminal papers on the subject. In this thesis both volume and surface integral equation formulations are used to compute the characteristic modes of penetrable objects for what appears to be the first time. This opens the way for the use of characteristic mode theory in the design of antennas made of penetrable material whose polarization current densities constitute the main radiating mechanism of the antenna. Volume formulations are shown to be reliable but computationally burdensome. It is demonstrated that surface formulations are computationally more efficient, but obtrude some non-physical modes in addition to the physical ones. Fortunately, certain field orthogonality checklists can be used to provide a straightforward means of unambiguously selecting only the physical modes. The sub-structure characteristic mode concept is extended to problems involving both perfectly conducting and penetrable materials. It is also argued that sub-structure modes can be viewed as characteristic modes that implicitly use modified Green’s functions, but without such Green’s functions being needed explicitly. This makes the concept really practical, since the desired modified Green’s functions are not known explicitly in most cases.