Alternative Computational Techniques for the Numerical Analysis of Characteristic Modes

The theory of characteristic modes (CM)has become extremely popular in the last 10 years.From the late 1960s (e.g., Garbacz 1968; Harrington et al., 1971) until now many advances have occurred.At its original form the electric field integral equation (EFIE) was used for the modal analysis of arbitrarily shaped perfect electric conductive (PEC) structures. For the case of dielectric and magnetic bodies a volume integral equation (VIE) formulationwas initially introduced. Although the VIE formulation was proven to be accurate, it requires a large number of unknowns when the electric size of the structure increases. To overcome this problem an equivalent surface integral equation (SIE) formulation was introduced in (Chang et al., 1977) which up to this day has dominated the field of characteristic mode analysis and several exceptional works have been proposed based on it (e.g., Yla-Oijala 2019).Despite the significance of all these works (see also the references in Yla-Oijala 2019), all theaforementioned CM techniques are based on method of moments (MoM), and they suffer from (a) inaccuracies as discussed in (e.g., Chen et al., 2015; Yla-Oijala 2019) and (b) several other issues related tounambiguous definitions of modes,tracking, and convergence. Here, we address the challenges traditional CM formulations have with the introduction of two alternative computational techniques. The first is a novel Green’s function-free characteristic modes formulation. Notably, our group was the first to propose this alternative CM formulation (e.g., Maximidis et al., 2012, Zekios et al., 2015, Paschaloudis et al., 2021] followed by others in the very recent years (e.g., Gustafsson et al,. 2022a; 2022b). Key advantage of the proposed formulation is that it does not require the evaluation of Green’sfunction, thereby the study of any arbitrarily shaped, multilayered geometry loaded with anisotropicand inhomogeneous materials is feasible. The second is a novel Green’s function formulation based on infinite ground plane Green’s functions. The key advantage of this formulation is its unique capability to identify only the real radiating modes over modes that appear as resonant (e.g., λ = 0) but in reality, they do not radiate despite the fact all traditional MoM formulations identify them as resonant with their eigenvalue λ = 0.