Theory of characteristic modes for lossy structures: Formulation and interpretation of eigenvalues

Abstract

Volume integral equation (VIE) and surface integral equation (SIE) based characteristic mode (CM) formulations are investigated in the case of lossy objects. Imperfectly conducting metallic structures modelled with an impedance boundary condition and lossy dielectric bodies are considered. Two types of CM formulations are studied. In the first one, the generalized eigenvalue equation is expressed in terms of the Hermitian parts of the integral operators. In the second one, the weighting operator of the eigenvalue equation is defined so that the eigenvectors form a weighted orthogonal set, weighted with respect to radiated power. The first approach gives real eigensolutions and is found to lead to clustering of the eigenvalues as losses are increased. From these solutions it is difficult to separate contributions of radiated, reactive, and dissipated power. This separation appears naturally in the second approach that gives complex eigensolutions. As applications including lossy materials, CM analyses of a graphene sheet and a plasmonic nanoparticle are presented.

Orthogonality Properties of Characteristic Modes for Lossy Structures

“…This formulation agrees with the first formulation of [10], and the eigenvalues have the following physical interpretation [18] λ n = P reac n…”

“…In the following, we consider only structures with constant ε 1 and Z s . The power quantities can also be expressed with operator inner products [18], [19]…”

Designing Hand-Immune Handset Antennas With Adaptive Excitation and Characteristic Modes

“…For a given operator L, operator M should be defined so that the eigensolutions are related to radiated fields. This guarantees that the far fields of the modes are orthogonal and the complex valued eigenvalues λ n have the following physical interpretation [20], [21] Re(λ n ) =…”

“…The generalized eigenvalue equation, used to find the characteristic eigenvalues and eigenvectors (eigencurrents) needs to be defined properly to guarantee that the obtained eigensolutions are useful and physically meaningful completely excluding non-physical, so called spurious solutions. This is particularly important for bodies having high dielectric constant and being also highly lossy, such as the human body [20]. Recently we have shown that CMA can be reliably applied for the analysis of combined PEC (antenna) and lossy dielectric (user) structures [21].…”

Variant Characteristic Mode Equations Using Different Power Operators for Material Bodies

“…Eliminating one of the electric or magnetic current is preferable but not essential. One needs to solve a double sized GEE without eliminating one of the currents [14], [15]. Eliminating one of them would need to perform a matrix inversion [10], but it may be avoided by using the single integral equation formulations [16].…”