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

Pasi Ylä-Oijala*, Henrik Wallén, Seppo Järvenpää

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Article numbere2627
Number of pages18
JournalInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Issue number2
Early online date1 Jan 2019
Publication statusPublished - 2020
MoE publication typeA1 Journal article-refereed


  • characteristic modes
  • dielectric object
  • impedance boundary condition
  • integral equation
  • lossy structure

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