Theory of Characteristic Modes for Nonsymmetric Surface Integral Operators

The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner p...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation Vol. 69; no. 3; pp. 1505 - 1512
Main Authors: Yla-Oijala, Pasi, Wallen, Henrik
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adjoint operator
characteristic modes (CMs)
Conductors
dielectric object
Dielectrics
Eigenvalues
Eigenvalues and eigenfunctions
Eigenvectors
Electric conductors
Impedance
impedance boundary condition (IBC)
Integral equations
Integrals
Magnetic resonance imaging
Operators (mathematics)
Orthogonality
perfect electric conductor (PEC)
Scattering
Surface impedance
surface integral operator
ISSN:0018-926X, 1558-2221
Online Access:Get full text
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Summary:The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner product defined with the weighting operator of the generalized eigenvalue equation. Rather, this orthogonality holds between the eigenvectors of the original equation and the adjoint equation, including adjoint operators. This implies that the modal expansion, used to express any scattering or radiation solution as a linear combination of the modes, requires these two sets of eigenvectors. For matrix equations, the eigenvectors of the adjoint equation correspond to the left eigenvectors of the original equation.
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content type line 14
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2020.3017437