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WAVE SPLITTING OF MAXWELL'S EQUATIONS WITH ANISOTROPIC HETEROGENEOUS CONSTITUTIVE RELATIONS
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-7269-5241
2009 (English)Article in journal (Refereed) Published
Abstract [en]

The equations for the electromagnetic field in an anisotropic media are written in a form containing only the transverse field components relative to a half plane boundary. The operator corresponding to this formulation is the electromagnetic system's matrix. A constructive proof of the existence of directional wave-field decomposition with respect to the normal of the boundary is presented. In the process of defining the wave-field decomposition (wave-splitting), the resolvent set of the time-Laplace representation of the system's matrix is analyzed. This set is shown to contain a strip around the imaginary axis. We construct a splitting matrix as a Dunford-Taylor type integral over the resolvent of the unbounded operator defined by the electromagnetic system's matrix. The splitting matrix commutes with the system's matrix and the decomposition is obtained via a generalized eigenvalue-eigenvector procedure. The decomposition is expressed in terms of components of the splitting matrix. The constructive solution to the question of the existence of a decomposition also generates an impedance mapping solution to an algebraic Riccati operator equation. This solution is the electromagnetic generalization in an anisotropic media of a Dirichlet-to-Neumann map.

Place, publisher, year, edition, pages
2009. Vol. 3, no 3, 405-452 p.
Keyword [en]
directional wave-field decomposition, wave-splitting, anisotropy, electromagnetic system's matrix, generalized eigenvalue problem, algebraic Riccati operator equation, generalized vertical wave number, splitting matrix, absorbing boundary-conditions, generalized bremmer series, screen, approximation, inverse scattering, time-reversal, elastic-wave, one-way, media, decomposition, propagation
Identifiers
URN: urn:nbn:se:kth:diva-18704DOI: 10.3934/ipi.2009.3.405ISI: 000269239400004OAI: oai:DiVA.org:kth-18704DiVA: diva2:336751
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-10Bibliographically approved

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Jonsson, B. Lars G.

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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