WAVE SPLITTING OF MAXWELL'S EQUATIONS WITH ANISOTROPIC HETEROGENEOUS CONSTITUTIVE RELATIONS
2009 (English)Article in journal (Refereed) Published
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.
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
IdentifiersURN: urn:nbn:se:kth:diva-18704DOI: 10.3934/ipi.2009.3.405ISI: 000269239400004OAI: oai:DiVA.org:kth-18704DiVA: diva2:336751
QC 201005252010-08-052010-08-052011-01-10Bibliographically approved