On the analysis of modes in a closed electromagnetic waveguide
Modal expansions are useful to understand wave propagation in an infinite closed electromagnetic waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that provide artificial boundary conditions for truncating a computational domain when discretizing the field by finite...
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.516/ |
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| author | Halla, Martin Monk, Peter |
| author_facet | Halla, Martin Monk, Peter |
| author_sort | Halla, Martin |
| collection | DOAJ |
| description | Modal expansions are useful to understand wave propagation in an infinite closed electromagnetic waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that provide artificial boundary conditions for truncating a computational domain when discretizing the field by finite elements. The modes of a waveguide arise as eigenfunctions of a non-symmetric eigenvalue problem, and the eigenvalues determine the propagation (or decay) of the modes along the waveguide. For the successful use of waveguide modes, it is necessary to know that the modes exist and form a dense set in a suitable function space containing the trace of the electric field in the waveguide. This paper is devoted to proving such a density result using the methods of Keldysh. We also show that the modes satisfy a useful orthogonality property, and show how the Dirichlet-to-Neumann map can be calculated. Our existence and density results are proved under realistic regularity assumptions on the cross section of the waveguide, and the electromagnetic properties of the materials in the waveguide, so generalizing existing results. |
| format | Article |
| id | doaj-art-9f4a253bd61845acbb4e5879fc505cb9 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-9f4a253bd61845acbb4e5879fc505cb92025-02-07T11:21:11ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G546947910.5802/crmath.51610.5802/crmath.516On the analysis of modes in a closed electromagnetic waveguideHalla, Martin0https://orcid.org/0000-0002-3010-3540Monk, Peter1https://orcid.org/0000-0003-4637-3059Institut für Numerische und Angewandte Mathematik, Georg-Augst Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Deutschland.Department of Mathematical Sciences University of Delaware, Newark DE 19716, USA.Modal expansions are useful to understand wave propagation in an infinite closed electromagnetic waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that provide artificial boundary conditions for truncating a computational domain when discretizing the field by finite elements. The modes of a waveguide arise as eigenfunctions of a non-symmetric eigenvalue problem, and the eigenvalues determine the propagation (or decay) of the modes along the waveguide. For the successful use of waveguide modes, it is necessary to know that the modes exist and form a dense set in a suitable function space containing the trace of the electric field in the waveguide. This paper is devoted to proving such a density result using the methods of Keldysh. We also show that the modes satisfy a useful orthogonality property, and show how the Dirichlet-to-Neumann map can be calculated. Our existence and density results are proved under realistic regularity assumptions on the cross section of the waveguide, and the electromagnetic properties of the materials in the waveguide, so generalizing existing results.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.516/ |
| spellingShingle | Halla, Martin Monk, Peter On the analysis of modes in a closed electromagnetic waveguide Comptes Rendus. Mathématique |
| title | On the analysis of modes in a closed electromagnetic waveguide |
| title_full | On the analysis of modes in a closed electromagnetic waveguide |
| title_fullStr | On the analysis of modes in a closed electromagnetic waveguide |
| title_full_unstemmed | On the analysis of modes in a closed electromagnetic waveguide |
| title_short | On the analysis of modes in a closed electromagnetic waveguide |
| title_sort | on the analysis of modes in a closed electromagnetic waveguide |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.516/ |
| work_keys_str_mv | AT hallamartin ontheanalysisofmodesinaclosedelectromagneticwaveguide AT monkpeter ontheanalysisofmodesinaclosedelectromagneticwaveguide |