Trapped modes in electromagnetic waveguides
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912777254207488 |
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| author | Dhia, Anne-Sophie Bonnet-Ben Chesnel, Lucas Fliss, Sonia |
| author_facet | Dhia, Anne-Sophie Bonnet-Ben Chesnel, Lucas Fliss, Sonia |
| contents | We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the existence of electromagnetic trapped modes, i.e. $L^2$ solutions of the problem without source term. These trapped modes are associated to eigenvalues of the Maxwell's operator, that can be either below the essential spectrum or embedded in it. First for homogeneous waveguides, we present different families of geometries for which we can prove the existence of eigenvalues. Then we exhibit certain non homogeneous waveguides with local perturbations of the dielectric constants that support trapped modes. Let us mention that some of the mechanisms we propose are very specific to Maxwell's equations and have no equivalent for the scalar Dirichlet or Neumann Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trapped modes in electromagnetic waveguides Dhia, Anne-Sophie Bonnet-Ben Chesnel, Lucas Fliss, Sonia Analysis of PDEs Spectral Theory 78A25, 78A40, 78A50, 35P15, 35Q61 We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the existence of electromagnetic trapped modes, i.e. $L^2$ solutions of the problem without source term. These trapped modes are associated to eigenvalues of the Maxwell's operator, that can be either below the essential spectrum or embedded in it. First for homogeneous waveguides, we present different families of geometries for which we can prove the existence of eigenvalues. Then we exhibit certain non homogeneous waveguides with local perturbations of the dielectric constants that support trapped modes. Let us mention that some of the mechanisms we propose are very specific to Maxwell's equations and have no equivalent for the scalar Dirichlet or Neumann Laplacians. |
| title | Trapped modes in electromagnetic waveguides |
| topic | Analysis of PDEs Spectral Theory 78A25, 78A40, 78A50, 35P15, 35Q61 |
| url | https://arxiv.org/abs/2512.17763 |