Homogenization of time-harmonic Maxwell’s equations in nonhomogeneous plasmonic structures
| Autor: | Antoine Mellet, Dionisios Margetis, Matthias Maier |
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| Rok vydání: | 2020 |
| Předmět: |
Permittivity
Condensed matter physics Applied Mathematics Physics::Optics 010103 numerical & computational mathematics Dielectric Weak formulation 01 natural sciences Homogenization (chemistry) Magnetic field 010101 applied mathematics Computational Mathematics symbols.namesake Maxwell's equations symbols Boundary value problem 0101 mathematics Anisotropy Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 377:112909 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2020.112909 |
| Popis: | We carry out the homogenization of time-harmonic Maxwell’s equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting, the tangential magnetic field exhibits a jump across each sheet. Our goal is the rigorous derivation of the effective dielectric permittivity of the system from the solution of a local cell problem via suitable averages. Each sheet has a fine-scale, inhomogeneous and possibly anisotropic surface conductivity that scales linearly with the microstructure scale, d . Starting with the weak formulation of the requisite boundary value problem, we prove the convergence of its solution to a homogenization limit as d approaches zero. The effective permittivity and cell problem express a bulk average from the host dielectric and a surface average germane to the 2D material (metallic layer). We discuss implications of this analysis in the modeling of plasmonic crystals. |
| Databáze: | OpenAIRE |
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