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arXiv · 1805.07671

Homogenization of time-harmonic Maxwell's equations in nonhomogeneous plasmonic structures

Matthias Maier·Dionisios Margetis·Antoine Mellet
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Abstract

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.

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Matthias Maier, Dionisios Margetis, Antoine Mellet. 2018-05-19. Homogenization of time-harmonic Maxwell's equations in nonhomogeneous plasmonic structures. https://arxiv.org/abs/1805.07671

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