2018/05/19 by Matthias Maier, Maier, Matthias, Dionisios Margetis +3
Computer Science · Engineering · Physics and Astronomy · #35B27 #35Q60 #74Q10 #78A40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1805.07671
openalex publication_date 2018/05/19 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
We carry out the homogenization of time-harmonic Maxwell's equations in a\nperiodic, layered structure made of two-dimensional (2D) metallic sheets\nimmersed in a heterogeneous and in principle anisotropic dielectric medium. In\nthis setting, the tangential magnetic field exhibits a jump across each sheet.\nOur goal is the rigorous derivation of the effective dielectric permittivity of\nthe system from the solution of a local cell problem via suitable averages.\nEach sheet has a fine-scale, inhomogeneous and possibly anisotropic surface\nconductivity that scales linearly with the microstructure scale, d. Starting\nwith the weak formulation of the requisite boundary value problem, we prove the\nconvergence of its solution to a homogenization limit as d approaches zero.\nThe effective permittivity and cell problem express a bulk average from the\nhost dielectric and a surface average germane to the 2D material (metallic\nlayer). We discuss implications of this analysis in the modeling of plasmonic\ncrystals.\n