dorsal/arxiv
View SchemaOn the Definition of Effective Permittivity and Permeability For Thin Composite Layers
| Authors | Elena Saenz, Pekka Ikonen, Ramon Gonzalo, Sergei Tretyakov |
|---|---|
| Categories | |
| ArXiv ID | physics/0703119 |
| URL | https://arxiv.org/abs/physics/0703119 |
| DOI | 10.1063/1.2743817 |
| Journal | Journal of Applied Physics, vol. 101, p. 114910, 2007. |
Abstract
The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for the design of novel metamaterials, where the realizable layers quite often have only one or two layers of particles across the sample thickness. Effective parameters which describe the averaged induced polarizations are introduced. As an explicit example, we develop an analytical model suitable for calculation of the effective material parameters $\epsilon_{\rm{eff}}$ and $\mu_{\rm{eff}}$ for double arrays of electrically small electrically polarizable scatterers. Electric and magnetic dipole moments induced in the structure and the corresponding reflection and transmission coefficients are calculated using the local field approach for the normal plane-wave incidence, and effective parameters are introduced through the averaged fields and polarizations. In the absence of losses both material parameters are purely real and satisfy the Kramers-Kronig relations and the second law of thermodynamics. We compare the analytical results to the simulated and experimental results available in the literature. The physical meaning of the introduced parameters is discussed in detail.
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"abstract": "The problem of definition of effective material parameters (permittivity and\npermeability) for composite layers containing only one-two parallel arrays of\ncomplex-shaped inclusions is discussed. Such structures are of high importance\nfor the design of novel metamaterials, where the realizable layers quite often\nhave only one or two layers of particles across the sample thickness. Effective\nparameters which describe the averaged induced polarizations are introduced. As\nan explicit example, we develop an analytical model suitable for calculation of\nthe effective material parameters $\\epsilon_{\\rm{eff}}$ and $\\mu_{\\rm{eff}}$\nfor double arrays of electrically small electrically polarizable scatterers.\nElectric and magnetic dipole moments induced in the structure and the\ncorresponding reflection and transmission coefficients are calculated using the\nlocal field approach for the normal plane-wave incidence, and effective\nparameters are introduced through the averaged fields and polarizations. In the\nabsence of losses both material parameters are purely real and satisfy the\nKramers-Kronig relations and the second law of thermodynamics. We compare the\nanalytical results to the simulated and experimental results available in the\nliterature. The physical meaning of the introduced parameters is discussed in\ndetail.",
"arxiv_id": "physics/0703119",
"authors": [
"Elena Saenz",
"Pekka Ikonen",
"Ramon Gonzalo",
"Sergei Tretyakov"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"doi": "10.1063/1.2743817",
"journal_ref": "Journal of Applied Physics, vol. 101, p. 114910, 2007.",
"title": "On the Definition of Effective Permittivity and Permeability For Thin Composite Layers",
"url": "https://arxiv.org/abs/physics/0703119"
},
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