Finite Element Method - Archive ouverte HAL
Chapitre D'ouvrage Année : 2012

Finite Element Method

Guillaume Demésy
  • Fonction : Auteur
  • PersonId : 865006
Frédéric Zolla
  • Fonction : Auteur
  • PersonId : 860490
André Nicolet
Benjamin Vial
  • Fonction : Auteur
ILM

Résumé

In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulation for both mono-dimensional gratings in TE/TM polarization cases (2D or scalar case) and for the most general bidimensional or crossed gratings (3D or vector case). The main advantage of this formulation is its complete generality with respect to the studied geometries and the material properties. Its principle remains independent of both the number of diffractive elements by period and number of stack layers. The flexibility of our approach makes it a handy and powerful tool for the study of metamaterials, finite size photonic crystals, periodic plasmonic structures...
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Dates et versions

hal-00785009 , version 1 (05-02-2013)

Identifiants

  • HAL Id : hal-00785009 , version 1

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Guillaume Demésy, Frédéric Zolla, André Nicolet, Benjamin Vial. Finite Element Method. E. Popov. Gratings: Theory and Numeric Applications, AMU, pp.5.1-5.47, 2012, 978-2-8539-9860-4. ⟨hal-00785009⟩
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