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Applied Physics A

, Volume 117, Issue 2, pp 567–572 | Cite as

Electromagnetic small-scale modeling of composite panels involving periodic arrays of circular fibers

  • C. Y. LiEmail author
  • D. Lesselier
  • Y. Zhong
Article

Abstract

Electromagnetic modeling of composite panels as planar multilayers involving a periodic set of circular cylindrical fibers in each constitutive layer is considered. As a first step, the case of a single layer is studied. Combining multipole method and plane-wave expansion leads to full-wave field representations in all space, yielding in particular reflection and transmission coefficients for TE/TM oblique plane-wave illuminations. Gaussian beams are accounted for via a Fourier transform and numerical quadrature scheme. Comparisons with data available for photonic crystals show the accuracy of the method, while results for fiber-reinforced composites illustrate its effectiveness.

Keywords

Transmission Coefficient Gaussian Beam Epoxy Matrix Scattered Field Perfect Electric Conductor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Y. Zhong et al., Electromagnetic response of anisotropic laminates to distributed sources. IEEE Trans. Antennas Propag. 62, 247–256 (2014)CrossRefGoogle Scholar
  2. 2.
    J.-P. Groby et al., Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions. J. Acoust. Soc. Am. 126, 685–693 (2009)CrossRefADSGoogle Scholar
  3. 3.
    J.-P. Groby, D. Lesselier, Localization and characterization of simple defects in finite-size photonic crystals. J. Opt. Soc. Am. A 25, 146–152 (2008)CrossRefADSGoogle Scholar
  4. 4.
    S. Wilcox et al., Modeling of defect modes in photonic crystals using the fictitious source superposition method. Phys. Rev. E 71, 056606-1–056606-11 (2005)CrossRefADSGoogle Scholar
  5. 5.
    L.C. Botten et al., Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method. J. Opt. Soc. Am. A 17, 2165–2176 (2000)CrossRefADSGoogle Scholar
  6. 6.
    J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968)Google Scholar
  7. 7.
    E.E. Kriezis et al., Diffraction of a Gaussian beam from a periodic planar screen. J. Opt. Soc. Am. A 11, 630–636 (1994)CrossRefADSGoogle Scholar
  8. 8.
    J. Yang et al., Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders. IEEE Trans. Geosci. Remote Sens. 43, 280–285 (2005)CrossRefADSGoogle Scholar
  9. 9.
    V. Twersky, On scattering of waves by the infinite grating of circular cylinders. IEEE Trans. Antennas Propag. 10, 737–765 (1962)CrossRefADSGoogle Scholar
  10. 10.
    K. Yasumoto et al., Efficient calculation of lattice sums for free-space periodic Green’s function. IEEE Trans. Antennas Propag. 47, 1050–1055 (1999)CrossRefADSGoogle Scholar
  11. 11.
    A. Moroz, Exponentially convergent lattice sums. Opt. Lett. 26, 1119–1121 (2001)CrossRefADSGoogle Scholar
  12. 12.
    M. Kavaklioglu, On Schlömilch series representation for the transverse electric multiple scattering by an infinite grating of insulating dielectric circular cylinders at oblique incidence. J. Phys. A Math. Gen. 35, 2229–2234 (2002)MathSciNetCrossRefzbMATHADSGoogle Scholar
  13. 13.
    C.M. Linton, Schlömilch series that arise in diffraction theory and their efficient computation. J. Phys. A Math. Gen. 39, 3325–3339 (2006)MathSciNetCrossRefzbMATHADSGoogle Scholar
  14. 14.
    H. Roussel et al., Electromagnetic scattering from dielectric and magnetic gratings of fibers—a T-matrix solution. J. Electromagn. Waves Appl. 10, 109–127 (1996)CrossRefGoogle Scholar
  15. 15.
    T. Kushta et al., Electromagnetic scattering from periodic array of two circular cylinders per unit cell. PIER 29, 69–85 (2000)CrossRefGoogle Scholar
  16. 16.
    J.A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, 2008)Google Scholar
  17. 17.
    M. Antunes et al., Broad-band electrical conductivity of carbon nanofibre-reinforced polypropylene foams. Carbon 49, 708–717 (2011)CrossRefGoogle Scholar
  18. 18.
    M. Hotta et al., Complex permittivity of graphite, carbon black and coal powders in the ranges of x-band frequencies (8.2 to 12.4 GHz) and between 1 and 10 GHz. ISIJ Int. 51, 1766–1772 (2011)CrossRefGoogle Scholar
  19. 19.
    A. Galehdar et al., The conductivity of unidirectional and quasi isotropic carbon fiber composites. 2010 European Microwave Conference (EuMC), 882–885 (2010)Google Scholar
  20. 20.
    X. Luo et al., Carbon-fiber/polymer-matrix composites as capacitors. Compos. Sci. Technol. 61, 885–888 (2001)CrossRefGoogle Scholar
  21. 21.
    Y.J. Kim et al., Electrical conductivity of chemically modified multiwalled carbon nanotube/epoxy composites. Carbon 43, 23–30 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Département de Recherche en Electromagnétisme-Laboratoire des Signaux et SystèmesUMR8506 (CNRS-SUPELEC-Univ Paris-Sud)Gif-sur-YvetteFrance
  2. 2.A*STAR Institution of High Performance ComputingSingaporeSingapore

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