Photonic Crystal Optics and Homogenization of 2D Periodic Composites

  • P. Halevi
  • A. A. Krokhin
  • J. Arriaga
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)


We study the long-wavelength limit for an arbitrary photonic crystal (PC) of 2D periodicity. Light propagation is not restricted to the plane of periodicity. We proved that 2D PC’s are uni-axial or bi-axial and derived compact, explicit formulas for the effective (“principal”) dielectric constants; these are plotted for silicon - air composites. This could facilitate the custom design of optical components for diverse spectral regions and applications. Our method of “homogenization” is not limited to optical properties, but is also valid for electrostatics, magnetostatics, DC conductivity, thermal conductivity, etc. Thus our results are applicable to the Physics of Inhomogeneous Media where exact, compact formulas are scarce. Our numerical method yields results with very high accuracy, even for very large dielectric contrasts and filling fractions.


Photonic Crystal Filling Fraction Phononic Crystal Electric Field Parallel Apartado Postal 
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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • P. Halevi
    • 1
  • A. A. Krokhin
    • 2
  • J. Arriaga
    • 2
  1. 1.Instituto de AstrofÍsica, Optica y ElectrónicaPueblaMéxico
  2. 2.Instituto de FísicaUniversidad Autónoma de PueblaPueblaMéxico

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