Two-scale approach to the homogenization of membrane photonic crystals

Wave propagation and diffraction in a membrane photonic crystal with finite height were studied in the case where the free-space wavelength is large with respect to the period of the structure. The photonic crystals studied are made of materials with anisotropic permittivity and permeability. Use of the concept of two-scale convergence allowed the photonic crystals to be homogenized.

[1]  D. Kinderlehrer,et al.  Homogenization and effective moduli of materials and media , 1986 .

[2]  Habib Ammari,et al.  Scattering of Electromagnetic Waves by Thin Dielectric Planar Structures , 2006, SIAM J. Math. Anal..

[3]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[4]  D. Felbacq,et al.  Anomalous homogeneous behaviour of metallic photonic crystals , 2000 .

[5]  G. Allaire Homogenization and two-scale convergence , 1992 .

[6]  D. Felbacq,et al.  Localization of Light by a Set of Parallel Cylinders , 1995 .

[7]  R. McPhedran,et al.  Homogenization of composites: dynamic and static theories , 2000 .

[8]  Guy Bouchitté,et al.  Negative refraction in periodic and random photonic crystals , 2005 .

[9]  R. McPhedran,et al.  Effective dielectic constant of arrays of elliptical cylinders , 1997 .

[10]  Lixin Ran,et al.  Experimental observation of left-handed behavior in an array of standard dielectric resonators. , 2007, Physical review letters.

[11]  Guy Bouchitté,et al.  Homogenization of a Wire Photonic Crystal: The Case of Small Volume Fraction , 2006, SIAM J. Appl. Math..

[12]  Guy Bouchitté,et al.  Bloch vector dependence of the plasma frequency in metallic photonic crystals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. Arriaga,et al.  Long-wavelength limit (homogenization) for two-dimensional photonic crystals , 2002 .

[14]  S. Guenneau,et al.  Homogenization of 3D finite chiral photonic crystals , 2007 .

[15]  Guy Bouchitté,et al.  Theory of mesoscopic magnetism in photonic crystals. , 2004, Physical review letters.

[16]  T. Tada,et al.  Si pillar photonic crystal slab with linear defects: transmittance and waveguide properties , 2002 .

[17]  Henri Benisty,et al.  Photonic crystals in two-dimensions based on semiconductors: fabrication, physics and technology , 2000 .

[18]  Guy Bouchitté,et al.  Homogenization of a set of parallel fibres , 1997 .

[19]  Guy Bouchitté,et al.  Left-handed media and homogenization of photonic crystals. , 2005, Optics letters.

[20]  Didier Felbacq,et al.  BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals. , 2004, Physical review letters.

[21]  J. Arriaga,et al.  Photonic Crystal Optics and Homogenization of 2D Periodic Composites , 1999 .