On the effective medium theory of subwavelength periodic structures

Abstract The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelen...

[1]  Pochi Yeh,et al.  A new optical model for wire grid polarizers , 1978 .

[2]  Ross C. McPhedran,et al.  Diffraction Gratings in the Quasi-static Limit , 1982 .

[3]  W H Southwell,et al.  Antireflection surfaces in silicon using binary optics technology. , 1992, Applied optics.

[4]  G. Michael Morris,et al.  Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings , 1995 .

[5]  Jari Turunen,et al.  Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles , 1994 .

[6]  N Nishida,et al.  Antireflection effect in ultrahigh spatial-frequency holographic relief gratings. , 1987, Applied optics.

[7]  W Stork,et al.  Artificial distributed-index media fabricated by zero-order gratings. , 1991, Optics letters.

[8]  J. L. Jackson,et al.  Bounds on Transport Coefficients of Two‐Phase Materials , 1968 .

[9]  O. Bryngdahl,et al.  Design of antireflection gratings with approximate and rigorous methods. , 1994, Applied optics.

[10]  Drew A. Pommet,et al.  Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings , 1994 .

[11]  Guy Bouchitté,et al.  Homogenization Techniques as Applied in the Electromagnetic Theory of Gratings , 1985 .

[12]  J. L. Jackson,et al.  Transport Coefficients of Composite Materials , 1968 .

[13]  B. Watrasiewicz,et al.  OSA annual meeting: Chicago, 21–24 October , 1970 .

[14]  H. Craighead,et al.  Diffractive phase elements based on two-dimensional artificial dielectrics. , 1995, Optics letters.

[15]  S. K. Case,et al.  Optical elements with ultrahigh spatial-frequency surface corrugations. , 1983, Applied optics.

[16]  Lifeng Li,et al.  Convergence of the coupled-wave method for metallic lamellar diffraction gratings , 1993 .

[17]  D. Flanders.  Submicrometer periodicity gratings as artificial anisotropic dielectrics , 1983 .

[18]  Robert Magnusson,et al.  Guided-mode resonances in planar dielectric-layer diffraction gratings , 1990 .

[19]  Ross C. McPhedran,et al.  Lossy Lamellar Gratings in the Quasistatic Limit , 1982 .

[20]  T. Gaylord,et al.  Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings. , 1986, Applied optics.

[21]  Raymond K. Kostuk,et al.  Effective-medium theory of sinusoidally modulated volume holograms , 1995 .

[22]  Raymond K. Kostuk,et al.  Effective-medium theory of zeroth-order lamellar gratings in conical mountings , 1993 .

[23]  M W Farn,et al.  Binary gratings with increased efficiency. , 1992, Applied optics.

[24]  N Streibl,et al.  Holographic quarterwave plates. , 1990, Applied optics.

[25]  G. M. Morris,et al.  Antireflection structured surfaces for the infrared spectral region. , 1993, Applied optics.