OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 8 — Apr. 17, 2006
  • pp: 3114–3128

Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization

Martin Foldyna, Razvigor Ossikovski, Antonello De Martino, Bernard Drevillon, Kamil Postava, Dalibor Ciprian, Jaromír Pištora, and Koki Watanabe  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3114-3128 (2006)
http://dx.doi.org/10.1364/OE.14.003114


View Full Text Article

Enhanced HTML    Acrobat PDF (298 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Anisotropic lamellar sub-wavelength gratings (nanogratings) are described by Effective Medium Approximation (EMA). Analytical formulas for effective medium optical parameters of nanogratings from arbitrary anisotropic materials are derived using approximation of zero-order diffraction mode. The method is based on Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement between EMA and the rigorous model is observed, where slight differences are explained by the influence of evanescent higher Fourier harmonics in the nanograting.

© 2006 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(160.1190) Materials : Anisotropic optical materials
(310.3840) Thin films : Materials and process characterization

ToC Category:
Diffraction and Gratings

History
Original Manuscript: January 30, 2006
Revised Manuscript: April 2, 2006
Manuscript Accepted: April 11, 2006
Published: April 17, 2006

Citation
Martin Foldyna, Razvigor Ossikovski, Antonello De Martino, Bernard Drevillon, Kamil Postava, Dalibor Ciprian, Jaromír Pištora, and Koki Watanabe, "Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization," Opt. Express 14, 3114-3128 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3114


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Allgair, D. Benoit, R. Hershey, L. C. Litt, I. Abdulhalim, B. Braymer, M. Faeyrman, J. C. Robinson, U. Whitney, Y. Xu, P. Zalicki, and J. Selingson, "Manufacturing considerations for implementattion of scatterometry for process monitoring," Proc. of SPIE 3998, 125-134 (2000). [CrossRef]
  2. H.-T. Huang and F. L. Terry and Jr., "Erratum to ’Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ and real-time process monitoring’," Thin Solid Films 468, 339-346 (2004). [CrossRef]
  3. G. P. Nordin and P. C. Deguzman, "Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region," Opt. Express 5, 163-168 (1999). [CrossRef] [PubMed]
  4. R . Haïýdar, G . Vincent, N . Guérineau, S. Collin, S. Velghe, and J. Primot, "Wollaston prism-like devices based on blazed dielectric subwavelength gratings," Opt. Express 13, 9941-9953 (2005). [CrossRef] [PubMed]
  5. H. Lajunen, J. Turunen, and J. Tervo, "Design of polarization gratings for broadband illumination," Opt. Express 13, 3055-3067 (2005). [CrossRef] [PubMed]
  6. D. E. Aspnes and J. B. Theeten, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979). [CrossRef]
  7. D. Stroud and A. Kazaryan, "Optical sum rules and effective-medium theories for a polycrystalline material: Application to a model for polypyrrole," Phys. Rev. B 53, 7076-7084 (1996). [CrossRef]
  8. F. Garc´ýa-Vidal, J. M. Pitarke, and J. B. Pendry, "Effective medium theory of the optical properties of aligned carbon nanotubes," Phys. Rev. B 78, 4289 (1997). [CrossRef]
  9. C.-Y. You, S.-C. Shin, and S.-Y. Kim, "Modified effective-medium theory for magneto-optical spectra of magnetic materials," Phys. Rev. B 55, 5953-5958 (1997). [CrossRef]
  10. H. Kikuta, H. Yoshida, and K. Iwata, "Ability and limitation of effective medium theory for subwavelength gratings," Opt. Rev. 2, 92-99 (1995). [CrossRef]
  11. C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, "Calculation of the effective dielectric function of composites with periodic geometry," Physica B 293, 16-32 (2000). [CrossRef]
  12. E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, "Use of diffraction theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001). [CrossRef]
  13. K. Rokushima and J. Yamakita, "Analysis of anisotropic dielectric gratings," J. Opt. Soc. Am. 73, 901-908 (1983). [CrossRef]
  14. M. Nevi`ere and E. Popov, Light Propagation in periodic media: Differential theory and design (Marcel Dekker, 2002).
  15. P. Lalanne and G. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-783 (1996). [CrossRef]
  16. G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]
  17. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870- 1876 (1996). [CrossRef]
  18. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996). [CrossRef]
  19. K. Watanabe, R. Petit, and M. Nevi`ere, "Differential theory of gratings made of anisotropic materials," J. Opt. Soc. Am. A 19, 325-334 (2002). [CrossRef]
  20. K. Watanabe and K. Yasumoto, "Fourier Modal Theory of Rectangular Dot Gratings Made of Anisotropic and Conducting Materials," Proc. of SPIE 5445, 218-221 (2004). [CrossRef]
  21. L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313-1334 (1998). [CrossRef]
  22. L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt. 5, 345-355 (2003). [CrossRef]
  23. G. Campbell and R. Kostuk, "Effective-medium theory of sinusoidally modulated volume holograms," J. Opt. Soc. Am. A 12, 1113-1117 (1995). [CrossRef]
  24. J. Turunen, "Form-birefringence limits of Fourier-expansion methods in grating theory," J. Opt. Soc. Am. A 13, 1013-1018 (1996). [CrossRef]
  25. J. Turunen, M. Kuittinen, and P. Vahimaa, "Form-birefringence limits of Fourier-expansion methods in grating theory: arbitrary angle of incidence," J. Opt. Soc. Am. A 14, 2314-2316 (1997). [CrossRef]
  26. W. Stork, N. Streibl, H. Haidner, and P. Kipfer, "Artificial distributed-index media fabricated by zero-order gratings," Opt. Lett. 16, 1921-1923 (1991). [CrossRef] [PubMed]
  27. S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).
  28. P. Lalanne and D. Lemercier-Lalanne, "Depth dependence of the effective properties of subwavelength gratings," J. Opt. Soc. Am. A 14, 450-458 (1997). [CrossRef]
  29. M. Foldyna, K. Postava, D. Ciprian, and J. Pi¡stora, "Modeling of magneto-optical properties of periodic nanostructures," J. Magn. Magn. Mater. 290-291, 120-123 (2005). [CrossRef]
  30. M. Foldyna, K. Postava, D. Ciprian, and J. Pi¡stora, "Modeling of magneto-optical properties of lamellar nanogratings," J. Alloy. Compd. (to be published) (2006).
  31. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, p. 149, 3rd ed. (North-Holland, Amsterdam, 1989).
  32. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++. The art of scientifique computing, 2nd ed. (Cambridge, 2002).
  33. H. Piller, "Silicon (Amorphous) (a-Si)," in Handbook of Optical Constants of Solids, E. D. Palik, ed., p. 571 (Academic Press, 1991).
  34. P. Johnson and R. W. Christy, "Optical constants of transition metals: Ti and V and Cr and Mn and Fe and Co and Ni and Pd," Phys. Rev. B 9, 5056-5070 (1974). [CrossRef]
  35. G. E. Jellison, "Generalized ellipsometry for materials characterization," Thin Solid Films 450, 42-50 (2004). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited