Optical Review

, Volume 2, Issue 2, pp 92–99 | Cite as

Ability and Limitation of Effective Medium Theory for Subwavelength Gratings

  • Hisao Kikuta
  • Hideo Yoshida
  • Koichi Iwata


In the recent researches of subwavelength relief gratings, the effective refractive indices are used for calculating the coefficients of reflection and transmission of light waves. The effective refractive indices are given by the effective medium theory for light waves propagating in a bulky stratified medium. This paper describes the ability and limitation of the theory applied to estimate the performance of such subwavelength gratings. The limitation is revealed by numerical calculations using a rigorous electromagnetic grating theory and the effective medium theory. As a result, an understanding of the wave behavior in the subwavelength grating has been acquired, which explains the limitation of the effective medium theory.

Key words

artificial refractive index effective medium theory effective refractive index diffraction grating subwavelength grating 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Aoyama and T. Yamashita: Proc. SPIE 1545 (1991) 241.CrossRefGoogle Scholar
  2. 2.
    P. Kipfer, M. Collischon, H. Haidner, J.T. Sheridan, J. Streibl and J. Lindolf: Opt. Eng. 33 (1994) 79.Google Scholar
  3. 3.
    M.W. Farn: Appl. Opt. 31 (1992) 4453.Google Scholar
  4. 4.
    M.G. Moharam and T.K. Gaylord: J. Opt. Soc. Am. 71 (1981) 811.Google Scholar
  5. 5.
    P. Vincent: Electromagnetic Theory of Gratings, ed. R. Petit (Springer-Verlag, Berlin, 1980) Chap. 4.Google Scholar
  6. 6.
    I.C. Botten, M.S. Craig, R.C. McPhedran, J.L. Adams and J.R. Andrewartha: Opt. Acta 28 (1981) 413.Google Scholar
  7. 7.
    T.K. Gaylord, W.E. Baird and M.G. Moharam: Appl. Opt. 25 (1986) 4562.Google Scholar
  8. 8.
    for example, M. Born and E. Wolf: Principles of Optics (Pergamon Press, Oxford, 1980) 6th ed., p. 705.Google Scholar
  9. 9.
    A. Yariv and P. Yhe: Optical Waves in Crystals (John Wiley & Sons, New York, 1984) Chap. 6.Google Scholar
  10. 10.
    S.M. Rytov: Sov. Phys. JETP 2 (1956) 466. [J. Exp. Theor. Phys. USSR 29 (1955) 605].Google Scholar
  11. 11.
    D.H. Raguin and G.H. Morris: Appl. Opt. 32 (1993) 1154.Google Scholar
  12. 12.
    S. Babin, H. Haidner, P. Kipfer, A. Lang, J.T. Sheridan, W. Strork and N. Streibl: Proc. SPIE 1751 (1992) 202.CrossRefGoogle Scholar
  13. 13.
    C.W. Haggans, L. Li and R.K. Kostuk: J. Opt. Soc. Am. A 10 (1993) 2217.Google Scholar
  14. 14.
    for example, M. Born and E. Wolf: Principles of Optics (Pergamon Press, Oxford, 1980) 6th ed., p. 325.Google Scholar
  15. 15.
    K. Matsumoto, K. Rokushima and J. Yamakita: J. Opt. Soc. Am. A 10 (1993) 269.Google Scholar
  16. 16.
    Y. Ono, Y. Kimura, Y. Ohta and N. Nishida: Appl. Opt. 26 (1987) 1142.Google Scholar

Copyright information

© The Optical Society of Japan 1995

Authors and Affiliations

  • Hisao Kikuta
    • 1
  • Hideo Yoshida
    • 1
  • Koichi Iwata
    • 1
  1. 1.Department of Mechanical System Engineering, College of EngineeringUniversity of Osaka PrefectureSakai, OsakaJapan

Personalised recommendations