Abstract

Rigorous coupled-wave analysis (RCWA) with a simplified eigenvalue problem is used to investigate the an-tireflective property of one-dimensional surface-relief gratings such as binary gratings, triangular gratings and gratings with triangle-like surface profiles. The convergence of RCWA is investigated by varying the number of layers and the number of space-harmonics used in the computation. For unpolarized light normally incident on a medium of refractive index 1.64 from vaccum, a triangle-like grating shows the reflectivity of <TEX>$1.6 {\times} 10^{-4}$</TEX> in contrast to a minimum reflectivity of <TEX>$3.8 {\times} 10^{-3}$</TEX> for a binary grating. We also study the dependence of reflectivity on the wavelength, and on the angle of incidence for a groove shape and depth which result in minimum reflectivity.

© 1997 Optical Society of Korea

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  1. R. Petit, Ed., Electromagnetic Theory of Gratings, Topics in Current Physics, Vol.22 (Springer-Verlag, Berlin, 1980)
  2. T. K. Gaylord and M. G. Moharam, "Analysis and Ap-plications of Optical Diffraction by Gratings," Proc. IEEE 73, 894-937 (1985)
    [Crossref]
  3. D. Maystre, Selected papers on diffraction gratings, SPIE Milestone Series Vol. MS83 (SPIE, Bellingham, 1993)
  4. E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, "Rigorous coupled-wave analysis and applications of grat-ing diffraction," in Diffractive and Miniaturized Optics, Crit-ical Reviews of Optical Science and Technology Vol. CR 49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.3-31
    [Crossref]
  5. D. H. Raguin, S. Norton and G. M. Morris, "Subwavelength structured surfaces and their applications," in Diffractive and Miniaturized Optics, Critical Reviews of Optical Science and Technology Vol. CR49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.234-261
  6. P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, "Subwavelength structures and their use in diffractive op-tics," Opt. Eng. 35, 726-731 (1996)
    [Crossref]
  7. W. H. Southwell, "Pyramid-array surface-relief structures producing antireflection index matching on optical sur-faces," J. Opt. Soc. Am. A8, 549-553 (1991)
    [Crossref]
  8. M. E. Motamedi, W. H. Southwell, and W. J. Gunning, "Antireflection surfaces in silicon using binary optics tech-nology," Appl. Opt. 31,4371-4375 (1992)
    [Crossref]
  9. T. K. Gaylord, W. E. Baird, and M. G. Moharam, "Zero-reflectivitv high spatial frequency rectangular-groove dielectric surface-relief gratings," Appl. Opt. 25, 4562-4567 (1986)
    [Crossref]
  10. Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, "Antireflection effect in ultrahigh spatial-frequency hol-ographic relief gratings," Appl. Opt. 26, 1142-1146 (1987)
    [Crossref]
  11. E. N. Glytsis and T. K. Gaylord, "Antireflection surface structure: dielectric layer( s) over a high spatial-frequency surface-relief gratings on a lossy substrate," Appl. Opt. 27, 4288-4304 (1988)
    [Crossref]
  12. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, "Homogeneous layer models for high- spatial-frequency dielectric surface-relief gratings: conical diffraction and an-tireflection designs," Appl. Opt. 33, 2695-2706 (1994)
    [Crossref]
  13. D. H. Raguin and G. M. Morris, "Antireflection struc-tured surfaces for the infrared spectral region," Appl. Opt. 32,1154-1167 (1993)
    [Crossref]
  14. D. H. Raguin and G. M. Morris, "Analysis of an-tireflection-structured surfaces with continuous one-di-mensional surface profiles," Appl. Opt. 32, 2582-2598 (1993)
    [Crossref]
  15. E. B. Grann, M. G. Moharam and D. A. Pommet, "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A 11, 2695-2703 (1994)
    [Crossref]
  16. E. B. Grann, M. G. Moharam and D. A. Pommet, "Optimal design for antireflective tapered two-di-mensional subwavelength grating structures," J. Opt. Soc. Am. A12, 333-339 (1995)
    [Crossref]
  17. E. B. Grann and M. G. Moharam, "Comparison between continuous and discrete subwavelength grating structures tor antireflectjon surfaces," J. Opt. Soc. Am. A13, 988-992 (1996)
    [Crossref]
  18. M, G, Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982)
    [Crossref]
  19. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am, 73, 1105-1112 (1983)
    [Crossref]
  20. M, G. Moharam, "Coupled-Wave Analysis of Two-di-mensional Dielectric Gratings," Proc. Soc. Photo-Opt. In-strum, Eng. 883, 8-11 (1988)
  21. S. T. Han, Y. Tsao, R. M. Walser, and M. F. Becker, "Electromagnetic scattering of two-dimensional surface-re-lief dielectric gratings," Appl. Opt. 31, 2343-2352 (1992)
    [Crossref]
  22. D. Cho, "Eigenvalue problem pertaining to the rigorous three-dimensional vector coupled-wave analysis of dif-fraction from surface-relief gratings," Hankook Kwanghak Hoeji 5, 439-444 (1994)
  23. netlib, Oak Ridge National Laboratory, Oak Ridge, TN, U.S.A.
  24. L. Li and C. W. Haggans, "Convergence of the coupled-wave methods for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A10, 1184-1189 (1993)
    [Crossref]

1996 (2)

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, "Subwavelength structures and their use in diffractive op-tics," Opt. Eng. 35, 726-731 (1996)
[Crossref]

E. B. Grann and M. G. Moharam, "Comparison between continuous and discrete subwavelength grating structures tor antireflectjon surfaces," J. Opt. Soc. Am. A13, 988-992 (1996)
[Crossref]

1995 (1)

E. B. Grann, M. G. Moharam and D. A. Pommet, "Optimal design for antireflective tapered two-di-mensional subwavelength grating structures," J. Opt. Soc. Am. A12, 333-339 (1995)
[Crossref]

1994 (3)

E. B. Grann, M. G. Moharam and D. A. Pommet, "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A 11, 2695-2703 (1994)
[Crossref]

D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, "Homogeneous layer models for high- spatial-frequency dielectric surface-relief gratings: conical diffraction and an-tireflection designs," Appl. Opt. 33, 2695-2706 (1994)
[Crossref]

D. Cho, "Eigenvalue problem pertaining to the rigorous three-dimensional vector coupled-wave analysis of dif-fraction from surface-relief gratings," Hankook Kwanghak Hoeji 5, 439-444 (1994)

1993 (6)

L. Li and C. W. Haggans, "Convergence of the coupled-wave methods for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A10, 1184-1189 (1993)
[Crossref]

D. H. Raguin and G. M. Morris, "Antireflection struc-tured surfaces for the infrared spectral region," Appl. Opt. 32,1154-1167 (1993)
[Crossref]

D. H. Raguin and G. M. Morris, "Analysis of an-tireflection-structured surfaces with continuous one-di-mensional surface profiles," Appl. Opt. 32, 2582-2598 (1993)
[Crossref]

D. Maystre, Selected papers on diffraction gratings, SPIE Milestone Series Vol. MS83 (SPIE, Bellingham, 1993)

E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, "Rigorous coupled-wave analysis and applications of grat-ing diffraction," in Diffractive and Miniaturized Optics, Crit-ical Reviews of Optical Science and Technology Vol. CR 49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.3-31
[Crossref]

D. H. Raguin, S. Norton and G. M. Morris, "Subwavelength structured surfaces and their applications," in Diffractive and Miniaturized Optics, Critical Reviews of Optical Science and Technology Vol. CR49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.234-261

1992 (2)

M. E. Motamedi, W. H. Southwell, and W. J. Gunning, "Antireflection surfaces in silicon using binary optics tech-nology," Appl. Opt. 31,4371-4375 (1992)
[Crossref]

S. T. Han, Y. Tsao, R. M. Walser, and M. F. Becker, "Electromagnetic scattering of two-dimensional surface-re-lief dielectric gratings," Appl. Opt. 31, 2343-2352 (1992)
[Crossref]

1991 (1)

W. H. Southwell, "Pyramid-array surface-relief structures producing antireflection index matching on optical sur-faces," J. Opt. Soc. Am. A8, 549-553 (1991)
[Crossref]

1988 (2)

E. N. Glytsis and T. K. Gaylord, "Antireflection surface structure: dielectric layer( s) over a high spatial-frequency surface-relief gratings on a lossy substrate," Appl. Opt. 27, 4288-4304 (1988)
[Crossref]

M, G. Moharam, "Coupled-Wave Analysis of Two-di-mensional Dielectric Gratings," Proc. Soc. Photo-Opt. In-strum, Eng. 883, 8-11 (1988)

1987 (1)

Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, "Antireflection effect in ultrahigh spatial-frequency hol-ographic relief gratings," Appl. Opt. 26, 1142-1146 (1987)
[Crossref]

1986 (1)

T. K. Gaylord, W. E. Baird, and M. G. Moharam, "Zero-reflectivitv high spatial frequency rectangular-groove dielectric surface-relief gratings," Appl. Opt. 25, 4562-4567 (1986)
[Crossref]

1985 (1)

T. K. Gaylord and M. G. Moharam, "Analysis and Ap-plications of Optical Diffraction by Gratings," Proc. IEEE 73, 894-937 (1985)
[Crossref]

1983 (1)

M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am, 73, 1105-1112 (1983)
[Crossref]

1982 (1)

M, G, Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982)
[Crossref]

1980 (1)

R. Petit, Ed., Electromagnetic Theory of Gratings, Topics in Current Physics, Vol.22 (Springer-Verlag, Berlin, 1980)

Applied Optics (8)

M. E. Motamedi, W. H. Southwell, and W. J. Gunning, "Antireflection surfaces in silicon using binary optics tech-nology," Appl. Opt. 31,4371-4375 (1992)
[Crossref]

T. K. Gaylord, W. E. Baird, and M. G. Moharam, "Zero-reflectivitv high spatial frequency rectangular-groove dielectric surface-relief gratings," Appl. Opt. 25, 4562-4567 (1986)
[Crossref]

Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, "Antireflection effect in ultrahigh spatial-frequency hol-ographic relief gratings," Appl. Opt. 26, 1142-1146 (1987)
[Crossref]

E. N. Glytsis and T. K. Gaylord, "Antireflection surface structure: dielectric layer( s) over a high spatial-frequency surface-relief gratings on a lossy substrate," Appl. Opt. 27, 4288-4304 (1988)
[Crossref]

D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, "Homogeneous layer models for high- spatial-frequency dielectric surface-relief gratings: conical diffraction and an-tireflection designs," Appl. Opt. 33, 2695-2706 (1994)
[Crossref]

D. H. Raguin and G. M. Morris, "Antireflection struc-tured surfaces for the infrared spectral region," Appl. Opt. 32,1154-1167 (1993)
[Crossref]

D. H. Raguin and G. M. Morris, "Analysis of an-tireflection-structured surfaces with continuous one-di-mensional surface profiles," Appl. Opt. 32, 2582-2598 (1993)
[Crossref]

S. T. Han, Y. Tsao, R. M. Walser, and M. F. Becker, "Electromagnetic scattering of two-dimensional surface-re-lief dielectric gratings," Appl. Opt. 31, 2343-2352 (1992)
[Crossref]

Diffractive and Miniaturized Optics (1)

E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, "Rigorous coupled-wave analysis and applications of grat-ing diffraction," in Diffractive and Miniaturized Optics, Crit-ical Reviews of Optical Science and Technology Vol. CR 49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.3-31
[Crossref]

JOSA (2)

M, G, Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982)
[Crossref]

M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am, 73, 1105-1112 (1983)
[Crossref]

JOSA A (5)

E. B. Grann, M. G. Moharam and D. A. Pommet, "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A 11, 2695-2703 (1994)
[Crossref]

E. B. Grann, M. G. Moharam and D. A. Pommet, "Optimal design for antireflective tapered two-di-mensional subwavelength grating structures," J. Opt. Soc. Am. A12, 333-339 (1995)
[Crossref]

E. B. Grann and M. G. Moharam, "Comparison between continuous and discrete subwavelength grating structures tor antireflectjon surfaces," J. Opt. Soc. Am. A13, 988-992 (1996)
[Crossref]

W. H. Southwell, "Pyramid-array surface-relief structures producing antireflection index matching on optical sur-faces," J. Opt. Soc. Am. A8, 549-553 (1991)
[Crossref]

L. Li and C. W. Haggans, "Convergence of the coupled-wave methods for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A10, 1184-1189 (1993)
[Crossref]

Korean Journal of Optics and Photonics (1)

D. Cho, "Eigenvalue problem pertaining to the rigorous three-dimensional vector coupled-wave analysis of dif-fraction from surface-relief gratings," Hankook Kwanghak Hoeji 5, 439-444 (1994)

Opt. Eng. (1)

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, "Subwavelength structures and their use in diffractive op-tics," Opt. Eng. 35, 726-731 (1996)
[Crossref]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, "Analysis and Ap-plications of Optical Diffraction by Gratings," Proc. IEEE 73, 894-937 (1985)
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M, G. Moharam, "Coupled-Wave Analysis of Two-di-mensional Dielectric Gratings," Proc. Soc. Photo-Opt. In-strum, Eng. 883, 8-11 (1988)

Other (4)

R. Petit, Ed., Electromagnetic Theory of Gratings, Topics in Current Physics, Vol.22 (Springer-Verlag, Berlin, 1980)

D. Maystre, Selected papers on diffraction gratings, SPIE Milestone Series Vol. MS83 (SPIE, Bellingham, 1993)

D. H. Raguin, S. Norton and G. M. Morris, "Subwavelength structured surfaces and their applications," in Diffractive and Miniaturized Optics, Critical Reviews of Optical Science and Technology Vol. CR49, S. H. Lee, ed. (SPIE, Bellingham, 1993) pp.234-261

netlib, Oak Ridge National Laboratory, Oak Ridge, TN, U.S.A.

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