Abstract

A systematic procedure using the effective index method and impedance matching has recently been developed Appl. Opt. 26, 3123 ( 1987)] for the design of antireflection high-spatial-frequency rectangular-groove gratings on lossy materials including high conductivity metals. The design procedure in turn can be used as a starting point to design antireflection metallic gratings with lower spatial frequencies using rigorous coupled-wave analysis. These lower spatial-frequency gratings have the advantage of being easier to fabricate. In the present work, a particular antireflection gold grating design (having a period of 1.0 μm, a filling factor of 50%, and a groove depth of 147.5 nm for use at a freespace wavelength of 500 nm, normal incidence, and polarization parallel to the grooves) was fabricated and its diffraction characteristics experimentally measured. The grating indeed showed very nearly zero specular reflection in the blue region of the spectrum. Unlike previously reported antireflection anomalies, the effect is broadband occurring over a broad range of wavelengths and angles of incidence, and for both orthogonal polarizations. This work clearly shows that the systematic design of zero specular reflection grating surfaces is possible.

© 1988 Optical Society of America

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References

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  1. P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-Selective Absorption Enhancement in Thin-Film Solar Cells,” Appl. Phys. Lett. 43, 579 (1983).
    [CrossRef]
  2. R. W. Wood, “On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum,” Philos. Mag. 4, 396 (1902).
    [CrossRef]
  3. R. W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928 (1935).
    [CrossRef]
  4. M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
    [CrossRef]
  5. E. G. Loewen, M. Neviere, “Dielectric Coated Gratings: A Curious Property,” Appl. Opt. 16, 3009 (1977).
    [CrossRef] [PubMed]
  6. L. Mashev, E. Popov, “Diffraction Efficiency Anomalies of Multicoated Dielectric Gratings,” Opt. Commun. 51, 131 (1984).
    [CrossRef]
  7. M. C. Hutley, “An Experimental Study of the Anomalies of Sinusoidal Diffraction Gratings,” Opt. Acta 20, 607 (1973).
    [CrossRef]
  8. M. C. Hutley, V. M. Bird, “A Detailed Experimental Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 20, 771 (1973).
    [CrossRef]
  9. R. C. McPhedran, D. Maystre, “A Detailed Theoretical Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 21, 413 (1974).
    [CrossRef]
  10. D. Maystre, F. Petit, “Brewster Incidence for Metallic Gratings,” Opt. Commun. 17, 196 (1976).
    [CrossRef]
  11. D. Maystre, M. Neviere, “Sur Une Methode D’Etude Theorique Quantitative des Anomalies de Wood des Reseaux de Diffraction: Application aux Anomalies de Plasmons,” J. Opt. Paris 8, 165 (1977).
    [CrossRef]
  12. M. C. Hutley, D. Maystre, “The Total Absorption of Light by a Diffraction Grating,” Opt. Commun. 19, 431 (1976).
    [CrossRef]
  13. E. G. Loewen, M. Neviere, D. Maystre, “Efficiency Optimization of Rectangular Groove Gratings for Use in the Visible and IR Regions,” Appl. Opt. 18, 2262 (1979).
    [CrossRef] [PubMed]
  14. K. Knop, “Reflection Grating Polarizer for the Infrared,” Opt. Commun. 26, 281 (1978).
    [CrossRef]
  15. J. Hagglund, F. Sellberg, “Reflection, Absorption, and Emission of Light by Opaque Optical Gratings,” J. Opt. Soc. Am. 56, 1031 (1966).
    [CrossRef]
  16. G. W. Ford, W. H. Weber, “Electromagnetic Interactions of Molecules with Metal Surfaces,” Phys. Rep. 113, 195 (1984).
    [CrossRef]
  17. M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
    [CrossRef]
  18. H. Raether, “Dispersion Relation of Surface Plasmons on Gold and Silver Gratings,” Opt. Commun. 42, 217 (1982).
    [CrossRef]
  19. V. Shah, T. Tamir, “Brewster Phenomena in Lossy Structures,” Opt. Commun. 23, 113 (1977).
    [CrossRef]
  20. V. Shah, T. Tamir, “Anomalous Absorption by Multi-Layered Media,” Opt. Commun. 37, 383 (1981).
    [CrossRef]
  21. M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-Relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
    [CrossRef]
  22. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-Reflectivity High Spatial-Frequency Rectangular-Groove Dielectric Surface-Relief Gratings,” Appl. Opt. 25, 4562 (1986).
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  24. R. C. Enger, S. K. Case, “Optical Elements with Ultrahigh Spatial-Frequency Surface Corrugations,” Appl. Opt. 22, 3220 (1983).
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  25. T. K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-Reflectivity Homogeneous Layers and High Spatial-Frequency Surface-Relief Gratings on Lossy Materials,” Appl. Opt. 26, 3123 (1987).
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  26. M. G. Moharam, T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Metallic Surface-Relief Gratings,” J. Opt. Soc. Am. A 3, 1780 (1986).
    [CrossRef]
  27. O. Wiener, “Die Theorie des Mischkorpers für das Feld der Stationaren Strömung,” Abh. Math. Phys. Kl. Sachs. Akad. Wiss. Leipzig 32, 509 (1912).
  28. G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–119.
  29. Newport Corp, 18235 Mt. Baldy Circle, Fountain Valley, CA 92728-8020.

1987 (1)

1986 (2)

1984 (2)

L. Mashev, E. Popov, “Diffraction Efficiency Anomalies of Multicoated Dielectric Gratings,” Opt. Commun. 51, 131 (1984).
[CrossRef]

G. W. Ford, W. H. Weber, “Electromagnetic Interactions of Molecules with Metal Surfaces,” Phys. Rep. 113, 195 (1984).
[CrossRef]

1983 (3)

1982 (2)

M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-Relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
[CrossRef]

H. Raether, “Dispersion Relation of Surface Plasmons on Gold and Silver Gratings,” Opt. Commun. 42, 217 (1982).
[CrossRef]

1981 (1)

V. Shah, T. Tamir, “Anomalous Absorption by Multi-Layered Media,” Opt. Commun. 37, 383 (1981).
[CrossRef]

1979 (1)

1978 (1)

K. Knop, “Reflection Grating Polarizer for the Infrared,” Opt. Commun. 26, 281 (1978).
[CrossRef]

1977 (4)

V. Shah, T. Tamir, “Brewster Phenomena in Lossy Structures,” Opt. Commun. 23, 113 (1977).
[CrossRef]

M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
[CrossRef]

D. Maystre, M. Neviere, “Sur Une Methode D’Etude Theorique Quantitative des Anomalies de Wood des Reseaux de Diffraction: Application aux Anomalies de Plasmons,” J. Opt. Paris 8, 165 (1977).
[CrossRef]

E. G. Loewen, M. Neviere, “Dielectric Coated Gratings: A Curious Property,” Appl. Opt. 16, 3009 (1977).
[CrossRef] [PubMed]

1976 (2)

M. C. Hutley, D. Maystre, “The Total Absorption of Light by a Diffraction Grating,” Opt. Commun. 19, 431 (1976).
[CrossRef]

D. Maystre, F. Petit, “Brewster Incidence for Metallic Gratings,” Opt. Commun. 17, 196 (1976).
[CrossRef]

1974 (2)

R. C. McPhedran, D. Maystre, “A Detailed Theoretical Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 21, 413 (1974).
[CrossRef]

M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
[CrossRef]

1973 (2)

M. C. Hutley, “An Experimental Study of the Anomalies of Sinusoidal Diffraction Gratings,” Opt. Acta 20, 607 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A Detailed Experimental Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 20, 771 (1973).
[CrossRef]

1966 (1)

1935 (1)

R. W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928 (1935).
[CrossRef]

1912 (1)

O. Wiener, “Die Theorie des Mischkorpers für das Feld der Stationaren Strömung,” Abh. Math. Phys. Kl. Sachs. Akad. Wiss. Leipzig 32, 509 (1912).

1902 (1)

R. W. Wood, “On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum,” Philos. Mag. 4, 396 (1902).
[CrossRef]

Baird, W. E.

Bird, V. M.

M. C. Hutley, V. M. Bird, “A Detailed Experimental Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 20, 771 (1973).
[CrossRef]

Bloch, A. N.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-Selective Absorption Enhancement in Thin-Film Solar Cells,” Appl. Phys. Lett. 43, 579 (1983).
[CrossRef]

Case, S. K.

Enger, R. C.

Ford, G. W.

G. W. Ford, W. H. Weber, “Electromagnetic Interactions of Molecules with Metal Surfaces,” Phys. Rep. 113, 195 (1984).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Hadley, L.

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–119.

Hagglund, J.

Hass, G.

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–119.

Hutley, M. C.

M. C. Hutley, D. Maystre, “The Total Absorption of Light by a Diffraction Grating,” Opt. Commun. 19, 431 (1976).
[CrossRef]

M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
[CrossRef]

M. C. Hutley, “An Experimental Study of the Anomalies of Sinusoidal Diffraction Gratings,” Opt. Acta 20, 607 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A Detailed Experimental Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 20, 771 (1973).
[CrossRef]

Knop, K.

K. Knop, “Reflection Grating Polarizer for the Infrared,” Opt. Commun. 26, 281 (1978).
[CrossRef]

Loewen, E. G.

Mashev, L.

L. Mashev, E. Popov, “Diffraction Efficiency Anomalies of Multicoated Dielectric Gratings,” Opt. Commun. 51, 131 (1984).
[CrossRef]

Maystre, D.

E. G. Loewen, M. Neviere, D. Maystre, “Efficiency Optimization of Rectangular Groove Gratings for Use in the Visible and IR Regions,” Appl. Opt. 18, 2262 (1979).
[CrossRef] [PubMed]

D. Maystre, M. Neviere, “Sur Une Methode D’Etude Theorique Quantitative des Anomalies de Wood des Reseaux de Diffraction: Application aux Anomalies de Plasmons,” J. Opt. Paris 8, 165 (1977).
[CrossRef]

M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
[CrossRef]

M. C. Hutley, D. Maystre, “The Total Absorption of Light by a Diffraction Grating,” Opt. Commun. 19, 431 (1976).
[CrossRef]

D. Maystre, F. Petit, “Brewster Incidence for Metallic Gratings,” Opt. Commun. 17, 196 (1976).
[CrossRef]

R. C. McPhedran, D. Maystre, “A Detailed Theoretical Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 21, 413 (1974).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, D. Maystre, “A Detailed Theoretical Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 21, 413 (1974).
[CrossRef]

M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
[CrossRef]

Moharam, M. G.

Neviere, M.

E. G. Loewen, M. Neviere, D. Maystre, “Efficiency Optimization of Rectangular Groove Gratings for Use in the Visible and IR Regions,” Appl. Opt. 18, 2262 (1979).
[CrossRef] [PubMed]

D. Maystre, M. Neviere, “Sur Une Methode D’Etude Theorique Quantitative des Anomalies de Wood des Reseaux de Diffraction: Application aux Anomalies de Plasmons,” J. Opt. Paris 8, 165 (1977).
[CrossRef]

E. G. Loewen, M. Neviere, “Dielectric Coated Gratings: A Curious Property,” Appl. Opt. 16, 3009 (1977).
[CrossRef] [PubMed]

M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
[CrossRef]

Petit, F.

D. Maystre, F. Petit, “Brewster Incidence for Metallic Gratings,” Opt. Commun. 17, 196 (1976).
[CrossRef]

Popov, E.

L. Mashev, E. Popov, “Diffraction Efficiency Anomalies of Multicoated Dielectric Gratings,” Opt. Commun. 51, 131 (1984).
[CrossRef]

Raether, H.

H. Raether, “Dispersion Relation of Surface Plasmons on Gold and Silver Gratings,” Opt. Commun. 42, 217 (1982).
[CrossRef]

Sellberg, F.

Shah, V.

V. Shah, T. Tamir, “Anomalous Absorption by Multi-Layered Media,” Opt. Commun. 37, 383 (1981).
[CrossRef]

V. Shah, T. Tamir, “Brewster Phenomena in Lossy Structures,” Opt. Commun. 23, 113 (1977).
[CrossRef]

Sheng, P.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-Selective Absorption Enhancement in Thin-Film Solar Cells,” Appl. Phys. Lett. 43, 579 (1983).
[CrossRef]

Stepleman, R. S.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-Selective Absorption Enhancement in Thin-Film Solar Cells,” Appl. Phys. Lett. 43, 579 (1983).
[CrossRef]

Tamir, T.

V. Shah, T. Tamir, “Anomalous Absorption by Multi-Layered Media,” Opt. Commun. 37, 383 (1981).
[CrossRef]

V. Shah, T. Tamir, “Brewster Phenomena in Lossy Structures,” Opt. Commun. 23, 113 (1977).
[CrossRef]

Verrill, J. F.

M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
[CrossRef]

Vincent, P.

M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
[CrossRef]

Weber, W. H.

G. W. Ford, W. H. Weber, “Electromagnetic Interactions of Molecules with Metal Surfaces,” Phys. Rep. 113, 195 (1984).
[CrossRef]

Wiener, O.

O. Wiener, “Die Theorie des Mischkorpers für das Feld der Stationaren Strömung,” Abh. Math. Phys. Kl. Sachs. Akad. Wiss. Leipzig 32, 509 (1912).

Wood, R. W.

R. W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928 (1935).
[CrossRef]

R. W. Wood, “On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum,” Philos. Mag. 4, 396 (1902).
[CrossRef]

Abh. Math. Phys. Kl. Sachs. Akad. Wiss. Leipzig (1)

O. Wiener, “Die Theorie des Mischkorpers für das Feld der Stationaren Strömung,” Abh. Math. Phys. Kl. Sachs. Akad. Wiss. Leipzig 32, 509 (1912).

Appl. Opt. (5)

Appl. Phys. Lett. (1)

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-Selective Absorption Enhancement in Thin-Film Solar Cells,” Appl. Phys. Lett. 43, 579 (1983).
[CrossRef]

J. Opt. Paris (2)

D. Maystre, M. Neviere, “Sur Une Methode D’Etude Theorique Quantitative des Anomalies de Wood des Reseaux de Diffraction: Application aux Anomalies de Plasmons,” J. Opt. Paris 8, 165 (1977).
[CrossRef]

M. Neviere, D. Maystre, P. Vincent, “Application du Calcul des Modes de Propagation a L’Etude Théorique des Anomalies des Reseaux Recouverts de Dielectrique,” J. Opt. Paris 8, 231 (1977).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Acta (3)

M. C. Hutley, “An Experimental Study of the Anomalies of Sinusoidal Diffraction Gratings,” Opt. Acta 20, 607 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A Detailed Experimental Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 20, 771 (1973).
[CrossRef]

R. C. McPhedran, D. Maystre, “A Detailed Theoretical Study of the Anomalies of a Sinusoidal Diffraction Grating,” Opt. Acta 21, 413 (1974).
[CrossRef]

Opt. Commun. (8)

D. Maystre, F. Petit, “Brewster Incidence for Metallic Gratings,” Opt. Commun. 17, 196 (1976).
[CrossRef]

M. C. Hutley, D. Maystre, “The Total Absorption of Light by a Diffraction Grating,” Opt. Commun. 19, 431 (1976).
[CrossRef]

M. C. Hutley, J. F. Verrill, R. C. McPhedran, “The Effect of a Dielectric Layer on the Diffraction Anomalies of an Optical Grating,” Opt. Commun. 11, 207 (1974).
[CrossRef]

H. Raether, “Dispersion Relation of Surface Plasmons on Gold and Silver Gratings,” Opt. Commun. 42, 217 (1982).
[CrossRef]

V. Shah, T. Tamir, “Brewster Phenomena in Lossy Structures,” Opt. Commun. 23, 113 (1977).
[CrossRef]

V. Shah, T. Tamir, “Anomalous Absorption by Multi-Layered Media,” Opt. Commun. 37, 383 (1981).
[CrossRef]

K. Knop, “Reflection Grating Polarizer for the Infrared,” Opt. Commun. 26, 281 (1978).
[CrossRef]

L. Mashev, E. Popov, “Diffraction Efficiency Anomalies of Multicoated Dielectric Gratings,” Opt. Commun. 51, 131 (1984).
[CrossRef]

Philos. Mag. (1)

R. W. Wood, “On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum,” Philos. Mag. 4, 396 (1902).
[CrossRef]

Phys. Rep. (1)

G. W. Ford, W. H. Weber, “Electromagnetic Interactions of Molecules with Metal Surfaces,” Phys. Rep. 113, 195 (1984).
[CrossRef]

Phys. Rev. (1)

R. W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928 (1935).
[CrossRef]

Other (2)

G. Hass, L. Hadley, “Optical Properties of Metals,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–119.

Newport Corp, 18235 Mt. Baldy Circle, Fountain Valley, CA 92728-8020.

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Figures (5)

Fig. 1
Fig. 1

Diffraction geometry of gold rectangular-groove surface-relief grating.

Fig. 2
Fig. 2

Experimental configuration for measurement of reflectance at normal incidence as a function of wavelength and polarization.

Fig. 3
Fig. 3

Experimentally measured reflectance of gold flat surface at normal incidence as a function of wavelength from present work (solid line) and from Handbook of Physics (dashed line).

Fig. 4
Fig. 4

Experimentally measured zero-order (specular) reflectance at normal incidence of gold antireflection grating as a function of wavelength for EK polarization (optical electric field parallel to grooves) and for HK polarization (optical electric field perpendicular to grooves). A very pronounced antireflection effect is apparent in the neighborhood of λ0 = 475 nm.

Fig. 5
Fig. 5

Zero-order (specular) reflectance of gold antireflection grating as a function of angle of incidence at λ0 = 500 nm. Experimentally measured values (open circles), calculated values from rigorous coupled-wave analysis (solid line), and calculated values from the homogeneous lossy layer that is equivalent to the grating in the short-period limit (dashed line) are shown. The very broad angular selectivity of the grating is apparent in all three sets of data.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

i λ 0 / n 1 = Λ ( sin θ + sin θ i ) ,
A ( λ 0 , P ) = r bs ( λ 0 , P ) I 0 ( λ 0 , P ) ,
B ( λ 0 , P ) = [ 1 - r bs ( λ 0 , P ) ] r obj ( λ 0 , P ) r bs ( λ 0 , P ) I 0 ( λ 0 , P ) ,
R ( λ 0 , P ) = B ( λ 0 , P ) / A ( λ 0 , P ) = [ 1 - r bs ( λ 0 , P ) ] r obj ( λ 0 , P ) .
r bs ( λ 0 , P ) = 1 - R ( λ 0 , P ) r obj ( λ 0 , P ) .
r obj ( λ 0 , P ) = R ( λ 0 , P ) 1 - r bs ( λ 0 , P ) .

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