Abstract

High-spatial-frequency gratings can be used as an alternative to thin-film antireflection coatings to reduce the reflectivity at the boundary between two different media. In the case of one-dimensional gratings, the conditions on the grating structure can be approximately determined by the effective medium theory (EMT) in combination with the thin-film theory. For two-dimensional gratings, which can be used to reduce the polarization sensitivity, a corresponding EMT does not exist. We present an estimation of the effective permittivity of two-dimensional gratings. The range of validity of the antireflection grating design by the EMT is determined by the use of rigorous electromagnetic theory. Beyond the validity of EMT, rigorous theory is used to design antireflection gratings with a maximized feature size.

© 1994 Optical Society of America

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References

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    [Crossref]
  2. C. M. Horwitz, “A new solar selective surface,” Opt. Commun. 11, 210–212 (1974).
    [Crossref]
  3. M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
    [Crossref]
  4. R. C. McPhedran, D. Maystre, “On the theory and solar applications of inductive grids,” Appl. Phys. 14, 1–20 (1977).
    [Crossref]
  5. G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
    [Crossref]
  6. S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
    [Crossref]
  7. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [Crossref] [PubMed]
  8. P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
    [Crossref]
  9. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [Crossref] [PubMed]
  10. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [Crossref] [PubMed]
  11. 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, 3123–3134 (1987).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [Crossref] [PubMed]
  16. D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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1993 (3)

1992 (3)

1991 (2)

1987 (2)

1986 (1)

1983 (2)

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[Crossref] [PubMed]

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[Crossref]

1982 (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[Crossref]

1979 (1)

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

1977 (2)

1976 (1)

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

1974 (1)

C. M. Horwitz, “A new solar selective surface,” Opt. Commun. 11, 210–212 (1974).
[Crossref]

1973 (1)

P. B. Clapham, M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature (London) 244, 281–282 (1973).
[Crossref]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1912 (1)

O. Wiener, “Die Theorie des Mischkörpers für das Feld der stationären Strömung,” Abh. Math. Phys. Kl. Saechs. Akad. Wiss. 32, 505–604 (1912).

Baird, W. E.

Bloch, A. N.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Bräuer, R.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[Crossref]

Bryngdahl, O.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[Crossref]

Case, S. K.

Clapham, P. B.

P. B. Clapham, M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature (London) 244, 281–282 (1973).
[Crossref]

Derrick, G. H.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

Enger, R. C.

Gaylord, T. K.

Glytsis, E. N.

Gunning, W. J.

Haidner, H.

Horwitz, C. M.

C. M. Horwitz, “A new solar selective surface,” Opt. Commun. 11, 210–212 (1974).
[Crossref]

Hutley, M. C.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[Crossref]

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

P. B. Clapham, M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature (London) 244, 281–282 (1973).
[Crossref]

Kimura, Y.

Kipfer, P.

Maystre, D.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

R. C. McPhedran, D. Maystre, “On the theory and solar applications of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

McPhedran, R. C.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

R. C. McPhedran, D. Maystre, “On the theory and solar applications of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

Miller, J. M.

Moharam, M. G.

Morris, G. M.

Motamedi, M. E.

Nevière, M.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

Nishida, N.

Noponen, E.

Ohta, Y.

Ono, Y.

Raguin, D. H.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sheng, P.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[Crossref]

Southwell, W. H.

Stepleman, R. S.

P. Sheng, A. N. Bloch, R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[Crossref]

Stork, W.

Streibl, N.

Taghizadeh, M. R.

Turunen, J.

Vasara, A.

Wiener, O.

O. Wiener, “Die Theorie des Mischkörpers für das Feld der stationären Strömung,” Abh. Math. Phys. Kl. Saechs. Akad. Wiss. 32, 505–604 (1912).

Wilson, S. J.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Yariv, A.

Yeh, P.

Abh. Math. Phys. Kl. Saechs. Akad. Wiss. (1)

O. Wiener, “Die Theorie des Mischkörpers für das Feld der stationären Strömung,” Abh. Math. Phys. Kl. Saechs. Akad. Wiss. 32, 505–604 (1912).

Appl. Opt. (8)

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[Crossref] [PubMed]

M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
[Crossref] [PubMed]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[Crossref] [PubMed]

D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
[Crossref] [PubMed]

D. H. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
[Crossref] [PubMed]

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

Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
[Crossref] [PubMed]

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, 3123–3134 (1987).
[Crossref] [PubMed]

Appl. Phys. (2)

R. C. McPhedran, D. Maystre, “On the theory and solar applications of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
[Crossref]

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, 579–581 (1983).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nature (London) (1)

P. B. Clapham, M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature (London) 244, 281–282 (1973).
[Crossref]

Opt. Acta (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[Crossref]

Opt. Commun. (3)

C. M. Horwitz, “A new solar selective surface,” Opt. Commun. 11, 210–212 (1974).
[Crossref]

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[Crossref]

Opt. Lett. (1)

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

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Figures (7)

Fig. 1
Fig. 1

Stratified medium that is periodic in one dimension.

Fig. 2
Fig. 2

Cross section of a binary structure that is periodic in two dimensions.

Fig. 3
Fig. 3

Approximation of a structure periodic in two dimensions by a structure periodic in one dimension. In (a) the effective index of the regions replaced by a homogeneous distribution was determined by EMT for the TM mode and in (b) by EMT for the TE mode. E , electric field vector.

Fig. 4
Fig. 4

Diffraction geometry and the grating parameters.

Fig. 5
Fig. 5

Relative feature width as a function of grating period, determined by zeroth- and second-order EMT and rigorous optimization. The indices of the substrate are n2 = 1.5 in (a), (c), and (e) and n2 = 3.2 in (b), (d), and (f), (a) and (b) represent a 1-D grating in the TE mode, (c) and (d) a 1-D grating in the TM mode, and (e) and (f) a 2-D grating. [i] indicates the period length from which the ±ith transmitted order is nonevanescent.

Fig. 6
Fig. 6

Reflectivities corresponding to the parameters depicted in Figs. 5(a)–5(f).

Fig. 7
Fig. 7

Profile heights and relative feature widths that result in zero reflectivity. The indices of the substrate are n2 = 1.5 in (a), (c), and (e) and n2 = 3.4 in (b), (d), and (f). In (a) and (b) a 1-D grating in the TE mode was optimized, in (c) and (d) a 1-D grating in the TM mode was optimized, in (e) and (f) a 2-D grating was optimized.

Tables (2)

Tables Icon

Table 1 Profile Heights and Effective Indices that Result from the TFT and Relative Feature Widths Determined by the Zeroth-Order EMTa

Tables Icon

Table 2 Maximum Grating Period, Feature Width, and Profile Height of a 2-D Binary Grating at 500 nm with n2 = 1.5 Achieved by Different Design Methods

Equations (10)

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

( 0 ) = ( 1 f ) 1 + f 2 ,
1 / ( 0 ) = ( 1 f ) / 1 + f / 2
( 2 ) | = | ( 0 ) [ 1 + π 2 3 ( d λ ) 2 f 2 ( 1 f ) 2 ( 2 1 ) 2 0 ( 0 ) ] ,
( 2 ) | = | ( 0 ) [ 1 + π 2 3 ( d λ ) 2 f 2 ( 1 f ) 2 × ( 2 1 ) 2 ( 0 ) 0 ( ( 0 ) 2 1 ) 2 ]
n ̅ = ( 1 f 2 ) n 1 + f 2 n 2
̂ 2 D ( 0 ) = ( 1 f ) 1 + f ( 0 ) ,
1 / ˇ 2 D ( 0 ) = ( 1 f ) / 1 + f / ( 0 ) ,
n 2 D ( 0 ) = [ n ̅ + 2 n ̂ 2 D ( 0 ) + 2 n ˇ 2 D ( 0 ) ] / 5 ,
n f = ( n 1 n 2 ) 1 / 2 ,
h = λ / 4 n f .

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