Abstract

The homogeneous behavior of periodic two-dimensional subwavelength surface-relief structures that contain both gratings and meshes (inverse gratings) are investigated. It is shown that when effective indices are synthesized near the higher index (substrate region), mesh structures yield larger feature sizes compared with their grating counterparts, whereas grating structures yield larger feature sizes when effective indices are synthesized near the lower index (incident region). For each type of structure investigated, a relation between the parameters of the structure and an effective refractive index is determined. It is shown that an equal area occupied by the high- or low-index media within the grating cell does not, in general, result in equal effective indices. The effective index of the grating is shown to be characterized by both the shape (local distribution) and the area of the high- or low-index medium within the unit grating cell. Finally, the advantages of subwavelength gratings and meshes are combined to produce hybrid grating–mesh structures that are less demanding on the fabrication process.

© 1996 Optical Society of America

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References

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  1. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  2. H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).
  3. W. Stork, N. Striebl, H. Hainer, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
    [CrossRef] [PubMed]
  4. M. W. Farn, “Binary gratings with increased efficiency,”Appl. Opt. 31, 4453–4458 (1992).
    [CrossRef] [PubMed]
  5. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
    [CrossRef]
  6. D. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–11671993).
    [CrossRef] [PubMed]
  7. D. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
    [CrossRef] [PubMed]
  8. E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
    [CrossRef]
  9. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).
  10. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  11. M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: P Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 8–111988).
  12. 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]

1994 (1)

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

1993 (2)

1992 (2)

1991 (2)

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

W. Stork, N. Striebl, H. Hainer, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

1990 (2)

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

1983 (1)

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

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Bagby, J. S.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

Cescato, L. H.

Farn, M. W.

Gaylord, T. K.

Gluch, E.

Glytsis, E. N.

Grann, E. B.

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

Haidner, H.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

Hainer, H.

Kipfer, P.

W. Stork, N. Striebl, H. Hainer, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

Magnusson, R.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

Moharam, M. G.

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

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

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

M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: P Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 8–111988).

Morris, G. M.

Pommet, D. A.

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

Raguin, D.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Stork, W.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

W. Stork, N. Striebl, H. Hainer, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

Streibl, N.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

Striebl, N.

Wang, S. S.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am (3)

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

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

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. 8, 1470–1475 (1990).
[CrossRef]

Opt. Lett. (1)

Optik (1)

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1991).

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Other (1)

M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: P Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 8–111988).

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Figures (11)

Fig. 1
Fig. 1

2D grating and mesh structures (na < nb).

Fig. 2
Fig. 2

Effective refractive indices of a symmetric 2D subwave-length-grating structure with a square feature within the unit cell plotted as a function of the filling factor f for na = 1.0 and nb = 3.0.

Fig. 3
Fig. 3

Effective refractive indices of a symmetric 2D subwavelength-mesh structure with a square feature within the unit cell plotted as a function of the removal factor r for na = 1.0 and nb = 3.0.

Fig. 4
Fig. 4

Grating and mesh structures (na < nb) with circular profiles within the unit cell.

Fig. 5
Fig. 5

Hybrid grating–mesh structure with a square profile within the unit cell.

Fig. 6
Fig. 6

Cross-shaped grating structure in which α is the sidelobe additive factor and f is the filling factor of a square feature.

Fig. 7
Fig. 7

Effective indices of the cross-shaped grating structure as a function of the sidelobe additive factor given a filling factor of 40.3% for na = 1.0 and nb = 3.0.

Fig. 8
Fig. 8

Three-dimensional illustration of the designed three-level square hybrid grating–mesh structure.

Fig. 9
Fig. 9

Reflectivity of the designed three-level antireflection structure for both the grating structure and an ideal thin-film structure (Λ = 1 μm, na = 1.0, and nb = 3.0). For the mesh level, r Λ = 597 nm and d = 1068 nm; for the cross-shaped grating level, f Λ = 403 nm, α = 83.75 nm, and d = 1797 nm.

Fig. 10
Fig. 10

Modified circular grating structure where β is the removal factor from the circular mesh structure.

Fig. 11
Fig. 11

Three-dimensional illustration of a three-level circular hybrid grating–mesh structure.

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