Abstract

We present a study on subwavelength-structured surfaces with optimized color properties and antireflection properties in the range of the visible spectrum. Problematic blueness of the nanostructured surface has been eliminated under viewing angles from 0 to 35deg by designing and optimizing the antireflective surface parameters. The rigorous diffraction theory is used to minimize the surface reflection by simultaneously keeping the chromaticity coordinates of the reflected light in the white domain. The theoretical results are experimentally verified, and the (x,y)-chromaticity coordinates of the surface are shown to be independent of the structure of the surface on small periods.

© 2007 Optical Society of America

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References

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  1. H. A. Macleod, Thin-Film Optical Filters (Hilger, 1979).
  2. U. Schulz, "AR-hard-coating with adjustable spectral bandwidth for plastic optics," MIICS 2004 (2005).
  3. "Anti-reflection coatings," http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/antiref.html.
  4. G. Bernhard, "Structural and functional adaptation in a visual system," Endeavour 26, 79-84 (1967).
  5. S. J. Wilson and M. C. Hutley, "The optical properties of 'moth eye' antireflection surfaces," Opt. Acta 29, 993-1009 (1982).
    [CrossRef]
  6. Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
    [CrossRef]
  7. P. B. Clapham and M. C. Hutley, "Reduction of lens reflexion by the moth eye principle," Nature 244, 281-282 (1973).
    [CrossRef]
  8. J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).
  9. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).
  10. E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 9, 2494-2502 (1994).
    [CrossRef]
  11. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  12. K. L. Kelly, "Color designation for lights," J. Opt. Soc. Am. 33, 627-632 (1943).
    [CrossRef]
  13. J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
    [CrossRef]

2006 (1)

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

2005 (1)

Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

1997 (1)

1994 (1)

E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 9, 2494-2502 (1994).
[CrossRef]

1982 (1)

S. J. Wilson and M. C. Hutley, "The optical properties of 'moth eye' antireflection surfaces," Opt. Acta 29, 993-1009 (1982).
[CrossRef]

1973 (1)

P. B. Clapham and M. C. Hutley, "Reduction of lens reflexion by the moth eye principle," Nature 244, 281-282 (1973).
[CrossRef]

1967 (1)

G. Bernhard, "Structural and functional adaptation in a visual system," Endeavour 26, 79-84 (1967).

1943 (1)

Bernhard, G.

G. Bernhard, "Structural and functional adaptation in a visual system," Endeavour 26, 79-84 (1967).

Chen, Y.

Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Clapham, P. B.

P. B. Clapham and M. C. Hutley, "Reduction of lens reflexion by the moth eye principle," Nature 244, 281-282 (1973).
[CrossRef]

Hutley, M. C.

S. J. Wilson and M. C. Hutley, "The optical properties of 'moth eye' antireflection surfaces," Opt. Acta 29, 993-1009 (1982).
[CrossRef]

P. B. Clapham and M. C. Hutley, "Reduction of lens reflexion by the moth eye principle," Nature 244, 281-282 (1973).
[CrossRef]

Kanamori, Y.

Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Kelly, K. L.

Kuittinen, M.

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Laukkanen, J.

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Li, L.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Hilger, 1979).

Noponen, E.

E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 9, 2494-2502 (1994).
[CrossRef]

Pietarinen, J.

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Roy, E.

Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Schulz, U.

U. Schulz, "AR-hard-coating with adjustable spectral bandwidth for plastic optics," MIICS 2004 (2005).

Siitonen, S.

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).

Tossavainen, N.

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Turunen, J.

E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 9, 2494-2502 (1994).
[CrossRef]

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

Wilson, S. J.

S. J. Wilson and M. C. Hutley, "The optical properties of 'moth eye' antireflection surfaces," Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Wyrowski, F.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).

Endeavour (1)

G. Bernhard, "Structural and functional adaptation in a visual system," Endeavour 26, 79-84 (1967).

J. Opt. Soc. Am. (1)

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

E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 9, 2494-2502 (1994).
[CrossRef]

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

Microelectron. Eng. (2)

J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, "Fabrication of Ni-shims using UV-moulding as an intermediate step," Microelectron. Eng. 83, 492-498 (2006).
[CrossRef]

Y. Kanamori, E. Roy, and Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectron. Eng. 78-79, 287-293 (2005).
[CrossRef]

Nature (1)

P. B. Clapham and M. C. Hutley, "Reduction of lens reflexion by the moth eye principle," Nature 244, 281-282 (1973).
[CrossRef]

Opt. Acta (1)

S. J. Wilson and M. C. Hutley, "The optical properties of 'moth eye' antireflection surfaces," Opt. Acta 29, 993-1009 (1982).
[CrossRef]

Other (5)

H. A. Macleod, Thin-Film Optical Filters (Hilger, 1979).

U. Schulz, "AR-hard-coating with adjustable spectral bandwidth for plastic optics," MIICS 2004 (2005).

"Anti-reflection coatings," http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/antiref.html.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).

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Figures (11)

Fig. 1
Fig. 1

Three-dimensional grating structure and profiles for (a) square-shaped pillars and (b) square-shaped holes.

Fig. 2
Fig. 2

Three optimization constructions: (a) square pillars/holes in a grid, (b) cylindrical pillars/holes in a grid, and (c) cylindrical pillars/holes in a hexagonal grid.

Fig. 3
Fig. 3

Effect of the grating period on the reflectance on cylinder-shaped pillars under three viewing angles. (a) The period’s are (a) 370 and (b) 270 nm . The subscript tf denotes that thin-film calculations have been used to obtain those reflectances.

Fig. 4
Fig. 4

Calculated transmittance curves for the periods (a) 270 and (b) 370 nm .

Fig. 5
Fig. 5

(a) Calculated reflectance curves with optimized parameters for cylinder-shaped pillars and (b) the corresponding CIE chromaticity coordinates. The period d x = d y = 270 nm .

Fig. 6
Fig. 6

(a) Calculated reflectance curves with optimized parameters for square-shaped pillars and (b) the corresponding CIE chromaticity coordinates. The period d x = d y = 270 nm .

Fig. 7
Fig. 7

(a) Calculated reflectance curves with the optimized parameters for cylinder-shaped pillars and (b) the corresponding CIE chromaticity coordinates. The period d x = d y = 370 nm .

Fig. 8
Fig. 8

(a) Calculated reflectance curves with optimized parameters for square-shaped pillars and (b) the corresponding CIE chromaticity coordinates. The period d x = d y = 370 nm .

Fig. 9
Fig. 9

(a) Experimental reflectance curves measured with an ellipsometer and (b) the corresponding CIE chromaticity coordinates. Period d x = d y = 370 nm .

Fig. 10
Fig. 10

(Color online) Effect of the height variation on the reflectance curves and the chromaticity coordinates. Subscripts − and + denote the height changes Δ h and + Δ h , respectively, at two incident angles for square-shaped pillars. The period d x = d y = 370 nm .

Fig. 11
Fig. 11

SEM illustrations of the fabricated element: (a) the top view and (b) the cross section.

Tables (2)

Tables Icon

Table 1 Reflectances for Different Structure Types at Three Wavelengths and Two Incident Angles

Tables Icon

Table 2 Reflectances for Different Structure Types at Three Wavelengths and Two Incident Angles a

Equations (3)

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

n e = γ k ,
k 2 n III 2 sin 2 θ m , n = ( k n I sin θ cos ϕ + 2 π m d x ) 2 + ( k n I sin θ cos θ + 2 π n d y ) 2 ,
d x , d y λ n .

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