Abstract

We propose omnidirectional reflective color filters based on metal-dielectric-metal subwavelength grating structure. By particle swarm optimization, the structural parameters of three color filters (yellow, magenta, cyan) are obtained. The optimized filters can present the same perceived specular color at unpolarized illumination for a broad range of incident angles. The reflectance curves at different incident angles keep almost invariable and the color difference is less than 6 in CIEDE2000 formula up to 45°. Angle-insensitive properties including the incident angular tolerance, azimuthal angular tolerance and the polarization effect are investigated thoroughly to construct a real omnidirectional color filter. Through the analysis of the magnetic field, the physical origin is verified that the total absorption band at specific wavelength results from the localized surface plasmon resonance responsible for the angle insensitive spectral filtering.

© 2014 Optical Society of America

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References

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2013

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

C. Yang, L. Hong, W. Shen, Y. Zhang, X. Liu, H. Zhen, “Design of reflective color filters with high angular tolerance by particle swarm optimization method,” Opt. Express 21(8), 9315–9323 (2013).
[CrossRef] [PubMed]

2012

J. Clausen, A. B. Christiansen, J. Garnaes, N. A. Mortensen, A. Kristensen, “Color effects from scattering on random surface structures in dielectrics,” Opt. Express 20(4), 4376–4381 (2012).
[CrossRef] [PubMed]

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

2010

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

2005

G. Sharma, W. Wu, E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30(1), 21–30 (2005).
[CrossRef]

2003

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

1997

1995

1994

1980

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. 22(3), 191–202 (1980).
[CrossRef]

1966

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Christiansen, A. B.

Clausen, J.

Dalal, E. N.

G. Sharma, W. Wu, E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30(1), 21–30 (2005).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Duan, H.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Garnaes, J.

Guo, L J.

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

Guo, L. J.

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

Hegde, R. S.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Hollowell, A. E

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

Hong, L.

Koh, S. C. W.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Kristensen, A.

Kumar, K.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Liu, X.

Luo, X.

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

Magnusson, R.

Mortensen, N. A.

Sharma, G.

G. Sharma, W. Wu, E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30(1), 21–30 (2005).
[CrossRef]

Shen, W.

Taflove, A.

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. 22(3), 191–202 (1980).
[CrossRef]

Tibuleac, S.

Wang, S. S.

Wei, J. N.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Wu, W.

G. Sharma, W. Wu, E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30(1), 21–30 (2005).
[CrossRef]

Wu, Y. K.

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

Wu, Y. K. R.

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

Xu, T.

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

Yang, C.

Yang, J. K. W.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Zhang, C.

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

Zhang, Y.

Zhen, H.

Appl. Opt.

Color Res. Appl.

G. Sharma, W. Wu, E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30(1), 21–30 (2005).
[CrossRef]

IEEE Trans. Antenn. Propag.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

IEEE Trans. Electromagn. Compat.

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. 22(3), 191–202 (1980).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Commun.

T. Xu, Y. K. Wu, X. Luo, L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).

Nat. Nanotechnol.

K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7(9), 557–561 (2012).
[CrossRef] [PubMed]

Nature

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Sci. Rep.

Y. K. R. Wu, A. E Hollowell, C. Zhang, L J. Guo, “Angle-insensitive structural colours based on metallic nanocavities and coloured pixels beyond the diffraction limit,” Sci. Rep. 3, 1194 (2013).

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, 1993).

T. Allen and C. H. Susan, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

R. C. Eberhart, J.Kennedy, and Y.Shi, Swarm Intelligence (Morgan Kaufmann, 2001).

CIE, Improvement to Industrial Colour Difference Evaluation (CIE, 2001).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

H. A. Macleod, Thin Film Optical Filters (Institute of Physics Pub, 2001).

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and S. A. Yanshin, “Design of multilayer coatings with specific angular dependencies of color properties,” in Conference on Optical Interference Coatings (Optical Society of America, 2007), paperWB2.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

The schematic geometry of the angle-insensitive reflective color filter of 2D sub-wavelength grating.

Fig. 2
Fig. 2

The reflection spectra of the color filters for the three colors of cyan, magenta, and yellow (CMY) color at normal incidence after optimization.

Fig. 3
Fig. 3

The reflection spectra of the proposed reflective color filters at various incident angles for unpolarized incidence (a) Yellow (b) Magenta (c) Cyan.

Fig. 4
Fig. 4

The CIE 1931 chromaticity coordinates of the three optimized color filters for the unpolarized light at the incident angles of 0°,10°, 20°, 30°, 40°, 50°, 60°.

Fig. 5
Fig. 5

The color difference calculated by CIEDE2000 formula at the oblique incidence up to 60° compared with the normal incidence.

Fig. 6
Fig. 6

The spectral reflectance curves of the optimized magenta filter for TE and TM polarized incidences at different incident angles (a) TE polarized (b) TM polarized.

Fig. 7
Fig. 7

The reflectance spectrum of the proposed yellow filter at various azimuthal angles with 45° incidence angle.

Fig. 8
Fig. 8

The magnetic field profile of the optimized yellow color filter at TM-polarized incidence.(a)-(b) The normal incidence with wavelength λ = 445nm and λ = 780 nm.

Tables (1)

Tables Icon

Table 1 Optimal Structural Parameters for CMY Color Filters

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