Abstract

We propose three color filters (red, green, blue) based on a two-dimensional (2D) grating, which maintain the same perceived specular colors for a broad range of incident angles with the average polarization. Particle swarm optimization (PSO) method is employed to design these filters for the first time to our knowledge. Two merit functions involving the reflectance curves and color difference in CIEDE2000 formula are respectively constructed to adjust the structural parameters during the optimization procedure. Three primary color filters located at 637nm, 530nm and 446nm with high saturation are obtained with the peak reflectance of 89%, 83%, 66%. The reflectance curves at different incident angles are coincident and the color difference is less than 8 for the incident angle up to 45°. The electric field distribution of the structure is finally studied to analyze the optical property.

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References

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    [CrossRef]
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    [CrossRef]
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2010

2009

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

2006

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett.18(20), 2126–2128 (2006).
[CrossRef]

2005

G. Sharma, W. Wu, and 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]

2001

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl.26(5), 340–350 (2001).
[CrossRef]

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. EMC22(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]

Chen, Q.

Cheong, B. H.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Cho, E.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Cho, Y. S.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Choi, H. Y.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Cui, G.

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl.26(5), 340–350 (2001).
[CrossRef]

Cumming, D. R. S.

Dalal, E. N.

G. Sharma, W. Wu, and 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]

Danner, A. J.

G. Y. Si, E. S. P. Leong, A. J. Danner, and J. H. Teng, “Plasmonic coaxial fabry-pérot nanocavity color filter,” Proc. SPIE7757, 7757 (2010).

Gu, P.

Hane, K.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett.18(20), 2126–2128 (2006).
[CrossRef]

Kanamori, Y.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett.18(20), 2126–2128 (2006).
[CrossRef]

Kim, H. S.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Leong, E. S. P.

G. Y. Si, E. S. P. Leong, A. J. Danner, and J. H. Teng, “Plasmonic coaxial fabry-pérot nanocavity color filter,” Proc. SPIE7757, 7757 (2010).

Liu, X.

Luo, M. R.

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl.26(5), 340–350 (2001).
[CrossRef]

Luo, Z.

Magnusson, R.

Prudnikov, O. N.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Rigg, B.

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl.26(5), 340–350 (2001).
[CrossRef]

Sharma, G.

G. Sharma, W. Wu, and 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.

Shimono, M.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett.18(20), 2126–2128 (2006).
[CrossRef]

Shin, S. T.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Si, G. Y.

G. Y. Si, E. S. P. Leong, A. J. Danner, and J. H. Teng, “Plasmonic coaxial fabry-pérot nanocavity color filter,” Proc. SPIE7757, 7757 (2010).

Taflove, A.

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC22(3), 191–202 (1980).
[CrossRef]

Teng, J. H.

G. Y. Si, E. S. P. Leong, A. J. Danner, and J. H. Teng, “Plasmonic coaxial fabry-pérot nanocavity color filter,” Proc. SPIE7757, 7757 (2010).

Tibuleac, S.

Wang, S. S.

Wu, W.

G. Sharma, W. Wu, and 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]

Xia, C.

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]

Yu, J.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

B. H. Cheong, O. N. Prudnikov, E. Cho, H. S. Kim, J. Yu, Y. S. Cho, H. Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett.94(21), 213104 (2009).
[CrossRef]

Chin. Opt. Lett.

Color Res. Appl.

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl.26(5), 340–350 (2001).
[CrossRef]

G. Sharma, W. Wu, and 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 Photon. Technol. Lett.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett.18(20), 2126–2128 (2006).
[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. EMC

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC22(3), 191–202 (1980).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

G. Y. Si, E. S. P. Leong, A. J. Danner, and J. H. Teng, “Plasmonic coaxial fabry-pérot nanocavity color filter,” Proc. SPIE7757, 7757 (2010).

Other

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

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).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th Ed. (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.

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

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

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Figures (10)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

The trend of the merit function Merit2 during the optimization with PSO method.

Fig. 3
Fig. 3

The reflectance curves of blue filters for the unpolarized light at various incident angles (a) the unoptimized blue filter (b) the optimized blue filter. Aimed at the expected central wavelength, the structure parameters of the unoptimized one are generated randomly with Λxy=260nm, Lx=Ly=80nm, dx=dy=50nm, and t=100nm, respectively.

Fig. 4
Fig. 4

The CIE 1931 chromaticity coordinates of the three primary color filters for the unpolarized light at the incident angles of 0°,15°,30°,45°.

Fig. 5
Fig. 5

The reflectance spectral characteristic of the optimized blue filter at TE and TM polarized incidences at different incident angles (a) TE polarized incidence (b) TM polarized incidence.

Fig. 6
Fig. 6

The reflectance of green and red color filters with initial structure parameters at the unpolarized incident light (a) green filter (b) red filter. For green filter, the structure parameters are Λxy=308nm, Lx=Ly=126nm, dx=dy=28nm, and t=112nm, while for red filter, the initial parameters are Λxy=396nm, Lx=Ly=162nm, dx=dy=36nm, and t=144nm, respectively.

Fig. 7
Fig. 7

The reflectance of the two optimized color filters at the unpolarized incident light (a) the optimized green filter (b) the optimized red filter. After optimization, for the green filter, the structure parameters are Λxy=340nm, Lx=Ly=140.5nm, dx=dy=29.5nm, and t=93nm, while for the red filter, the initial parameters are Λxy=444nm, Lx=Ly=178nm, dx=dy=44nm, and t=123nm, respectively.

Fig. 8
Fig. 8

The color difference calculated by CIE DE2000 formula at different incident angle compared with the normal incidence.

Fig. 9
Fig. 9

The electric field profile of the optimized green color filter at TM-polarized incidence. (a)-(b) The normal incidence with wavelength λ = 530 nm and λ = 610 nm. (c)-(d) The incident angle of 45° with wavelength λ = 530 nm and λ = 610 nm. The electric field profile records the electric filed in the yz plane, while the incident light propagating in the xz plane, with TM polarization.

Fig. 10
Fig. 10

The electric field profile of the optimized green color filter at TE-polarized incidence. (a)-(b) The normal incidence with wavelength λ = 530 nm and λ = 610 nm. (c)-(d) The incident angle of 45° with wavelength λ = 530 nm and λ = 610 nm. The electric field profile records the electric filed in the xz plane, while the incident light propagating in the xz plane, with TE polarization.

Equations (2)

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Merit1= λ=380 λ=780 W 1 ( λ ) ( R 0 ( λ ) R target ( λ ) ) 2 + λ=380 λ=780 W 2 ( λ ) ( ( R θ,TM ( λ )+ R θ,TE ( λ ) ) /2 R 0 ( λ ) ) 2
Merit2= λ=380 λ=780 W 1 ( λ ) ( R 0 ( λ ) R target ( λ ) ) 2 + W 3 ×Δ E 00

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