Abstract

A thin film of dielectric material on metal provides a simple and cost-effective platform for absorbing light of a specific wavelength that can be desirably tuned by tailoring the thin film thickness. This property of controlled absorption can lead to realizing various exciting applications such as absorbers and color filters. The primary concern, however, in using such multilayer configurations for color filtering is color purity, which is generally low as compared to patterned resonant structures that employ costly nanofabrication techniques. We report a practical design technique to achieve filters of cyan, magenta, and yellow (CMY) with enhanced color purity, polarization-insensitive, and angle-insensitive functionalities. The design involves dielectric thin film layer sandwiched between an ultra-thin metal-layer and ground plane. We demonstrate several multilayer material configurations that provide advantages over the current state-of-the-art color filters in terms of color purity. The proposed devices can find applications in high-resolution color printing, digital imaging, holographic displays, and sensing.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Color filters based on a nanoporous Al-AAO resonator featuring structure tolerant color saturation

Wenjing Yue, Yang Li, Cong Wang, Zhao Yao, Sang-Shin Lee, and Nam-Young Kim
Opt. Express 23(21) 27474-27483 (2015)

Thin film characterization for modeling and optimization of silver-dielectric color filters

Laurent Frey, Pascale Parrein, Léopold Virot, Catherine Pellé, and Jacques Raby
Appl. Opt. 53(8) 1663-1673 (2014)

Enhanced structural color generation in aluminum metamaterials coated with a thin polymer layer

Fei Cheng, Xiaodong Yang, Daniel Rosenmann, Liliana Stan, David Czaplewski, and Jie Gao
Opt. Express 23(19) 25329-25339 (2015)

References

  • View by:
  • |
  • |
  • |

  1. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [Crossref]
  2. W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
    [Crossref]
  3. N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
    [Crossref]
  4. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
    [Crossref]
  5. M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
    [Crossref]
  6. L.-L. Liu, H.-F. Zhang, and L.-L. Wang, “A novel broadband metamaterial absorber based on the fractal structure,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 1928–1931.
  7. L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
    [Crossref]
  8. F.-J. Ko and H.-P. D. Shieh, “High-efficiency micro-optical color filter for liquid-crystal projection system applications,” Appl. Opt. 39(7), 1159–1163 (2000).
    [Crossref]
  9. Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
    [Crossref]
  10. J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
    [Crossref]
  11. K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
    [Crossref]
  12. A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.
  13. I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
    [Crossref]
  14. D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
    [Crossref]
  15. S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
    [Crossref]
  16. V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
    [Crossref]
  17. F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
    [Crossref]
  18. C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
    [Crossref]
  19. S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
    [Crossref]
  20. J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
    [Crossref]
  21. V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
    [Crossref]
  22. B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
    [Crossref]
  23. Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
    [Crossref]
  24. M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
    [Crossref]
  25. M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
    [Crossref]
  26. S. S. Mirshafieyan and J. Guo, “Silicon colors: spectral selective perfect light absorption in single layer silicon films on aluminum surface and its thermal tunability,” Opt. Express 22(25), 31545–31554 (2014).
    [Crossref]
  27. V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
    [Crossref]
  28. C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
    [Crossref]
  29. J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
    [Crossref]
  30. K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
    [Crossref]
  31. C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
    [Crossref]
  32. K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
    [Crossref]
  33. C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
    [Crossref]
  34. E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114(8), 083106 (2013).
    [Crossref]
  35. E. D. Palik, Handbook of optical constants of solids vol. 3: Academic press, 1998.
  36. M. A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
    [Crossref]

2018 (2)

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

2017 (6)

K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
[Crossref]

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
[Crossref]

2016 (5)

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

M. A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

2015 (5)

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
[Crossref]

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

2014 (6)

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

S. S. Mirshafieyan and J. Guo, “Silicon colors: spectral selective perfect light absorption in single layer silicon films on aluminum surface and its thermal tunability,” Opt. Express 22(25), 31545–31554 (2014).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

2013 (3)

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114(8), 083106 (2013).
[Crossref]

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

2010 (1)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

2009 (2)

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

2008 (1)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

2006 (1)

Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
[Crossref]

2000 (1)

Aizenberg, J.

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

Almpanis, E.

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114(8), 083106 (2013).
[Crossref]

Aydin, K.

Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
[Crossref]

Bedu, F. d. r.

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Bingham, C.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Blanchard, R.

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

Boltasseva, A.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Bonod, N.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Butun, B.

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

Butun, S.

Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
[Crossref]

Byrnes, S. J.

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

Capasso, F.

M. A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

Cheng, F.

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

Cho, Y.

Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
[Crossref]

Choi, D.-Y.

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

Choi, Y.

Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
[Crossref]

Dereshgi, S. A.

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

Duan, Y.

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

Duan, Z.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Duempelmann, L.

L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
[Crossref]

Eong, H. J.

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

Fang, B.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

Fang, X.

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

Gallas, B.

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Gallinet, B.

L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
[Crossref]

Gao, J.

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

Gao, Y.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Genevet, P.

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

Ghobadi, A.

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Guan, J.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Guler, U.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Guo, J.

Guo, L. J.

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

Hajian, H.

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

Han, S. Y.

K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
[Crossref]

Hegde, R. S.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

Hobson, P. A.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

Ji, C.

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

Jokerst, N.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Kats, M. A.

M. A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

Kildishev, A. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Kim, E.-S.

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

Kim, I.

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

Kinsey, N.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Ko, F.-J.

Kolle, M.

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

Krawczyk, M.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Landy, N.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

Lawrence, C. R.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

Lee, J. Y.

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

Lee, K. T.

K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

Lee, K.-T.

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

Lee, S.-S.

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

Li, K.

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

Li, W.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Li, Z.

Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
[Crossref]

Lin, J.

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

Liu, D.

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

Liu, L.-L.

L.-L. Liu, H.-F. Zhang, and L.-L. Wang, “A novel broadband metamaterial absorber based on the fractal structure,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 1928–1931.

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Liu, X.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

Luk, T. S.

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

Luo, S.

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

Mehmood, M. Q.

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Mirshafieyan, S. S.

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

Naik, G. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Novotny, L.

L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
[Crossref]

Ozbay, E.

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

Ozerov, I.

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Padilla, W.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids vol. 3: Academic press, 1998.

Papanikolaou, N.

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114(8), 083106 (2013).
[Crossref]

Park, C.-S.

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

Park, H. J.

K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
[Crossref]

Peng, H.

Proust, J.

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Rana, A. S.

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

Rho, J.

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

Seo, S.

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

Serebryannikov, A. E.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Shalaev, V. M.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

Shen, W.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

Shieh, H.-P. D.

Shrestha, V. R.

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

Smith, D.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

So, S.

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

Sohn, S.

Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
[Crossref]

Song, Q.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Sun, S.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Tyler, T.

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Vaidya, G.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Vashistha, V.

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Wang, L.-L.

L.-L. Liu, H.-F. Zhang, and L.-L. Wang, “A novel broadband metamaterial absorber based on the fractal structure,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 1928–1931.

Wang, X.

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Xiao, S.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Yang, C.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

Yang, X.

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

Yang, Z.

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

Yu, H.

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

Zhang, C.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Zhang, H.-F.

L.-L. Liu, H.-F. Zhang, and L.-L. Wang, “A novel broadband metamaterial absorber based on the fractal structure,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 1928–1931.

Zhang, X.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

Zhang, Y.

B. Fang, C. Yang, W. Shen, X. Zhang, Y. Zhang, and X. Liu, “Highly efficient omnidirectional structural color tuning method based on dielectric–metal–dielectric structure,” Appl. Opt. 56(4), C175–C180 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

C. Yang, W. Shen, Y. Zhang, H. Peng, X. Zhang, and X. Liu, “Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure,” Opt. Express 22(9), 11384–11391 (2014).
[Crossref]

Zhao, D.

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

Zhou, J.

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

Zhou, Z.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

Zuo, D.

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

ACS Nano (2)

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

J. Proust, F. d. r. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon Mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

ACS Photonics (3)

V. Vashistha, G. Vaidya, R. S. Hegde, A. E. Serebryannikov, N. Bonod, and M. Krawczyk, “All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut,” ACS Photonics 4(5), 1076–1082 (2017).
[Crossref]

Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015).
[Crossref]

L. Duempelmann, B. Gallinet, and L. Novotny, “Multispectral imaging with tunable plasmonic filters,” ACS Photonics 4(2), 236–241 (2017).
[Crossref]

Adv. Mater. (2)

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref]

K. T. Lee, S. Seo, J. Y. Lee, and L. J. Guo, “Strong Resonance Effect in a Lossy Medium-Based Optical Cavity for Angle Robust Spectrum Filters,” Adv. Mater. 26(36), 6324–6328 (2014).
[Crossref]

Adv. Opt. Mater. (2)

K. T. Lee, S. Y. Han, and H. J. Park, “Omnidirectional Flexible Transmissive Structural Colors with High-Color-Purity and High-Efficiency Exploiting Multicavity Resonances,” Adv. Opt. Mater. 5(14), 1700284 (2017).
[Crossref]

C. Yang, W. Shen, J. Zhou, X. Fang, D. Zhao, X. Zhang, C. Ji, B. Fang, Y. Zhang, and X. Liu, “Angle robust reflection/transmission plasmonic filters using ultrathin metal patch array,” Adv. Opt. Mater. 4(12), 1981–1986 (2016).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

M. A. Kats, S. J. Byrnes, R. Blanchard, M. Kolle, P. Genevet, J. Aizenberg, and F. Capasso, “Enhancement of absorption and color contrast in ultra-thin highly absorbing optical coatings,” Appl. Phys. Lett. 103(10), 101104 (2013).
[Crossref]

Y. Cho, Y. Choi, and S. Sohn, “Optical properties of neodymium-containing polymethylmethacrylate films for the organic light emitting diode color filter,” Appl. Phys. Lett. 89(5), 051102 (2006).
[Crossref]

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, P. A. Hobson, and C. R. Lawrence, “Thin resonant structures for angle and polarization independent microwave absorption,” Appl. Phys. Lett. 94(4), 041913 (2009).
[Crossref]

J. Appl. Phys. (1)

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114(8), 083106 (2013).
[Crossref]

Laser Photonics Rev. (1)

M. A. Kats and F. Capasso, “Optical absorbers based on strong interference in ultra-thin films,” Laser Photonics Rev. 10(5), 735–749 (2016).
[Crossref]

Light: Sci. Appl. (1)

K.-T. Lee, J. Y. Lee, S. Seo, and L. J. Guo, “Colored ultrathin hybrid photovoltaics with high quantum efficiency,” Light: Sci. Appl. 3(10), e215 (2014).
[Crossref]

Nano Lett. (2)

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Aluminum plasmonics based highly transmissive polarization-independent subtractive color filters exploiting a nanopatch array,” Nano Lett. 14(11), 6672–6678 (2014).
[Crossref]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Nano Res. (1)

D. Liu, H. Yu, Z. Yang, and Y. Duan, “Ultrathin planar broadband absorber through effective medium design,” Nano Res. 9(8), 2354–2363 (2016).
[Crossref]

Nanophotonics (1)

I. Kim, S. So, A. S. Rana, M. Q. Mehmood, and J. Rho, “Thermally robust ring-shaped chromium perfect absorber of visible light,” Nanophotonics 7(11), 1827–1833 (2018).
[Crossref]

Nat. Mater. (1)

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[Crossref]

Opt. Commun. (1)

J. Lin, S. Luo, D. Zuo, and X. Wang, “Multilayer structure for highly transmissive angle-tolerant color filter,” Opt. Commun. 427, 158–162 (2018).
[Crossref]

Opt. Express (2)

Phys. Rev. B (1)

N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

Phys. Rev. Lett. (1)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref]

Sci. Rep. (6)

J. Y. Lee, K.-T. Lee, S. Seo, and L. J. Guo, “Decorative power generating panels creating angle insensitive transmissive colors,” Sci. Rep. 4(1), 4192 (2015).
[Crossref]

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5(1), 11045 (2015).
[Crossref]

S. A. Dereshgi, A. Ghobadi, H. Hajian, B. Butun, and E. Ozbay, “Ultra-broadband, lithography-free, and large-scale compatible perfect absorbers: the optimum choice of metal layers in metal-insulator multilayer stacks,” Sci. Rep. 7(1), 14872 (2017).
[Crossref]

C. Yang, W. Shen, Y. Zhang, K. Li, X. Fang, X. Zhang, and X. Liu, “Compact multilayer film structure for angle insensitive color filtering,” Sci. Rep. 5(1), 9285 (2015).
[Crossref]

V. R. Shrestha, S.-S. Lee, E.-S. Kim, and D.-Y. Choi, “Non-iridescent transmissive structural color filter featuring highly efficient transmission and high excitation purity,” Sci. Rep. 4(1), 4921 (2015).
[Crossref]

C.-S. Park, V. R. Shrestha, S.-S. Lee, and D.-Y. Choi, “Trans-reflective color filters based on a phase compensated etalon enabling adjustable color saturation,” Sci. Rep. 6(1), 25496 (2016).
[Crossref]

Other (3)

E. D. Palik, Handbook of optical constants of solids vol. 3: Academic press, 1998.

A. S. Rana, M. Q. Mehmood, H. J. Eong, I. Kim, and J. Rho, “Ultra-Broadband Tungsten Absorber,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, pp. 297–300.

L.-L. Liu, H.-F. Zhang, and L.-L. Wang, “A novel broadband metamaterial absorber based on the fractal structure,” in 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 1928–1931.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Layer description of multilayer color filter showing the thickness of top ultra-thin metal layer d1 and sandwiched semiconductor layer d2 and bottom metal layer’s thickness (d3) is fixed at 100 nm.
Fig. 2.
Fig. 2. Two-layer reflection against the variable thickness of silicon. The black vertical line shows 517 nm and horizontal lines show the thickness of Silicon needed to achieve that response.
Fig. 3.
Fig. 3. (a) Reflection plot for a fixed 10 nm thickness of Titanium and 100 nm Ag with variable Si thickness. The black vertical line shows 517 nm and horizontal lines show the thickness of Silicon needed to achieve that response. (b) Reflection curves for pure CMY color filters achieved from Single resonance (SR) and dual resonance (DR) responses with different thicknesses of Silicon and fixed thicknesses for Ag (100 nm) and Ti (10 nm).
Fig. 4.
Fig. 4. CIE 1931 plot for (a) Two-layered multilayer structure and (b) Three-layer proposed multilayer structure. The black triangle shows pure CMY values obtained from the conversion matrix.
Fig. 5.
Fig. 5. Predicted color plot of the surface by changing the angle of multilayer structure (Ag-Si-Ti) under p- (a-d) and s-polarizations (e-h).
Fig. 6.
Fig. 6. Predicted color plot of the surface for different material combinations of multilayer color filters. Here (a-d) use Ag as bottom metal layer, (e-h) use Cu and (i-l) use Al. In the case of sandwiched semiconductor layers, (a, b, e, f, i, j) use Si and (c, d, g, h, k, l) GaN. Lastly for top metal layers, (a, c, e, g, i, k) have Ti as top layer whereas (b, d, f, h, j, l) have Cr as a top metal layer.
Fig. 7.
Fig. 7. (a) Analytical and measured reflection curves of single-resonance CMY filters. (b) Fabricated CMY color filters. SEM images of fabricated samples for (c) cyan, (d) magenta and (e) yellow color filters.
Fig. 8.
Fig. 8. Three-layered structure showing three different mediums represented by n1, n2, and n3 with d1 and d2 as the thickness of first and second layer whereas third metal layer is supposed as infinitely thick to avoid transmission.

Tables (2)

Tables Icon

Table 1. Literature survey of the selected research along with their limitations

Tables Icon

Table 2. Comparison of RD with related literature. Ag-Si-Ti Single Resonance (SR) and Dual Resonance (DR) designs are compared here with existing literature where curves for CMY were provided. MM represents metamaterial structures that employ nanostructures whereas ML represents multilayer designs.

Equations (22)

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

[ X Y Z ] = [ 0 .4124564  0 .3575761  0 .1804375 0 .2126729   0 .7151522 0 .0721750 0 .0193339 0 .1191920 0 .9503041 ] [ R G B ]  
r = r 01 + r 12 e i 2 β 1 1 + r 01 r 12 e i 2 β 1
R = | r | 2
A = 1 R
r 01 + r 12 e i 2 β 1 = 0
R = E 0 b E 0 f = r 01 + r 12 e i 2 β 1 + ( r 01 r 12 + e i 2 β 1 ) r 23 e i 2 β 2 1 + r 01 r 12 e i 2 β 1 + ( r 12 + r 01 e i 2 β 1 ) r 23 e i 2 β 2
r 01 + r 12 e i 2 β 1 + ( r 01 r 12 + e i 2 β 1 ) r 23 e i 2 β 2 = 0
E 1 f = t 01 E 0 f + r 10 E 1 b
E 0 f = 1 t 01 ( E 1 f + r 01 E 1 b )
E 0 b = r 01 E 0 f + t 10 E 1 b
E 0 b = 1 t 01 ( r 01 E 1 f + E 1 b )
E 1 f = 1 t 12 ( E 2 f + r 12 E 2 b ) e i β 1
E 1 b = 1 t 12 ( r 12 E 2 f + E 2 b ) e i β 1
E 2 f = 1 t 23 E 3 f e i β 2
E 2 b = r 23 t 23 E 3 f e i β 2
E 1 f = E 3 f t 12 t 23 ( e i β 2 + r 12 r 23 e i β 2 ) e i β 1
E 1 b = E 3 f t 12 t 23 ( r 12 e i β 2 + r 23 e i β 2 ) e i β 1
E 0 f = E 3 f t 01 t 12 t 23 ( ( e i β 2 + r 12 r 23 e i β 2 ) e i β 1 + r 01 ( r 12 e i β 2 + r 23 e i β 2 ) e i β 1 )
T = E 3 f E 0 f = t 01 t 12 t 23 e i ( β 1 + β 2 ) 1 + r 01 r 12 e i 2 β 1 + ( r 12 + r 01 e i 2 β 1 ) r 23 e i 2 β 2
E 0 b = E 3 f t 01 t 12 t 23 ( ( r 01 e i β 2 + r 01 r 12 r 23 e i β 2 ) e i β 1 + ( r 12 e i β 2 + r 23 e i β 2 ) e i β 1 )
R = E 0 b E 0 f = r 01 + r 12 e i 2 β 1 + ( r 01 r 12 + e i 2 β 1 ) r 23 e i 2 β 2 1 + r 01 r 12 e i 2 β 1 + ( r 12 + r 01 e i 2 β 1 ) r 23 e i 2 β 2
A = 1 R ,

Metrics