## Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure |

Optics Express, Vol. 22, Issue 9, pp. 11384-11391 (2014)

http://dx.doi.org/10.1364/OE.22.011384

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### 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

## 1. Introduction

6. S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A **14**(7), 1617–1626 (1997). [CrossRef]

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

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

11. C. Yang, L. Hong, W. Shen, Y. Zhang, X. Liu, and 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]

## 2. Structure and design

_{2}dielectric grating layer, serving as the modulating layer. Aluminum is chosen as the metal material because it is easier for fabrication and more stable than gold and silver. The side lengths of square grating is denoted by

*a*, the interval between the units is denoted by

*d*and the period of the structure is denoted by

*p*while the thicknesses of the top aluminum layer and the SiO

_{2}dielectric layer are represented by

*t*and

_{1}*t*, respectively. A simple geometric relationships p = a + 2d could be obtained. The linearly polarized light is launched at an incident angle θ and an azimuthal angle φ towards the color filter, as shown in Fig. 1. In the paper, the incidence angle θ varies from 0° to 60° while the azimuthal angle changes from 0° to 45° due to the symmetry of the square “pixels”. The incident medium and substrate are air and quartz, whose refractive indices are n

_{2}_{0}= 1.0 and n

_{s}= 1.46 respectively. The refractive index of silicon dioxide is set to n

_{SiO2}= 1.5. The material coefficient of aluminum comes from the data in the book [12] (data between the nodes derived from linear interpolation).

## 3. Results and analysis

_{2}was chosen as the subwavelength dielectric material. Figure 2 shows the reflectance curves of the optimized color filters for unpolarized incidence. The optimized structures are able to trap light as much as 94% at the specific resonant wavelength. Since the thickness of the bottom aluminum film is thick enough (>100nm), there is no light transmitting the structure. Thus, the equation A + R = 1 could be obtained apparently. So the efficient color filtering feature could be ascribed to the strong absorption at the selected wavelength range, excited by the MDM structure as seen in the insert. The absorption band is red-shifted as the size of the constituent unit increases. Moreover, if the pattern chooses the circle pattern instead of the square one, the bandwidth will become wider and the color saturation will deteriorate. This is the reason why the square pattern is chosen.

19. 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]

3. 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]

_{2}and top aluminum grating at the reflection dip wavelength. Though Fabry–Pérot resonance could be excited by the MDM structure in most cases, considering such a thin cavity constructed, this resonance is absent in this work. Only surface plasmon resonance [20

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

## 4. Conclusion

## Acknowledgments

## References and links

1. | M. Born and E. Wolf, |

2. | H. A. Macleod, |

3. | 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] |

4. | S. S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. |

5. | S. S. Wang and R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. |

6. | S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A |

7. | T. Xu, Y. K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. |

8. | K. Kumar, H. Duan, R. S. Hegde, S. C. W. Koh, J. N. Wei, and J. K. W. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. |

9. | J. Clausen, A. B. Christiansen, J. Garnaes, N. A. Mortensen, and A. Kristensen, “Color effects from scattering on random surface structures in dielectrics,” Opt. Express |

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

11. | C. Yang, L. Hong, W. Shen, Y. Zhang, X. Liu, and H. Zhen, “Design of reflective color filters with high angular tolerance by particle swarm optimization method,” Opt. Express |

12. | E. D. Palik, |

13. | K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. |

14. | A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. |

15. | K. S. Kunz and R. J. Luebbers, |

16. | T. Allen and C. H. Susan, |

17. | R. C. Eberhart, J.Kennedy, and Y.Shi, |

18. | CIE, |

19. | G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. |

20. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature |

**OCIS Codes**

(050.6624) Diffraction and gratings : Subwavelength structures

(230.7408) Optical devices : Wavelength filtering devices

**ToC Category:**

Optical Devices

**History**

Original Manuscript: April 3, 2014

Revised Manuscript: April 25, 2014

Manuscript Accepted: April 28, 2014

Published: May 2, 2014

**Citation**

Chenying Yang, Weidong Shen, Yueguang Zhang, Hao Peng, Xing Zhang, and Xu Liu, "Design and simulation of omnidirectional reflective color filters based on metal-dielectric-metal structure," Opt. Express **22**, 11384-11391 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11384

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### References

- 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]
- S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19(12), 919–921 (1994). [CrossRef] [PubMed]
- S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34(14), 2414–2420 (1995). [CrossRef] [PubMed]
- S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997). [CrossRef]
- 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).
- 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]
- 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]
- 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]
- E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
- 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]
- 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]
- 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).
- 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]
- W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

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