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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6519–6525
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Wide-angle polarization-insensitive transparency of a continuous opaque metal film for near-infrared light

Zhengyong Song and Baile Zhang  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6519-6525 (2014)
http://dx.doi.org/10.1364/OE.22.006519


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Abstract

Here we show that a continuous highly conducting metal film can be made transparent for wide-angle and polarization-insensitive incidence of near-infrared light by depositing periodic metal patches on top of the metal film. Based on the optimized computations, the whole system could suppress the reflection and enhance the transmission. This design of transparent metal film can be useful in applications, such as optoelectronic electrodes, solar cells, and micro-electronic displays, where both high electrical conductivity and high optical transmittance are desirable.

© 2014 Optical Society of America

1. Introduction

In this paper, we propose a new type of TCM to make a continuous (apertureless, seamless) metal film optically transparent on a substrate at near-infrared frequencies. Since our design does not require any perforations on the metal film, its full electric and mechanical properties can be preserved. Moreover, the transparency is robust against polarization and incidence angle. In terms of fabrication, our design requires only planar operation which does not involve complicated three-dimensional construction.

Our paper is organized as follows. We first numerically calculated transmission behavior of the proposed model system in Sec. 2. The interesting transparent metal film at near-infrared frequencies is verified based on full-wave simulations. In Sec. 3, we discussed the underlying physics behind this phenomenon. After presenting the properties of wide angle and polarization insensitivy of our proposed system in Sec. 4, we concluded our paper in the last section.

2. Numerical calculations on the designed system

Further numerical simulations were also performed to investigate the relationship between the transmission spectrum and the geometric dimension of the silver patches. Figure 3
Fig. 3 Transmittance as a function of wavelength and the width of square silver patches. Other geometric parameters are fixed to be h1=30nm, h2=10nm, h3=20nm, and P=200nm.
shows the transmittance as a function of wavelength (λ) and width (w) of silver patches with other geometric parameters h1=30nm, h2=10nm, h3=20nm, and P=200nm fixed. By increasing the width of silver patches from 100 nm to 180 nm with a step of 5 nm while keeping the other parameters unchanged, the transparency wavelength gradually changes from 1.1 μm to 2.0 μm, demonstrating the flexibility of our approach.

3. Discussion on physics behind this phenomenon

Inspired by optical scattering from nanoparticles due to the interference between the electric and magnetic dipoles [22

22. M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73(6), 765–767 (1983). [CrossRef]

25

25. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013). [PubMed]

], we qualitatively identify that high transmission at the wavelength of 1.55μm could be attributed to the constructive interference between the electric and magnetic dipoles in the forward propagating direction. Especially, the results in [24

24. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013). [CrossRef] [PubMed]

] tell that the system with large aspect ratio will have a noticeable increase in the forward scattering. The aspect ratio of our designed structure is 145nm/(30nm+10nm+20nm)2.4, which is consistent with the effect of high transmission. Herein, the electric dipole with charges accumulated at the sides of the silver patch is easily understood to be parallel to the electric field of incidence wave, and the magnetic dipole parallel to the magnetic field of incoming light originates from the circular displacement currents. A bare silver patch has only electric response to electromagnetic radiation. But when a silver film is added, near-field coupling between the silver patch and the silver film generates electric currents flowing oppositely on each of them, which then form a circulating current loop and lead to a magnetic resonance [26

26. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef] [PubMed]

,27

27. Y. Zeng, H. T. Chen, and D. A. R. Dalvit, “The role of magnetic dipoles and non-zero-order Bragg waves in metamaterial perfect absorbers,” Opt. Express 21(3), 3540–3546 (2013). [CrossRef] [PubMed]

]. The corresponding magnetic field intensity (|H/H0|) at the wavelength of 1.55 μm is illustrated in Fig. 4
Fig. 4 Distributions of normalized magnetic field (colormap) and electric displacement (arrows) at the wavelength of 1.55 μm. The rectangles represent the positions of the studied structure.
. We find that the magnetic field is strongly enhanced in the dielectric layer, as a characteristic feature of this phenomenon. We also plotted in Fig. 4 the distribution of electric displacement inside this structure at the wavelength of 1.55 μm. Clearly, the electric displacement vectors represented by the arrows in both the silver patches and the silver film are opposite to each other, which generate a significant magnetic response aided by strongly enhanced magnetic fields localized in the gaps between the silver patches and the silver film. In principle, the contributions of different modes in this system could be expected to be rigorously analyzed by multipole decomposition method in the future [28

28. S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5(2–3), 64–73 (2011). [CrossRef]

]. Alternatively, this phenomenon can also be interpreted from the perspective of scattering cancellation mechanism [10

10. Z. Y. Song, Q. He, S. Y. Xiao, and L. Zhou, “Making a continuous metal film transparent via scattering cancellations,” Appl. Phys. Lett. 101(18), 181110 (2012). [CrossRef]

,12

12. R. Malureanu, M. Zalkovskij, Z. Y. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012). [CrossRef] [PubMed]

] or interference-based principle [29

29. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]

,30

30. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

]. By modeling the distributed array of square silver patches as a homogeneous impedance-tuned interface, the destructive and constructive interferences, respectively, due to the superpositions of the multiple reflections and transmissions, are responsible for the reduction of reflection and enhancement of transmission.

4. Polarization-insensitive and large tolerance of oblique incidence

In addition, for this newly designed TCM, this high transmission is robust against polarization and oblique incidence. Simulations were performed to verify these features with the same optimized dimensions in Fig. 2. The simulated transmittances as a function of frequencies (f) and incidence angles (θ) are shown in Fig. 5(a)
Fig. 5 Simulated transmittance as a function of frequency and incidence angle for (a) TE- and (b) TM-polarized incident waves, where h1=30nm, h2=10nm, h3=20nm, w=145nm, and P=200nm.
for transverse-electric (TE) polarization and Fig. 5(b) for transverse-magnetic (TM) polarization. Numerical results reveal that the transmittance is rather stable even for the incidence angles up to 70° for TE waves and 50° for TM waves.

5. Conclusions

To summarize, we have presented a new TCM based on the plasmonic nanostructure on a substrate at near-infrared wavelengths. Numerical results show that the high transmission is insensitive for the wide variation of incidence angles for both TE and TM polarizations, and can be tuned by adjusting the geometric dimension. Furthermore, the fabrication of this configuration can be straightforwardly fabricated by focused ion beam etching or electron beam lithography technique. This TCM design may find applications in photovoltaic cells, touch screens, and other display devices, where transparent electrodes are in significant demand.

Acknowledgments

References and links

1.

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998). [CrossRef]

2.

M. ven Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B Condens. Matter 41(17), 12140–12149 (1990).

3.

M. G. Kang, M. S. Kim, J. Kim, and L. J. Guo, “Organic solar cells using nanoimprinted transparent metal electrodes,” Adv. Mater. 20(23), 4408–4413 (2008). [CrossRef]

4.

J. Y. Lee, S. T. Connor, Y. Cui, and P. Peumans, “Solution-processed metal nanowire mesh transparent electrodes,” Nano Lett. 8(2), 689–692 (2008). [CrossRef] [PubMed]

5.

A. Boltasseva and H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011). [CrossRef] [PubMed]

6.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

7.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999). [CrossRef]

8.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94(24), 243905 (2005). [CrossRef]

9.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005). [CrossRef] [PubMed]

10.

Z. Y. Song, Q. He, S. Y. Xiao, and L. Zhou, “Making a continuous metal film transparent via scattering cancellations,” Appl. Phys. Lett. 101(18), 181110 (2012). [CrossRef]

11.

M. Elbahri, M. K. Hedayati, V. S. Kiran Chakravadhanula, M. Jamali, T. Strunkus, V. Zaporojtchenko, and F. Faupel, “An omnidirectional transparent conducting-metal-based plasmonic nanocomposite,” Adv. Mater. 23(17), 1993–1997 (2011). [CrossRef] [PubMed]

12.

R. Malureanu, M. Zalkovskij, Z. Y. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012). [CrossRef] [PubMed]

13.

Z. Q. Liu, G. Q. Liu, X. S. Liu, K. Huang, Y. H. Chen, Y. Hu, and G. L. Fu, “Tunable plasmon-induced transparency of double continuous metal films sandwiched with a plasmonic array,” Plasmonics 8(2), 1285–1292 (2013). [CrossRef]

14.

Z. Q. Liu, G. Q. Liu, H. Q. Zhou, X. S. Liu, K. Huang, Y. H. Chen, and G. L. Fu, “Near-unity transparency of a continuous metal film via cooperative effects of double plasmonic arrays,” Nanotechnology 24(15), 155203 (2013). [CrossRef] [PubMed]

15.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010). [CrossRef]

16.

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Metallic subwavelength structures for a broadband infrared absorption control,” Opt. Lett. 32(8), 994–996 (2007). [CrossRef] [PubMed]

17.

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

18.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983). [CrossRef] [PubMed]

19.

H. Kim, C. M. Gilmore, A. Piqué, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999). [CrossRef]

20.

N. P. Logeeswaran Vj, M. S. Kobayashi, W. Islam, P. Wu, N. X. Chaturvedi, S. Y. Fang, Wang, and R. S. Williams, “Ultrasmooth silver thin films deposited with a germanium nucleation layer,” Nano Lett. 9(1), 178–182 (2009). [CrossRef] [PubMed]

21.

J. M. Phillips, R. J. Cava, G. A. Thomas, S. A. Carter, J. Kwo, T. Siegrist, J. J. Krajewski, J. H. Marshall, W. F. Peck, and D. H. Rapkine, “Zinc-indium-oxide: A high conductivity transparent conducting oxide,” Appl. Phys. Lett. 67(15), 2246–2248 (1995). [CrossRef]

22.

M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73(6), 765–767 (1983). [CrossRef]

23.

J. M. Geffrin, B. Garcıa-Camara, R. Gomez-Medina, P. Albella, L. S. Froufe-Perez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012). [CrossRef]

24.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013). [CrossRef] [PubMed]

25.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013). [PubMed]

26.

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef] [PubMed]

27.

Y. Zeng, H. T. Chen, and D. A. R. Dalvit, “The role of magnetic dipoles and non-zero-order Bragg waves in metamaterial perfect absorbers,” Opt. Express 21(3), 3540–3546 (2013). [CrossRef] [PubMed]

28.

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5(2–3), 64–73 (2011). [CrossRef]

29.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]

30.

H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

OCIS Codes
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: November 20, 2013
Revised Manuscript: January 7, 2014
Manuscript Accepted: January 14, 2014
Published: March 13, 2014

Citation
Zhengyong Song and Baile Zhang, "Wide-angle polarization-insensitive transparency of a continuous opaque metal film for near-infrared light," Opt. Express 22, 6519-6525 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6519


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References

  1. R. B. H. Tahar, T. Ban, Y. Ohya, Y. Takahashi, “Tin doped indium oxide thin films: electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998). [CrossRef]
  2. M. ven Exter, D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B Condens. Matter 41(17), 12140–12149 (1990).
  3. M. G. Kang, M. S. Kim, J. Kim, L. J. Guo, “Organic solar cells using nanoimprinted transparent metal electrodes,” Adv. Mater. 20(23), 4408–4413 (2008). [CrossRef]
  4. J. Y. Lee, S. T. Connor, Y. Cui, P. Peumans, “Solution-processed metal nanowire mesh transparent electrodes,” Nano Lett. 8(2), 689–692 (2008). [CrossRef] [PubMed]
  5. A. Boltasseva, H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011). [CrossRef] [PubMed]
  6. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  7. J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999). [CrossRef]
  8. L. Zhou, W. J. Wen, C. T. Chan, P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94(24), 243905 (2005). [CrossRef]
  9. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005). [CrossRef] [PubMed]
  10. Z. Y. Song, Q. He, S. Y. Xiao, L. Zhou, “Making a continuous metal film transparent via scattering cancellations,” Appl. Phys. Lett. 101(18), 181110 (2012). [CrossRef]
  11. M. Elbahri, M. K. Hedayati, V. S. Kiran Chakravadhanula, M. Jamali, T. Strunkus, V. Zaporojtchenko, F. Faupel, “An omnidirectional transparent conducting-metal-based plasmonic nanocomposite,” Adv. Mater. 23(17), 1993–1997 (2011). [CrossRef] [PubMed]
  12. R. Malureanu, M. Zalkovskij, Z. Y. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012). [CrossRef] [PubMed]
  13. Z. Q. Liu, G. Q. Liu, X. S. Liu, K. Huang, Y. H. Chen, Y. Hu, G. L. Fu, “Tunable plasmon-induced transparency of double continuous metal films sandwiched with a plasmonic array,” Plasmonics 8(2), 1285–1292 (2013). [CrossRef]
  14. Z. Q. Liu, G. Q. Liu, H. Q. Zhou, X. S. Liu, K. Huang, Y. H. Chen, G. L. Fu, “Near-unity transparency of a continuous metal film via cooperative effects of double plasmonic arrays,” Nanotechnology 24(15), 155203 (2013). [CrossRef] [PubMed]
  15. J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010). [CrossRef]
  16. G. Biener, A. Niv, V. Kleiner, E. Hasman, “Metallic subwavelength structures for a broadband infrared absorption control,” Opt. Lett. 32(8), 994–996 (2007). [CrossRef] [PubMed]
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  18. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983). [CrossRef] [PubMed]
  19. H. Kim, C. M. Gilmore, A. Piqué, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999). [CrossRef]
  20. N. P. Logeeswaran Vj, M. S. Kobayashi, W. Islam, P. Wu, N. X. Chaturvedi, S. Y. Fang, Wang, R. S. Williams, “Ultrasmooth silver thin films deposited with a germanium nucleation layer,” Nano Lett. 9(1), 178–182 (2009). [CrossRef] [PubMed]
  21. J. M. Phillips, R. J. Cava, G. A. Thomas, S. A. Carter, J. Kwo, T. Siegrist, J. J. Krajewski, J. H. Marshall, W. F. Peck, D. H. Rapkine, “Zinc-indium-oxide: A high conductivity transparent conducting oxide,” Appl. Phys. Lett. 67(15), 2246–2248 (1995). [CrossRef]
  22. M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73(6), 765–767 (1983). [CrossRef]
  23. J. M. Geffrin, B. Garcıa-Camara, R. Gomez-Medina, P. Albella, L. S. Froufe-Perez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012). [CrossRef]
  24. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013). [CrossRef] [PubMed]
  25. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013). [PubMed]
  26. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef] [PubMed]
  27. Y. Zeng, H. T. Chen, D. A. R. Dalvit, “The role of magnetic dipoles and non-zero-order Bragg waves in metamaterial perfect absorbers,” Opt. Express 21(3), 3540–3546 (2013). [CrossRef] [PubMed]
  28. S. Mühlig, C. Menzel, C. Rockstuhl, F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5(2–3), 64–73 (2011). [CrossRef]
  29. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]
  30. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

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