Abstract

In this article, we propose a simple scheme to make a metallic film on a semi-infinite substrate optically transparent, thus obtaining a completely transparent electrode in a desired frequency range. By placing a composite layer consisting of dielectric and metallic stripes on top of the metallic one, we found that the back-scattering from the metallic film can be almost perfectly canceled by the composite layer under certain conditions, leading to transparency of the whole structure. We performed proof-of-concept experiments in the terahertz domain to verify our theoretical predictions, using carefully designed metamaterials to mimic plasmonic metals in optical regime. Experiments are in excellent agreement with full-wave simulations.

© 2012 OSA

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References

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  1. D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
    [CrossRef] [PubMed]
  2. M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
    [CrossRef]
  3. R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: electrical properties,” J. App. Phys. 83, 2631–2645 (1998).
    [CrossRef]
  4. D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
    [CrossRef]
  5. 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, 667–669 (1998).
    [CrossRef]
  6. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
    [CrossRef]
  7. H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
    [CrossRef] [PubMed]
  8. L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 243905 (2005).
    [CrossRef]
  9. Comsol Multiphysics by COMSOL ©, ver. 3.5, network license (2008).
  10. D. Bergman, “The dielectric constant of a composite material - a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
    [CrossRef]
  11. K. Busch, C. T. Chan, and C. M. Soukoulis, in Photonic Band Gap Materials edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996) 16, 267–269 (1999).
  12. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
    [CrossRef] [PubMed]
  13. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
    [CrossRef]
  14. CST ©Studio Suit, ver. 2011.
  15. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, 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.,  22,1099–1119 (1983).
    [CrossRef] [PubMed]
  16. N. J. Cronin, ‘in Microwave and Optical Waveguides (Taylor & Francis, 1995).
  17. C. A. Balanis, in Advanced Electromagnetics Engineering (Prentice Hall, 1989).
  18. P. Yeh, in Optical Waves in Layered Media (Wiley Online library, 1988).

2012

M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
[CrossRef]

2011

D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef] [PubMed]

2010

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

2007

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

2005

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

2000

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

1999

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

1998

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, 667–669 (1998).
[CrossRef]

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

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

1983

1978

D. Bergman, “The dielectric constant of a composite material - a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Alexander, R. W.

Azad, A. K.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Balanis, C. A.

C. A. Balanis, in Advanced Electromagnetics Engineering (Prentice Hall, 1989).

Ban, T.

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

Bao, Z.

M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bergman, D.

D. Bergman, “The dielectric constant of a composite material - a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Busch, K.

K. Busch, C. T. Chan, and C. M. Soukoulis, in Photonic Band Gap Materials edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996) 16, 267–269 (1999).

Cairns, D. R.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Chan, C. T.

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

K. Busch, C. T. Chan, and C. M. Soukoulis, in Photonic Band Gap Materials edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996) 16, 267–269 (1999).

Chen, F.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Chen, H.-T.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Crawford, G. P.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Cronin, N. J.

N. J. Cronin, ‘in Microwave and Optical Waveguides (Taylor & Francis, 1995).

Ebbesen, T. W.

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, 667–669 (1998).
[CrossRef]

Garcia-Vidal, F. J.

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

Ghaemi, H. F.

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, 667–669 (1998).
[CrossRef]

Hecht, D. S.

D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Hu, L.

D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef] [PubMed]

Irvin, G.

D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef] [PubMed]

Lezec, H. J.

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, 667–669 (1998).
[CrossRef]

Lipomi, D. J.

M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
[CrossRef]

Long, L. L.

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Newton, R. R.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

OHara, J. F.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Ohya, Y.

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

Ordal, M. A.

Paine, D. C.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Pendry, J. B.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Porto, J. A.

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

Sachsman, S. M.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Sheng, P.

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

Soukoulis, C. M.

K. Busch, C. T. Chan, and C. M. Soukoulis, in Photonic Band Gap Materials edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996) 16, 267–269 (1999).

Sparacin, D. K.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Tahar, R. B. H.

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

Takahashi, Y.

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

Taylor, A. J.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Thio, T.

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, 667–669 (1998).
[CrossRef]

Vosgueritchian, M.

M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
[CrossRef]

Ward, C. A.

Wen, W.

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

Witte, R. P.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Wolff, P. A.

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, 667–669 (1998).
[CrossRef]

Yeh, P.

P. Yeh, in Optical Waves in Layered Media (Wiley Online library, 1988).

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Zhou, J.

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

Zhou, L.

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

Adv. Func. Mater.

M. Vosgueritchian, D. J. Lipomi, and Z. Bao, “Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes,” Adv. Func. Mater. 22, 421–428 (2012).
[CrossRef]

Adv. Mater.

D. S. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef] [PubMed]

App. Phys. Lett.

D. R. Cairns, R. P. Witte, D. K. Sparacin, S. M. Sachsman, D. C. Paine, G. P. Crawford, and R. R. Newton, “Strain-dependent electrical resistance of tin-doped indium oxide on polymer substrates,” App. Phys. Lett. 76, 1425–1427 (2000).
[CrossRef]

Appl. Opt.

J. App. Phys.

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

J. Appl. Phys.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Nature

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, 667–669 (1998).
[CrossRef]

Phys. Rep.

D. Bergman, “The dielectric constant of a composite material - a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Phys. Rev. Lett.

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

H.-T. Chen, J. Zhou, J. F. OHara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).
[CrossRef] [PubMed]

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Other

CST ©Studio Suit, ver. 2011.

N. J. Cronin, ‘in Microwave and Optical Waveguides (Taylor & Francis, 1995).

C. A. Balanis, in Advanced Electromagnetics Engineering (Prentice Hall, 1989).

P. Yeh, in Optical Waves in Layered Media (Wiley Online library, 1988).

Comsol Multiphysics by COMSOL ©, ver. 3.5, network license (2008).

K. Busch, C. T. Chan, and C. M. Soukoulis, in Photonic Band Gap Materials edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996) 16, 267–269 (1999).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic illustration of the proposed structure. (b) Transmittance (colorful scale) as the function of εB and P/λ. All other parameters are fixed, as described in the text.

Fig. 2
Fig. 2

The unit cells as seen from the xy plane (a) and the proposed structure in xz plane (b). The E field is parallel to the y-axis. The AB mesh is obtained by sectioning the B mesh and introducing a stripe of material, the A layer, in the cut. The width of the A stripe is calculated such that to reach the desired effective permittivity. The dotted line represents the demarcation between the C and the AB metamaterial. Not on scale.

Fig. 3
Fig. 3

(a) simulated transmittance (red) and reflectance (blue) spectra of the proposed configuration in Fig. 2 (solid line) as well as of the simple C-layer mesh (dash line). (b) the compared transmittance of ideal and randomized structure. (c) and (d) respectively represent the behavior of the structure when varying the incidence angle in the (x,z) plane and (y,z) plane. The incident field is polarized along the Y axis

Fig. 4
Fig. 4

Structures, their circuit models and transmittance spectra. (a) Single interface between two dielectrics; (b) thin dielectric layer between two homogeneous dielectrics; (c) equivalent transmission line model for the thin layer; (d) layer C and the TL model; (e) layer AB and the TL model; (f) complete system and the TL model. The incident radiation is normal to the structures with the E field parallel to the middle line of the ”H”-like structure.

Fig. 5
Fig. 5

Schematic of the fabrication procedure, not on scale. (1) Initial wafer with deposited Al; (2) photoresist deposition and masked optical exposure for defining the structures; (3) develop of photoresist and Al etch; (4)removal of the photoresist and deposit silica layer. After this step, the process is repeated for the next layer.

Fig. 6
Fig. 6

Fabrication results. (a) Bottom layer; (b) top layer. The shadow of the bottom layer can be distinguished in the background.

Fig. 7
Fig. 7

Measured transmittance and reflectance intensity data. (a) Various pulse lengths and (b) their respective transmittance spectra showing the importance of correctly defining the cutting time-point; (c) transmittance (red) and reflectance (blue) for both the whole ABC device (solid lines) and C MTM layer (dashed). The averaged data for four devices and two mesh samples are presented.

Fig. 8
Fig. 8

Transmittance and reflectance data comparison. Full lines are the simulated results. The difference between the transmittance max amplitude is mainly due to the difficulty in finding the optimum cutting point as well as neglecting the losses in the silica layer in simulations.

Equations (8)

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

1 ε A B = 1 ε A w A P + 1 ε B w B P .
( t 0 ) = Q ( 1 r ) .
Q 21 = ( 1 1 ε sub ) + i [ ( 1 | ε C | + | ε C | ε sub ) tanh ( | ε C | d C / λ 0 ) ] + + i [ ( 1 ε A B ε A B ε sub ) tan ( ε A B d A B / λ 0 ) ] ( ε A B | ε C | + | ε C | ε A B ε sub ) tan ( ε A B d A B / λ 0 ) tanh ( | ε C | d C / λ 0 )
T = 4 η 1 η 2 ( η 1 + η 2 ) 2
T = η 1 η 2 | t 1 η t η 2 1 r η 1 r η 2 exp ( i k d ) | 2
t = 2 η 1 1 η 1 + 1 η 2 + 1 η eq
r = 1 η 1 1 η 2 1 η eq 1 η 1 + 1 η 2 + 1 η eq ,
Z total = Z 1 Z 2 Z 1 + Z 2 = i ω L C ( ω L A B 1 ω C A B ) ω ( L C + L A B ) 1 ω C A B

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