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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21425–21431
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Broadband transparency achieved with the stacked metallic multi-layers perforated with coaxial annular apertures

Zeyong Wei, Yang Cao, Yuancheng Fan, Xing Yu, and Hongqiang Li  »View Author Affiliations


Optics Express, Vol. 19, Issue 22, pp. 21425-21431 (2011)
http://dx.doi.org/10.1364/OE.19.021425


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Abstract

It is generally believed that, in the phenomena of extraordinary optical transmission, perfect transparency only occurs at a single or a multiple of discrete frequencies. This report presents for the first time that a stacked metallic multi-layered system, being perforated with coaxial annular apertures (CAAs), can be perfectly transparent in a broad frequency range. The phenomenon arises from the coupling of guided resonance modes in CAAs among different metallic layers. The transparency bandwidth is extended to about 40% of the central frequency with only 2–3 metallic layers. Measured transmission spectra in microwave regime are in good agreement with calculations which are semi-analytically resolved by modal expansion method.

© 2011 OSA

1. Introduction

2. Descriptions of model and modal expansion method

Our model system contains n metallic layers which are perforated with square arrays of CAAs. To see more clearly the role of metallic multilayers in the transparency band extension, transmission spectra are investigated for three models containing one, two and three metallic layers respectively. We also fabricate three samples with printed circuit board by etching and stacking technique. The samples each have the same geometric parameters as those of their corresponding models. Figure 1 presents a top-view photo and a 3D schematic of a sample comprised of three thin metallic layers(n = 3) and two sandwiched dielectric spacer layers. The aperture arrays on different metallic layers are aligned along the z direction with zero displacement in xy plane. The geometric parameters are the lattice constant p = 10mm of square array, the outer and inner radii R = 4.8mm, r = 3.8mm of CAAs, and the thickness t = 0.035mm of metallic layer, respectively. Each dielectric layer has a thickness of h = 1.575mm and a permittivity of ɛr = 2.65.

Fig. 1 (a) Top-view photo and (b) 3D schematic of our sample with three metallic layers (n = 3). The metallic layers are perforated with coaxial annular apertures(CAAs).

Fig. 2 Transmission spectra through the models with (a) n=1, (b) n=2, (c) n=3, (d) n=10 metallic layers. Solid lines for calculated results by Modal expansion method(MEM), circular dots for measured results in microwave regime.

3. Broad transparent band

We see from Fig. 2(a) that there exists a perfect transmission peak for the n = 1 sample at fA = 8.7GHz due to the excitation of guided TE11 resonance mode in CAAs. We also see from Figs. 2(b) and 2(c) that there are two perfect transmission peaks at fB = 9.1GHz, and fC = 12.3GHz for the n = 2 sample, three peaks at fD = 8.2GHz, fE = 11.64GHz and fF = 12.35GHz for the n = 3 sample, respectively. It is quite obvious that, with the existence of these transparency frequencies, a broad transparency band emerges in each of the both figures. As we can see in Figs. 2(b) and 2(c), the transmittance between adjacent transmission peaks dips to as much as 25% for the sample with two metallic layers, and 40% for the sample with three metallic layers. Figure 2(d) presents the calculated transmission spectra of an n = 10 model system. With the increase of metallic layers, more transmission peaks emerge, resulting in more fluctuations in transmission spectra, but the transmittance is still above 50% at all frequencies within the pass-band. The feature implies that the system can be analogous to a chain of coupled atoms in some extent. It is also noticeable that for the n = 10 model the pass-band have very steep cut-off edges and the suppression outside the pass-band is perfect, the calculated transmittance outside the pass-band is very low (-20 -50 dB). The low-noise performance is also favored in potential applications. In contrast, for the multilayered systems governed by resonant tunneling of SPPs, nearly zero transmission usually occurs at a certain frequency between the frequencies of two adjacent transmission peaks as a result of in-plane evanescent Bragg scatterings which inevitably introduces both the strongly frequency-dispersive and the spatially dispersive signatures in transmission spectra.

4. The coupling and hybridization of guided resonance modes

More calculations show that, for the n = 2 sample, at an on-resonance frequency fB = 9.1GHz or fC = 12.3GHz of perfect transparency, the spatial distributions of electric field [see Figs. 3(a) and 3(b)] are symmetric or anti-symmetric about the xy plane, and the transmitted waves hold a phase difference of 0 (in phase) or π (out phase) with respect to the incident waves respectively. Therefore it is reasonable to say that the peaks at fB and fC arise from the excitations of the symmetric and anti-symmetric coupling modes for the two-layered model. The results unambiguously present a physical picture of mode splitting of coupled apertures (or meta-atoms). Similar results can be found for the n = 3 model. Figures 3(c)3(e) present the spatial field distribution at frequencies of the three transparency modes for the n = 3 model. Comparing the mode symmetry shown in Fig. 3(c)∼(e) and that shown in Figs. 3(a) and 3(b) of two-layered model. We can reasonably deduced that, the anti-symmetric mode at fC = 12.3GHz of the n = 2 model splits into two modes of the n = 3 model, one at fE = 11.64GHz is anti-symmetric [Fig. 3(d)], and the other at fF = 12.35GHz is symmetric [Fig. 3(e)], while the resonant mode at the lowest frequency fD = 8.2GHz inherits a symmetric feature in field distribution [Fig. 3(c)] from the symmetric mode at fB of the n = 2 model, it also applies an in-phase signature for the transmitted waves. It is worth noting that, the transparency band of the n = 3 sample becomes broadened as compared to the n = 2 sample, and the band edges are even sharper.

Fig. 3 Spatial distribution of electric fields in the xz plane at on-resonance frequencies of (a) fB = 9.1GHz, (b) fC = 12.3GHz for the n = 2 model, and (c) fD = 8.2GHz, (d) fE = 11.64GHz, (e) fF = 12.35GHz for the n = 3 model.

Figure 4(a) presents the dispersion relation of a bulk material by assuming that it is periodically constructed with layered CAAs. The band structure is calculated with MEM algorithm by assuming periodic boundary conditions along the z axis. The process of mode splitting shown in Fig. 4(b) depicts the evolution of the frequencies of transmission peaks from the n = 1 system to the n = 3 system. It is interesting to note that the pass-band between fb = 6.77GHz and ft = 12.7GHz shown in Fig. 4(a), predicting the passband of the n = 10 model quite well, is also a good measure of the bandwidth of the n = 3 sample. The transparency bandwidth shown in Figs. 2(b) and 2(c) is about 40% of the central frequency. It is also worth noting that, the transparency band we observed is not sensitive to the incident angle (not shown), which is contrary to the case when the resonant tunneling of SPP modes dominates the EOT of the system.

Fig. 4 (a) Dispersion relation of bulk material periodically constructed by layered CAAs. The inset shows a unit cell of the bulk material. (b) The frequencies of resonant modes (transmission peaks) for the n =1, 2 and 3 models. The thin lines denote the process of mode splitting. fA = 8.7GHz and fA = 12.1GHz refer to the frequencies of the transmission peaks of the n = 1 sample with and without dielectric layer.

5. Conclusion

Acknowledgments

This work was supported by NSFC (No. 11174221, 10974144), CNKBRSF (Grant No. 2011CB922001), NCET ( 07-0621), STCSM and SHEDF (No. 06SG24).

References and links

1.

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]

2.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998). [CrossRef]

3.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

4.

F. J. G. de Abajo and J. J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901 (2005). [CrossRef] [PubMed]

5.

G. Gay, O. Alloschery, B. V. de Lesegno, J. Weiner, and H. J. Lezec, “Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry,” Phys. Rev. Lett. 96, 213901 (2006). [CrossRef] [PubMed]

6.

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008). [CrossRef] [PubMed]

7.

X. A. Xiao, W. Jinbo, Y. Sasagawa, F. Miyamaru, M. Y. Zhang, M. W. Takeda, C. Y. Qiu, W. J. Wen, and P. Sheng, “Resonant terahertz transmissions through metal hole array on silicon substrate,” Opt. Express 18, 18558–18564 (2010). [CrossRef] [PubMed]

8.

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous Band Formation in Arrays of Terahertz Nanoresonators,” Phys. Rev. Lett. 106, 013902 (2011). [CrossRef] [PubMed]

9.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

10.

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

11.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B: Lasers Opt. 79, 1–8 (2004). [CrossRef]

12.

W. J. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metallic coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005). [CrossRef] [PubMed]

13.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005). [CrossRef] [PubMed]

14.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72, 045421 (2005). [CrossRef]

15.

W. J. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwave-length fractal slits in a metallic plate,” Phys. Rev. B 72, 153406 (2005). [CrossRef]

16.

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006). [CrossRef] [PubMed]

17.

Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photon. Nanostruct. 8, 94–101 (2010). [CrossRef]

18.

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71, 165408–165405 (2005). [CrossRef]

19.

Y. H. Ye and J. Y. Zhang, “Enhanced light transmission through cascaded metal films perforated with periodic hole arrays,” Opt. Lett. 30, 1521–1523 (2005). [CrossRef] [PubMed]

20.

H. B. Chan, Z. Marcet, K. Woo, D. B. Tanner, D. W. Carr, J. E. Bower, R. A. Cirelli, E. Ferry, F. Klemens, J. Miner, C. S. Pai, and J. A. Taylor, “Optical transmission through double-layer metallic subwavelength slit arrays,” Opt. Lett. 31, 516–518 (2006). [CrossRef] [PubMed]

21.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76, 195405–195408 (2007). [CrossRef]

22.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polari-tons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009). [CrossRef]

23.

Z. Marcet, Z. H. Hang, C. T. Chan, I. Kravchenko, J. E. Bower, R. A. Cirelli, F. Klemens, W. M. Mansfield, J. F. Miner, C. S. Pai, and H. B. Chan, “Optical transmission through double-layer, laterally shifted metallic subwavelength hole arrays,” Opt. Lett. 35, 2124–2126 (2010). [CrossRef] [PubMed]

24.

L. Zhou, C. P. Huang, S. Wu, X. G. Yin, Y. M. Wang, Q. J. Wang, and Y. Y. Zhu, “Enhanced optical transmission through metal-dielectric multilayer gratings,” Appl. Phys. Lett. 97, 011905 (2010). [CrossRef]

25.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982). [CrossRef]

26.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000). [CrossRef]

27.

Z. Y. Wei, H. Q. Li, C. Wu, Y. Cao, J. Z. Ren, Z. H. Hang, H. Chen, D. Z. Zhang, and C. T. Chan, “Anomalous reflection from hybrid metamaterial slab,” Opt. Express 18, 12119–12126 (2010). [CrossRef] [PubMed]

28.

Z. Y. Wei, H. Q. Li, Y. Cao, C. Wu, J. Z. Ren, Z. H. Hang, H. Chen, D. Z. Zhang, and C. T. Chan, “Spatially coherent surface resonance states derived from magnetic resonances,” N. J. Phys. 12, 093020 (2010). [CrossRef]

29.

Z. Y. Wei, Y. Cao, J. Han, C. Wu, Y. C. Fan, and H. Q. Li, “Broadband negative refraction in stacked fishnet metamaterial,” Appl. Phys. Lett. 97, 141901 (2010). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(240.6680) Optics at surfaces : Surface plasmons
(160.3918) Materials : Metamaterials

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 16, 2011
Revised Manuscript: September 12, 2011
Manuscript Accepted: September 12, 2011
Published: October 14, 2011

Citation
Zeyong Wei, Yang Cao, Yuancheng Fan, Xing Yu, and Hongqiang Li, "Broadband transparency achieved with the stacked metallic multi-layers perforated with coaxial annular apertures," Opt. Express 19, 21425-21431 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21425


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References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998). [CrossRef]
  2. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998). [CrossRef]
  3. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001). [CrossRef] [PubMed]
  4. F. J. G. de Abajo and J. J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett.95, 233901 (2005). [CrossRef] [PubMed]
  5. G. Gay, O. Alloschery, B. V. de Lesegno, J. Weiner, and H. J. Lezec, “Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry,” Phys. Rev. Lett.96, 213901 (2006). [CrossRef] [PubMed]
  6. H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature452, 728–731 (2008). [CrossRef] [PubMed]
  7. X. A. Xiao, W. Jinbo, Y. Sasagawa, F. Miyamaru, M. Y. Zhang, M. W. Takeda, C. Y. Qiu, W. J. Wen, and P. Sheng, “Resonant terahertz transmissions through metal hole array on silicon substrate,” Opt. Express18, 18558–18564 (2010). [CrossRef] [PubMed]
  8. Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous Band Formation in Arrays of Terahertz Nanoresonators,” Phys. Rev. Lett.106, 013902 (2011). [CrossRef] [PubMed]
  9. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  10. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003). [CrossRef] [PubMed]
  11. F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B: Lasers Opt.79, 1–8 (2004). [CrossRef]
  12. W. J. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metallic coaxial-aperture arrays,” Opt. Express13, 4406–4413 (2005). [CrossRef] [PubMed]
  13. W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett.94, 033902 (2005). [CrossRef] [PubMed]
  14. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B72, 045421 (2005). [CrossRef]
  15. W. J. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwaves through subwave-length fractal slits in a metallic plate,” Phys. Rev. B72, 153406 (2005). [CrossRef]
  16. Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett.96, 233901 (2006). [CrossRef] [PubMed]
  17. Z. Y. Wei, J. X. Fu, Y. Cao, C. Wu, and H. Q. Li, “The impact of local resonance on the enhanced transmission and dispersion of surface resonances,” Photon. Nanostruct.8, 94–101 (2010). [CrossRef]
  18. F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B71, 165408–165405 (2005). [CrossRef]
  19. Y. H. Ye and J. Y. Zhang, “Enhanced light transmission through cascaded metal films perforated with periodic hole arrays,” Opt. Lett.30, 1521–1523 (2005). [CrossRef] [PubMed]
  20. H. B. Chan, Z. Marcet, K. Woo, D. B. Tanner, D. W. Carr, J. E. Bower, R. A. Cirelli, E. Ferry, F. Klemens, J. Miner, C. S. Pai, and J. A. Taylor, “Optical transmission through double-layer metallic subwavelength slit arrays,” Opt. Lett.31, 516–518 (2006). [CrossRef] [PubMed]
  21. Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B76, 195405–195408 (2007). [CrossRef]
  22. R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polari-tons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009). [CrossRef]
  23. Z. Marcet, Z. H. Hang, C. T. Chan, I. Kravchenko, J. E. Bower, R. A. Cirelli, F. Klemens, W. M. Mansfield, J. F. Miner, C. S. Pai, and H. B. Chan, “Optical transmission through double-layer, laterally shifted metallic subwavelength hole arrays,” Opt. Lett.35, 2124–2126 (2010). [CrossRef] [PubMed]
  24. L. Zhou, C. P. Huang, S. Wu, X. G. Yin, Y. M. Wang, Q. J. Wang, and Y. Y. Zhu, “Enhanced optical transmission through metal-dielectric multilayer gratings,” Appl. Phys. Lett.97, 011905 (2010). [CrossRef]
  25. P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B26, 2907–2916 (1982). [CrossRef]
  26. P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt.2, 48–51 (2000). [CrossRef]
  27. Z. Y. Wei, H. Q. Li, C. Wu, Y. Cao, J. Z. Ren, Z. H. Hang, H. Chen, D. Z. Zhang, and C. T. Chan, “Anomalous reflection from hybrid metamaterial slab,” Opt. Express18, 12119–12126 (2010). [CrossRef] [PubMed]
  28. Z. Y. Wei, H. Q. Li, Y. Cao, C. Wu, J. Z. Ren, Z. H. Hang, H. Chen, D. Z. Zhang, and C. T. Chan, “Spatially coherent surface resonance states derived from magnetic resonances,” N. J. Phys.12, 093020 (2010). [CrossRef]
  29. Z. Y. Wei, Y. Cao, J. Han, C. Wu, Y. C. Fan, and H. Q. Li, “Broadband negative refraction in stacked fishnet metamaterial,” Appl. Phys. Lett.97, 141901 (2010). [CrossRef]

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