Abstract

We experimentally demonstrate the ability to create additional transmission resonances in a double-layer aperture array by varying the interlayer gap spacing. In the case of periodic aperture arrays, these additional resonances are sharply peaked, while for random aperture arrays the resonances are broad. Surprisingly, these additional resonances only occur when the interlayer gap spacing is greater than half the aperture spacing on a single array. Since there is no corresponding periodicity in the random arrays, these resonances occur regardless of how small the gap spacing is made. This phenomenon can be accurately modeled only if the correct frequency-dependent complex dielectric function of a metal film perforated with subwavelength apertures is used. Using THz time-domain spectroscopy, we are able to directly obtain the complex dielectric response function from the THz experimental transmission measurements. We conclude by demonstrating several passive free-space THz filters using multilayer aperture arrays. Importantly, we show that the magnitude of the lowest order resonance can be approximately maintained, while the background transmission can be significantly suppressed leading to a significant improvement in the optical filter fidelity.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  7. H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  18. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
    [CrossRef]
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    [CrossRef]
  20. T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
    [CrossRef]

2010 (1)

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

2009 (2)

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H, 73940H-7 (2009).
[CrossRef]

2008 (2)

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

2007 (2)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[CrossRef]

2006 (2)

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(4), 516–518 (2006).
[CrossRef] [PubMed]

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

2005 (4)

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
[CrossRef]

Y. H. Ye and J. Y. Zhang, “Enhanced light transmission through cascaded metal films perforated with periodic hole arrays,” Opt. Lett. 30(12), 1521–1523 (2005).
[CrossRef] [PubMed]

J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, D. S. Kim, S. C. Jeoung, Ch. Lienau, and Q.-H. Park, “Invisible plasmonic meta-materials through impedance matching to vacuum,” Opt. Express 13(26), 10681–10687 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

2004 (3)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004).
[CrossRef] [PubMed]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

2003 (1)

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

2002 (1)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

1998 (1)

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

1983 (1)

Agrawal, A.

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

Ahn, Y. H.

Alexander, R. W.

Barnes, W. L.

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

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bower, J. E.

Brown, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

Cao, H.

Carr, D. W.

Chan, H. B.

Cirelli, R. A.

Dereux, A.

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

Ebbesen, T. W.

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

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

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

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Ferry, E.

García-Meca, C.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Ghaemi, H. F.

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

Hangyo, M.

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

Jeoung, S. C.

Kim, D. S.

Klemens, F.

Kuipers, L.

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

Lee, J. W.

Lezec, H. J.

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

Li, H.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Lienau, Ch.

Liu, Q.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Long, L. L.

Marcet, Z.

Martí, J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Martínez, A.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

Menon, R.

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

Miner, J.

Miyamaru, F.

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
[CrossRef]

Nahata, A.

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H, 73940H-7 (2009).
[CrossRef]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12(6), 1004–1010 (2004).
[CrossRef] [PubMed]

Nguyen, T. D.

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H, 73940H-7 (2009).
[CrossRef]

Ordal, M. A.

Ortuño, R.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Pai, C. S.

Park, Q.-H.

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Rodríguez-Fortuño, F. J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

Seo, M. A.

Sohn, J. Y.

Tanner, D. B.

Taylor, J. A.

Thio, T.

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

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[CrossRef]

Vardeny, Z. V.

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H, 73940H-7 (2009).
[CrossRef]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

Ward, C. A.

Wolff, P.

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

Woo, K.

Xie, S.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Ye, Y. H.

Yuan, M.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Zhang, J. Y.

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Zhou, R.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Zhou, X.

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Matsui, Z. V. Vardeny, A. Agrawal, A. Nahata, and R. Menon, “Resonantly-enhanced transmission through a periodic array of subwavelength apertures in heavily-doped conducting polymer films,” Appl. Phys. Lett. 88(7), 071101 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. Phys. Condens. Matter (1)

H. Li, S. Xie, R. Zhou, Q. Liu, X. Zhou, and M. Yuan, “Two different transmission tunnels of light through double-layer gold nanohole arrays,” J. Phys. Condens. Matter 20(41), 415223 (2008).
[CrossRef]

Nat. Mater. (1)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Nat. Photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[CrossRef]

Nature (3)

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

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

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (2)

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
[CrossRef]

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. D. Nguyen, A. Nahata, and Z. V. Vardeny, “THz anomalous transmission in plasmonic lattices: incidence angle dependence,” Proc. SPIE 7394, 73940H, 73940H-7 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Science (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a double layer aperture array with aperture diameter, D = 750µm, periodicity, a = 1500 µm, metal film thickness, h = 75 µm and gap spacing, d, taking on values between 0 and 3000 µm.

Fig. 2
Fig. 2

THz electric field transmission spectra, t(ω), using a double layer periodic array (a) t(ω) of a single layer periodic aperture array using the parameters given in Fig. 1 , where the resonances (Ri) and anti-resonances (ARi) are denoted. (b) t(ω) for the double layer structure as a function of the gap spacing, d. The new transmission bands are labeled MFP1 and MFP2 (see text). The plots are vertically offset from the origin in units of ~0.4 for clarity. (c) Summary of the experimental resonant frequencies, ω/2π, for R1, MFP1 and MFP2 bands in t(ω) as a function of d.

Fig. 3
Fig. 3

Numerical calculations of t(ω) for a double layer periodic aperture array, assuming that ε(ω) is that of an unperforated metal at THz frequencies (ε ~-3x104 + i106). The spectra are offset from the origin in units of 1 for clarity.

Fig. 4
Fig. 4

Numerical calculations of t(ω) for a double layer periodic aperture array. (a) Real and imaginary components of the effective ε(ω) response for a single layer periodic aperture array extracted from the amplitude and phase of t(ω) (red traces). The fit (blue lines) is calculated using Eq. (2). (b) Numerical simulation of the transmission spectra for the double-layer structure using the dielectric properties obtained in (a). MFP1, MFP2 and R1 resonances are denoted (c) Summary of the experimental (red diamonds from Fig. 2(c)) and calculated (blue triangles) resonant frequencies, ω/2π for R1, MFP1 and MFP2 bands in t(ω) spectra, as a function of d.

Fig. 5
Fig. 5

Electric field transmission spectra as in Figs. 2 and 4, but for a commensurate double layer random hole array with apertures of diameter, D = 750µm, metal thickness, h = 75 µm and spacing, d that varies between 0 and 3000 µm. (a) Experimentally measured t(ω) of a single layer random aperture array. (b) Experimentally measured t(ω) for the double layer structure for three different values of d. MFP1 through MFP4 represent the different orders of MFP resonances. (c) Experimental (red line) and calculated (blue line) real and imaginary ε(ω) components of the individual random array extracted from t(ω) in (a). (d) Numerical simulation of t(ω) for the double-layer hole array structure using the same parameters as in (c). (e) Summary of the experimental (red diamonds) and calculated (blue triangles) resonant frequencies, ω/2π for the MFP1 through MFP4 bands in t(ω) as a function of d.

Fig. 6
Fig. 6

t(ω) spectra of multi-layer periodic aperture arrays. (a) Comparison between a double layer structure with spacing d = 0 (blue line) and d = 0.8 mm (red line). (b) Comparison between a single layer periodic array (black line) and a triple layer aperture array structure (red line) with d ~1 cm. (Inset) Schematic diagram of the triple-layer transmission measurement. The middle plate is rotated from the normal by 5°.

Tables (2)

Tables Icon

Table 1 The “best fit” parameters for the effective ε(ω) of periodic aperture arrays with lattice spacing, a = 1.5 mm and diameter, D = 750 µm. The parameters are defined in Eq. (2). In the fit, the TO resonant frequencies, ω T j , were set to the AR frequencies in the transmission spectra, while the LO resonant frequencies, ω L j , were set to the frequencies corresponding to the resonance peaks, R j .

Tables Icon

Table 2 The “best fit” parameters for the effective ε(ω) of random aperture arrays with D = 750 µm. The parameters are defined in Eq. (2).

Equations (2)

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t ( ω ) = | t ( ω ) | exp [ φ ( ω ) ] = E t r a n s m i t t e d ( ω ) E i n c i d e n t ( ω )
ε ˜ ( ω ) = ε r ( 1 ω ˜ p 2 ω 2 + i γ ω ) + j i ε p j ω L j 2 ω 2 ω T j 2 ω 2 i γ j ω ,

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