Abstract

We have systematically measured ε(ω) of subwavelength aperture arrays fabricated in metal films as a function of aperture size and incidence angle using terahertz time-domain spectroscopy. This approach simultaneously yields both the real and imaginary ε(ω) components, enabling deeper insight into the underlying mechanism of the ‘enhanced optical transmission’ (EOT) phenomenon. For random aperture arrays we find that ε(ω) has a plasma response, with an effective plasma frequency that is determined by the waveguide mode cutoff frequency of the individual apertures. However ε(ω) in plasmonic lattices is strongly modulated at discrete resonant frequencies that correspond to the reciprocal vectors in the structure factor that are superposed on the plasma envelope response and appear as dips in the EOT spectrum. The existence of a sum rule for the discrete resonance oscillator strengths when the aperture size or incidence angle are changed validates our approach and allows for engineering of the individual resonances in the EOT spectrum.

©2008 Optical Society of America

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  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. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517–521 (2007).
    [Crossref] [PubMed]
  3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  4. 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]
  5. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [Crossref] [PubMed]
  6. L. Martin-Moreno, F. J. Garcia-Videl, 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]
  7. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).
    [Crossref]
  8. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
    [Crossref] [PubMed]
  9. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
    [Crossref] [PubMed]
  10. H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 10041–1010 (2004).
    [Crossref]
  11. J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
    [Crossref]
  12. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
    [Crossref] [PubMed]
  13. F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays” Phys. Rev. B 74, 153416 (2006).
    [Crossref]
  14. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [Crossref] [PubMed]
  15. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. Pure Appl. Opt. 7, S97–S101 (2005).
    [Crossref]
  16. M. Sarrazin, J.-P. Vigneron, and J-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
    [Crossref]
  17. A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
    [Crossref]
  18. C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75, 245421 (2007)
    [Crossref]
  19. P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
    [Crossref]
  20. N. Marcuvitz, Waveguide Handbook (McGraw-Hill, 1951).
  21. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
    [Crossref] [PubMed]
  22. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976).
  23. E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier B.V., 2004).
  24. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [Crossref]
  25. A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96, 063903 (2006).
    [Crossref] [PubMed]

2008 (2)

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

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[Crossref]

2007 (3)

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
[Crossref]

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75, 245421 (2007)
[Crossref]

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

2006 (2)

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays” Phys. Rev. B 74, 153416 (2006).
[Crossref]

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96, 063903 (2006).
[Crossref] [PubMed]

2005 (2)

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

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

2004 (4)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 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, 10041–1010 (2004).
[Crossref]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[Crossref] [PubMed]

2003 (3)

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).
[Crossref]

J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[Crossref]

M. Sarrazin, J.-P. Vigneron, and J-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

2001 (1)

L. Martin-Moreno, F. J. Garcia-Videl, 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]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

1998 (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]

1996 (1)

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]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Agrawal, A.

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

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
[Crossref]

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier B.V., 2004).

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976).

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

Cao, H.

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 10041–1010 (2004).
[Crossref]

Catrysse, P. B.

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[Crossref]

Cottam, M. G.

E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier B.V., 2004).

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

L. Martin-Moreno, F. J. Garcia-Videl, 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]

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]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Fan, S.

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[Crossref]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Garcia-Vidal, F. J.

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

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

Garcia-Videl, F. J.

L. Martin-Moreno, F. J. Garcia-Videl, 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]

Genet, C.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).
[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]

Gomez-Rivas, J.

J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[Crossref]

Grischkowsky, D.

Hangyo, M.

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays” Phys. Rev. B 74, 153416 (2006).
[Crossref]

Haring-Bolivar, P.

J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[Crossref]

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
[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]

Huang, C.

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75, 245421 (2007)
[Crossref]

Kurz, H.

J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[Crossref]

Lalanne, P.

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

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Videl, 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]

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]

Liu, H.

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

Loidl, A.

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96, 063903 (2006).
[Crossref] [PubMed]

Marcuvitz, N.

N. Marcuvitz, Waveguide Handbook (McGraw-Hill, 1951).

Martin-Moreno, L.

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

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

L. Martin-Moreno, F. J. Garcia-Videl, 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]

Matsui, T.

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

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
[Crossref]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976).

Miyamaru, F.

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays” Phys. Rev. B 74, 153416 (2006).
[Crossref]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

Nahata, A.

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

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
[Crossref]

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 10041–1010 (2004).
[Crossref]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Videl, 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]

Pendry, J. B.

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

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

L. Martin-Moreno, F. J. Garcia-Videl, 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]

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]

Pimenov, A.

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96, 063903 (2006).
[Crossref] [PubMed]

Qu, D.

Sambles, J. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Sarrazin, M.

M. Sarrazin, J.-P. Vigneron, and J-M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

Schotsch, C.

J. Gomez-Rivas, C. Schotsch, P. Haring-Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003).
[Crossref]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

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]

Tanaka, M.

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays” Phys. Rev. B 74, 153416 (2006).
[Crossref]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Videl, 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]

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]

van Exter, M. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).
[Crossref]

Vardeny, Z. V.

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

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, “Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays,” J. Opt. Soc. Am. B 24, 2545–2555 (2007).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75, 245421 (2007)
[Crossref]

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P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Determination of the real and imaginary components of ε(ω) for a random aperture array with D=800 µm and fractional aperture area of 12%. a) The amplitude transmission, t(ω) and phase, φ(ω) (Inset) spectra measured using THz-TDS. b) Spectra of real and imaginary ε(ω) components (red line) obtained from t(ω) and φ(ω) shown in (a). εreal (ω) is shown to pass through zero value at fc =0.19 THz. The modeled ε(ω) of the effective plasma (blue line) is based on Eq. (2) with parameters given in Table I.

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Fig. 2.
Fig. 2.

Determination of the real and imaginary components of ε(ω) for a plasmonic lattice with D=800 µm and a=2 mm. (a) The amplitude transmittance, t(ω) and (b) phase, φ(ω) spectra of the periodic aperture array measured using THz-TDS. (c) Spectra of real and (d) imaginary ε(ω) components (red line) obtained from t(ω) and φ(ω) in (a) and (b); the effective plasma frequency, fc =0.19 THz is assigned. The modeled ε(ω) of the effective plasma (blue line) is based on Eq. (3) with parameters given in Table II. (e) The amplitude reflectance, r(ω), and (f) absorption, α (ω) spectra directly obtained from ε(ω) shown in (c) and (d). Note that α(ω) exhibits peaks at the anti-resonance (AR) frequencies in t(ω).

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Fig. 3.
Fig. 3.

THz-TDS studies of stainless steel foils perforated with periodic (red line) and random (blue line) aperture arrays that were designed to have the same fractional aperture area and aperture diameter D as the corresponding periodic arrays. (a)–(d), t(ω) spectra for structures with a=2 mm and (a) D=500 µm (b) 700 µm (c) 800 µm and (d) 1200 µm. The resonant (Ri) and anti-resonant (ARi) frequencies are assigned, along with the cutoff frequency, fc for the individual apertures. (The inset in (d) is the ratio of the transmittance, t R1 at the R1 (±1, 0) resonance in the periodic EOT spectrum, to the peak transmittance, t NR of the non-resonant background in the corresponding random array spectrum, as a function of D/a.

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Fig. 4.
Fig. 4.

Calculated t(ω) spectra of the group of hole arrays shown in Fig. 3, based on the dielectric functions given in Eq. (2) for random (blue curves) and Eq. (3) for periodic (red curves) aperture arrays. The fitting parameters are given in Tables I and II, respectively. (a)–(d) are in the same order as in Fig. 3.

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Fig. 5.
Fig. 5.

Left Axis: The dependence of ε∞ on D (blue circles), obtained from the fit to ε(ω) for the random aperture arrays with a=2 mm (shown in Fig. 3) using Eq. (2) (and given in Table I). The corresponding solid blue line through the data points is an exponential fit. Right Axis: The red triangles show the sum of the oscillator strengths for all Rj resonances obtained from the fits to ε(ω) spectra (Table II). The horizontal red line through the points demonstrates the existence of oscillator strengths sum rule in ε(ω) spectra. Inset: the dependence of the effective plasma frequency, ω ˜ P on 1/D for the same aperture arrays (squares) with an accompanying least squares linear fit showing that in fact, ω ˜ P is determined by the individual aperture cut-off frequency, fc (~1/D).

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Fig. 6.
Fig. 6.

Incident angle dependent transmission studies on a stainless steel foil perforated with random and periodic aperture arrays with D=750 µm.t(ω) spectra for random array (a) and periodic array a=1.5 mm (b) at various angles θ between the incident beam and the surface normal. The fundamental (1, 0) SP resonance at ~0.19 THz splits into two resonances at frequencies ωT1′ and ωT1″ for θ≠0. (c) The corresponding spectra of the real (Left Axis) and imaginary (Right Axis) ε(ω) components obtained from t(ω) and φ(ω) at various θ. Inset in c shows the split and change of the resonance frequency ωT1 as a function of incidence angle θ. The transverse frequencies are fit using the equations ωT1′~c(G1,0-k ‖) and ωT1″~c(G1,0+k ‖), where k ‖=(2π/λ)sinθ. (d) The incident angle, θ dependence of the resonance strengths S1′ (red circles; left axis) and S1″ (blue circles; right axis) as obtained from the ε(ω) response shown in (c) and using Eq. (3) (parameters given in Table III). The corresponding solid lines through the data points are guide to the eye. With increasing θ, the oscillator strength (S1′) at frequency ωT1′ decreases, whereas the oscillator strength (S1″) at frequency ωT1″ increases in a corresponding manner, thereby keeping the sum of oscillator strengths (ΣS) constant (see Table III).

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Tables (3)

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Table I. The “best fit” parameters for the measured ε(ω) response of random aperture arrays with average spacing a=2 mm and various aperture diameters, D using Eq. (2).a

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Table II. The “best fit” parameters for the measured ε(ω) response of a group of periodic aperture arrays with fixed periodicity, a=2 mm and various aperture diameters, D using the effective dielectric model given in Eq. (3). b

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Table III: The “best fit” parameters for modeling the effective ε(ω) of periodic aperture array with periodicity, a=1.5 mm, aperture diameter, D=750 µm at various angles, θ between the incident beam and the surface normal (Fig. 6), using the model given in Eq. (3).c

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Equations (4)

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t ( ω ) = ∣ t ( ω ) ∣ exp ⁡ [ i φ ( ω ) ] = E transmitted ( ω ) E incident ( ω )
ε ˜ ( ω ) = ε ∞ ( 1 − ω ˜ p 2 ω 2 + i γ ω ) ,
ε ˜ ( ω ) = ε ∞ ( 1 − ω ˜ p 2 ω 2 + i γ ω ) + ∑ j ω L 2 j − ω 2 ω T 2 j − ω 2 − i γ j ω ,
ω T j = 2 π c a m 2 + n 2

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