Abstract

A modal method is developed analytically to investigate the THz optical transmission and reflection of a metallic thin film perforated by a 2D array of rectangular apertures. For subwavelength apertures, this optical model is interpreted in terms of passive electrical circuits, with interface admittances accounting for the THz surface conduction properties of the metallic film. The reactive component of the admittance of the evanescent diffraction cloud is shown to exhibit resonant behavior governed by the shape factors of the array. Interaction of such an electrodynamic resonance with the Rayleigh diffraction orders may alter their standard Fano profiles. Experimental evidence of the resonance is obtained owing to lineshape analysis of transmittance measurements in the THz range on metallic thin films deposited on a dielectric substrate, both above and below the first Wood–Rayleigh anomaly.

© 2019 Optical Society of America

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    [Crossref]
  2. R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
    [Crossref]
  3. F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
    [Crossref]
  4. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
    [Crossref]
  5. 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]
  6. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
    [Crossref]
  7. M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
    [Crossref]
  8. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [Crossref]
  9. L. O. Goldstone and A. A. Oliner, “Note on surface waves along corrugated structures,” IEEE Trans. Antennas Propag. 7, 274–276 (1959).
    [Crossref]
  10. F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
    [Crossref]
  11. C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).
  12. R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17, 5571–5579 (2009).
    [Crossref]
  13. J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
    [Crossref]
  14. F. J. García de Abajo and J. J. Sáenz, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 233901 (2005).
    [Crossref]
  15. Y. Todorov and C. Minot, “Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure,” J. Opt. Soc. Am. A 24, 3100–3114 (2007).
    [Crossref]
  16. C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
    [Crossref]
  17. A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
    [Crossref]
  18. A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
    [Crossref]
  19. L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
    [Crossref]
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    [Crossref]
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    [Crossref]
  24. D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
    [Crossref]
  25. D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
    [Crossref]
  26. F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
    [Crossref]
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    [Crossref]
  29. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A 7, S97–S101 (2005).
    [Crossref]

2017 (1)

J. M. Woo, S. Hussain, and J. H. Jang, “A terahertz in-line polarization converter based on through via connected double layer slot structure,” Sci. Rep. 7, 42952 (2017).
[Crossref]

2015 (1)

A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
[Crossref]

2013 (1)

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

2012 (1)

J. Lloyd-Hughes and T. I. Jeon, “A review of the terahertz conductivity of bulk and nano-materials,” J. Infrared Millim. Terahertz Waves 33, 871–925 (2012).
[Crossref]

2010 (3)

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[Crossref]

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

2009 (3)

2008 (3)

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[Crossref]

2007 (2)

2006 (1)

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
[Crossref]

2005 (4)

F. J. García de Abajo and J. J. Sáenz, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
[Crossref]

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

2004 (1)

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

2003 (1)

2002 (1)

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[Crossref]

1999 (1)

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

1998 (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]

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

1959 (1)

L. O. Goldstone and A. A. Oliner, “Note on surface waves along corrugated structures,” IEEE Trans. Antennas Propag. 7, 274–276 (1959).
[Crossref]

Ahn, Y. H.

Alexopóulos, N. G.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

Armand, D.

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

Ashry, I.

A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
[Crossref]

Brolo, A. G.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Carbonell, J.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

Choi, S. B.

Coutaz, J. L.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

Croënne, C.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

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 (London) 391, 667–669 (1998).
[Crossref]

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]

Fan, S.

García de Abajo, F. J.

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[Crossref]

F. J. García de Abajo and J. J. Sáenz, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref]

García-Vidal, F. J.

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[Crossref]

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
[Crossref]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

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

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

Garet, F.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

Ghaemi, H. F.

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]

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

Goldstone, L. O.

L. O. Goldstone and A. A. Oliner, “Note on surface waves along corrugated structures,” IEEE Trans. Antennas Propag. 7, 274–276 (1959).
[Crossref]

Gordon, R.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Greffet, J. J.

J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[Crossref]

Grupp, D. E.

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]

Gu, Z. F.

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

Hussain, S.

J. M. Woo, S. Hussain, and J. H. Jang, “A terahertz in-line polarization converter based on through via connected double layer slot structure,” Sci. Rep. 7, 42952 (2017).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), p. 240.

Jang, J. H.

J. M. Woo, S. Hussain, and J. H. Jang, “A terahertz in-line polarization converter based on through via connected double layer slot structure,” Sci. Rep. 7, 42952 (2017).
[Crossref]

Jelinek, L.

Jeon, T. I.

J. Lloyd-Hughes and T. I. Jeon, “A review of the terahertz conductivity of bulk and nano-materials,” J. Infrared Millim. Terahertz Waves 33, 871–925 (2012).
[Crossref]

Jeong, M. S.

Jimenez Broas, R. F.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

Joannopoulos, J. D.

Kang, C.

Kavanagh, K. L.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Kim, D. S.

Laroche, M.

J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[Crossref]

Lerer, A. M.

A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
[Crossref]

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 (London) 391, 667–669 (1998).
[Crossref]

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]

Lheurette, E.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

Lippens, D.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

Lloyd-Hughes, J.

J. Lloyd-Hughes and T. I. Jeon, “A review of the terahertz conductivity of bulk and nano-materials,” J. Infrared Millim. Terahertz Waves 33, 871–925 (2012).
[Crossref]

Mahros, A. M.

A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
[Crossref]

Marqués, R.

R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17, 5571–5579 (2009).
[Crossref]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[Crossref]

Marquier, F.

J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[Crossref]

Martín-Moreno, L.

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[Crossref]

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
[Crossref]

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

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

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

Medina, F.

R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17, 5571–5579 (2009).
[Crossref]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[Crossref]

Mesa, F.

R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17, 5571–5579 (2009).
[Crossref]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[Crossref]

Minot, C.

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

Y. Todorov and C. Minot, “Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure,” J. Opt. Soc. Am. A 24, 3100–3114 (2007).
[Crossref]

Moreno, E.

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
[Crossref]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

Oliner, A. A.

L. O. Goldstone and A. A. Oliner, “Note on surface waves along corrugated structures,” IEEE Trans. Antennas Propag. 7, 274–276 (1959).
[Crossref]

Park, D. J.

Pendry, J. B.

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

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

Porto, J. A.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

Pozar, D. M.

D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, 2012), p. 194.

Rotermund, F.

Sáenz, J. J.

F. J. García de Abajo and J. J. Sáenz, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref]

Schuchinsky, A. G.

A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
[Crossref]

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

Sinton, D.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Sohn, I. B.

Suh, W.

Tharwat, M. M.

A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
[Crossref]

Thio, T.

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]

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

Todorov, Y.

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

Y. Todorov and C. Minot, “Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure,” J. Opt. Soc. Am. A 24, 3100–3114 (2007).
[Crossref]

Treacy, M. M. J.

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[Crossref]

Wang, C. C.

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

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 (London) 391, 667–669 (1998).
[Crossref]

Woo, J. M.

J. M. Woo, S. Hussain, and J. H. Jang, “A terahertz in-line polarization converter based on through via connected double layer slot structure,” Sci. Rep. 7, 42952 (2017).
[Crossref]

Yablonovitch, E.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

Zelenchuk, D. E.

A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
[Crossref]

Zhang, L.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

Zhou, X.

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

Zhu, C. Q.

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

Appl. Comput. Electromagn. Soc. J. (1)

C. C. Wang, C. Q. Zhu, X. Zhou, and Z. F. Gu, “Calculation and analysis of shielding effectiveness of the rectangular enclosure with apertures,” Appl. Comput. Electromagn. Soc. J. 28, 535–545 (2013).

IEEE J. Sel. Top. Quantum Electron. (1)

D. Armand, Y. Todorov, F. Garet, C. Minot, and J. L. Coutaz, “Study of the transmission of subwavelength metallic grids in the THz frequency range,” IEEE J. Sel. Top. Quantum Electron. 14, 513–520 (2008).
[Crossref]

IEEE Trans. Antennas Propag. (1)

L. O. Goldstone and A. A. Oliner, “Note on surface waves along corrugated structures,” IEEE Trans. Antennas Propag. 7, 274–276 (1959).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[Crossref]

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alexopóulos, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[Crossref]

J. Appl. Phys. (1)

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108, 014907 (2010).
[Crossref]

J. Eur. Opt. Soc. (1)

A. M. Mahros, M. M. Tharwat, and I. Ashry, “Exploring the impact of rotating rectangular plasmonic nano-hole arrays on the transmission spectra and its application as a plasmonic sensor,” J. Eur. Opt. Soc. 10, 15023 (2015).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

J. Lloyd-Hughes and T. I. Jeon, “A review of the terahertz conductivity of bulk and nano-materials,” J. Infrared Millim. Terahertz Waves 33, 871–925 (2012).
[Crossref]

J. Opt. A (3)

A. G. Schuchinsky, D. E. Zelenchuk, and A. M. Lerer, “Enhanced transmission in microwave arrays of periodic sub-wavelength apertures,” J. Opt. A 7, S102–S109 (2005).
[Crossref]

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94–S97 (2006).
[Crossref]

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

J. Opt. Soc. Am. A (2)

J. Phys. Condens. Matter (1)

L. Martín-Moreno and F. J. García-Vidal, “Minimal model for optical transmission through holey metal films,” J. Phys. Condens. Matter 20, 304214 (2008).
[Crossref]

Laser Photon. Rev. (1)

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Nature (London) (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 (London) 391, 667–669 (1998).
[Crossref]

Opt. Express (2)

Phys. Rev. B (3)

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[Crossref]

C. Minot, Y. Todorov, D. Armand, F. Garet, and J. L. Coutaz, “Long-wavelength limit and Fano profiles of extraordinary transmission through metallic slit gratings in the THz range,” Phys. Rev. B 80, 153410 (2009).
[Crossref]

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]

Phys. Rev. Lett. (3)

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref]

J. J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[Crossref]

F. J. García de Abajo and J. J. Sáenz, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref]

Rev. Mod. Phys. (1)

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[Crossref]

Sci. Rep. (1)

J. M. Woo, S. Hussain, and J. H. Jang, “A terahertz in-line polarization converter based on through via connected double layer slot structure,” Sci. Rep. 7, 42952 (2017).
[Crossref]

Science (1)

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

Other (2)

D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, 2012), p. 194.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), p. 240.

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Figures (9)

Fig. 1.
Fig. 1. Schematic drawing of sample under classical incidence α = sin θ i in plane ( x , z ), for incidence angle θ i . The geometry is displayed with colors for the dielectric constant ε of the metallic thin film (gray), the dielectric layers (yellow), and the substrate (blue) and superstrate (transparent).
Fig. 2.
Fig. 2. Signal flow graph of the metallic film as a function of the reflection ( r A , r B ) and transmission ( t A , t B ) coefficients of either interface (A, B). η is the reduced surface impedance of the metal, Z ¯ the reduced characteristic impedance of the aperture, and θ its phase length.
Fig. 3.
Fig. 3. Schematic view of the current and charge densities generated near a rectangular metallic aperture by incident wave and TE 10 mode. The currents are generated inductively by the components of the magnetic field parallel to the surface, the charges capacitively by the component of the electric field normal to the surface.
Fig. 4.
Fig. 4. Absolute value of susceptance as a function of the aperture duty cycles according to Eqs. (13) and (14), (a) in perpendicular polarization with d x = 100 μm , d y = 24 μm , (b) in parallel polarization with d x = 24 μm , d y = 100 μm . The wavelength is λ = 300 μm . Points 1 and 2 position samples S 1 and S 2 .
Fig. 5.
Fig. 5. Interaction between Fano profile of m-line at δ ϕ 1 = 0 and SPMI resonance at δ ϕ 1 = δ ϕ 1 r as a function of the distance between the two resonances. The other parameters are S 0 / s = 1 , s / s = 0.25 .
Fig. 6.
Fig. 6. THz transmittance of sample S 1 at normal incidence for ( ) perpendicular polarization (red lines) and ( / / ) parallel polarization (blue lines). Open squares and circles are experimental data. Solid lines: one-mode model. Thick dashed lines: long wavelength limit of the one-mode model based on Eqs. (13) and (14). Thin and dark short-dashed-dotted lines: two-mode model ( TE 10 and TE 30 ). The G i and G i ( i > 0 ) label first-order guided-mode resonances.
Fig. 7.
Fig. 7. Same as Fig. 6 for sample S 2 .
Fig. 8.
Fig. 8. Same as Fig. 6 for sample S 3 except long wavelength limits for perpendicular polarization (red dashed lines): thin lines are based on Eqs. (13) and (14) in the one-mode model, thick lines on Eq. (15) and empirical adjustment of the capacitance and inductance of the metallic surface or interface. The two bars (dotted line) are markers for the splitting of the first m-line observed in experiment.
Fig. 9.
Fig. 9. Same as Fig. 8 for sample S 4 , only changing the substrate thickness.

Tables (1)

Tables Icon

Table 1. Geometrical Parameters of the Samples a

Equations (50)

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M 1 = 1 2 [ 1 e i μ 10 h e i μ 10 h 1 ]
M 2 = [ ( Z ¯ 10 η ) e i μ 10 h ( Z ¯ 10 + η ) e i μ 10 h ( Z ¯ 10 + η ) ( Z ¯ 10 η ) ]
M S = [ S B h h 0 0 S A h h ]
T B h = T M B h t M A h γ ¯ A S 0 2 Z ¯ ϒ A ( + ) ϒ B ( + ) e i θ ϒ A ( ) ϒ B ( ) e i θ ,
ϒ A B ( ± ) = 1 ± 2 ( Z ¯ η ) S ¯ A B h h .
S 0 = a d x b d y | J 01 ( a ) I 00 ( b ) | 2
r A B = 1 2 ( Z ¯ + η ) S ¯ A B h h 1 + 2 ( Z ¯ η ) S ¯ A B h h , t A B = 2 1 + 2 ( Z ¯ η ) S ¯ A B h h ,
T B h = T M B h t M A h γ ¯ A S 0 Z ¯ 1 2 t A t B 1 r A r B e 2 i θ .
t A B = 1 + r A B 1 2 η S ¯ A B h h .
R A h = ρ M A h + ( t M A h ) 2 γ ¯ A S 0 [ Z ¯ η ] ϒ B ( + ) e i θ + [ Z ¯ + η ] ϒ B ( ) e i θ ϒ A ( + ) ϒ B ( + ) e i θ ϒ A ( ) ϒ B ( ) e i θ .
R A h = ρ M A h + ( t M A h ) 2 γ ¯ A S 0 Z ¯ 1 2 ( 1 η Z ¯ ) t A + ( 1 + η Z ¯ ) t A r B e 2 i θ 1 r A r B e 2 i θ .
Z ¯ A B = 1 2 S ¯ A B h h .
T B h = T M B h t M A h γ ¯ A S 0 Z ¯ × e i θ z A / / z B cos θ [ 1 η Z ¯ ϒ c ] i sin θ [ z A / / z B + 1 z A + z B η Z ¯ ϒ s ] ,
ϒ c = 2 z A + z B , ϒ s = 1 η Z ¯ 1 z A + z B .
T B h = T M B h t M A h γ ¯ A S 0 Z ¯ z A / / z B ,
S A h h = a b d x d y p q J p 1 + ( a ) I q 0 + ( b ) J p 1 ( a ) I q 0 ( b ) α ¯ p 2 + β ¯ q 2 × [ α ¯ p 2 ε A α ¯ p 2 β ¯ q 2 1 + η ε A α ¯ p 2 β ¯ q 2 + β ¯ q 2 ε A η ε A + ε A α ¯ p 2 β ¯ q 2 ] .
S A TE ( α ) = a d x p 0 | J p 1 ( a ) | 2 ε A α ¯ p 2 1 + η ε A α ¯ p 2 ,
S A TM ( β ) = b d y q 0 | I q 0 ( b ) | 2 ε A η ε A + ε A β ¯ q 2 ,
S A h h a b d x d y | J 01 ( a ) I 00 ( b ) | 2 ε A α ¯ 2 1 + η ε A α ¯ 2 + b d y | I 00 ( b ) | 2 S A TE S ( α ) + 1 2 S A TM s ( 0 ) ,
S A h h a b d x d y | J 01 ( a ) I 00 ( b ) | 2 ε A η ε A + ε A β ¯ 2 + a d x | J 01 ( a ) | 2 S A TM S ( β ) + S A TE s ( 0 ) .
S α ( r s ) ( a d x ) = p = 1 ( p + α d x 2 π ) cos 2 ( p π a d x + α a 2 ) ( p + α d x 2 π + d x 2 a ) r ( p + α d x 2 π d x 2 a ) s
S β ( r ) ( b d y ) = q = 1 sin 2 ( q π b d y + β b 2 ) ( q + β d y 2 π ) r .
S A TE ( α ) = i λ a ( d x 2 π a ) 2 [ S α ( 22 ) ( a d x ) + S α ( 22 ) ( a d x ) ] 1 i ω L A ( α )
S A TM ( β ) = i ε A b λ ( d y 2 π b ) 2 [ S β ( 3 ) ( b d y ) + S β ( 3 ) ( b d y ) ] i ω C A ( β ) ,
a d x | J p 1 ( a ) | 2 [ ε A α ¯ p 2 1 + η ε A α ¯ p 2 i | α ¯ p | 1 + i η | α ¯ p | ] ,
b d y | I q 0 ( b ) | 2 [ ε A η ε A + ε A β ¯ q 2 ε A η ε A + i | β ¯ q | ] .
S B h h = a b d x d y | J 01 ( a ) I 00 ( b ) | 2 ε 1 F 00 e + b d y | I 00 ( b ) | 2 i ω L B i ω C B 2
S B h h = a b d x d y | J 01 ( a ) I 00 ( b ) | 2 ε 1 F 00 h + i ω L B a d x | J 01 ( a ) | 2 i ω C B
T B / / h = 1 2 T M B h t M A h γ ¯ A Z ¯ S 0 i S / / ,
S = Z ¯ 2 S 0 [ ω ( C A + C B ) 1 ω L A / / L B 2 b d y | I 00 ( b ) | 2 ]
S / / = Z ¯ S 0 [ ω ( C A + C B ) a d x | J 01 ( a ) | 2 1 ω L A / / L B ] .
| T M B h | 2 = 4 ε 1 1 + 4 r B ( 1 r B ) 2 cos 2 ( γ 1 L 1 ) ,
r B = ε 1 1 ε 1 + 1 .
T 0 0 = 1 1 + S 2 4 1 1 + F ( S ) sin 2 ( γ 1 L 1 ) + G ( S ) cos ( 2 γ 1 L 1 )
F ( S ) = F 2 π 2 1 ϵ 1 ϵ 1 1 S 2 1 + S 2 4 , G ( S ) = F 2 π 2 1 ϵ 1 S 1 + S 2 4 .
F = π r B 1 r B = π 2 ε 1 1 ,
t 0 1 = t 0 0 ( S 0 i S ) S 0 i S + 2 i S 1 ,
S 1 = | J 11 ( a ) | 2 | J 01 ( a ) | 2 ( i ε 1 α ¯ 1 2 F 10 e | α ¯ 1 | )
S 1 / / = | I 10 ( b ) | 2 | I 00 ( b ) | 2 ( i ε 1 F 01 h ε 1 β ¯ 1 2 + ε 1 | β ¯ 1 | )
S 1 ( ϕ 1 e ) = | J 11 ( a ) | 2 | J 01 ( a ) | 2 ( α ¯ 1 + ϕ 1 e ϕ 0 ϕ 1 e + ε 1 ϕ B e tan ϕ 1 e ε 1 ϕ B e ϕ 1 e tan ϕ 1 e )
S 1 / / ( ϕ 1 h ) = ε 1 | I 10 ( b ) | 2 | I 00 ( b ) | 2 ( 1 β ¯ 1 + ϕ 0 ϕ 1 h ϕ B h ϕ 1 h tan ϕ 1 h ϕ 1 h + ϕ B h tan ϕ 1 h ) ,
I p m ± ( a ) = 1 a 0 a e ± i α p x cos ν m x d x ,
J p m ± ( a ) = 1 a 0 a e ± i α p x sin ν m x d x ,
α p = α + 2 π p d x ,
S A ( r r ) h h = a b 2 η d x d y p q J p m + ( a ) I q n + ( b ) J p m ( a ) I q n ( b ) α ¯ p 2 + β ¯ q 2 × [ α ¯ p 2 ( 1 ρ M A h , p q ) + β ¯ q 2 ( 1 + ρ M A e , p q ) ] ,
S A ( r r ) h e = a b 2 η d x d y p q J p m + ( a ) I q n + ( b ) I p m ( a ) J q n ( b ) α ¯ p 2 + β ¯ q 2 × α ¯ p β ¯ q ( ρ M A e , p q + ρ M A h , p q ) ,
1 ± R M B e h , p q = ( 1 ± ρ M 1 e h , p q ) F p q e h ,
ρ M 1 e , p q = η ε 1 γ ¯ 1 , p q η ε 1 + γ ¯ 1 , p q , ρ M 1 h , p q = 1 η γ ¯ 1 , p q 1 + η γ ¯ 1 , p q ,
γ ¯ i , p q = ε i α ¯ p 2 β ¯ q 2 ( i = 1 , A , B ) ,
F p q e h = 1 ± ρ 1 B e h , p q e 2 i γ 1 , p q L 1 1 + ρ M 1 e h , p q ρ 1 B e h , p q e 2 i γ 1 , p q L 1 .

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