Abstract

When illuminated by incident plane waves, conducting screens pierced by an array of holes may permit strong diffusions through them even at frequencies where the size of each hole is considerably less than the wavelength, amounting to extraordinary transmission (ET). This well-known phenomenon is herein further investigated beyond conventional topologies by considering square holes with tapered profiles, which are thereupon used as the vehicle for characterizing the degree of ET in a quantifiable manner, achieved by relating the transmissivity of an actual screen with that predicted by classical Bethe's theory. In terms of such quantified ET, the ordinary subwavelength square hole array is compared with a screen of equal thickness and perforated by holes of the same size as the former at the input side but get larger as they tunnel through to the exit apertures. It is found that the latter flared holes provide higher levels of ET than their unflared counterparts, the advantage being more pronounced for larger ratios of exit-to-entry hole sizes. Investigations of several hole-flare profiles also reveal that the flanged-type small input diaphragm directly peering (abruptly flared) into a single large square hole provides the greatest degree of ET. Oblique angles of incidence and conductor losses are investigated as well. Prototypes of perforated screens were also manufactured and measured with success in corroborating with theoretical predictions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes

R. Marqués, F. Mesa, L. Jelinek, and F. Medina
Opt. Express 17(7) 5571-5579 (2009)

Extraordinary optical transmission through incommensurate metal hole arrays in the terahertz region

Yoji Jimba, Keisuke Takano, Masanori Hangyo, and Hiroshi Miyazaki
J. Opt. Soc. Am. B 30(9) 2476-2482 (2013)

References

  • View by:
  • |
  • |
  • |

  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(6668), 667–669 (1998).
    [Crossref]
  2. J. R. Sambles, “More than transparent,” Nature (London) 391(6668), 641–642 (1998).
    [Crossref]
  3. T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
    [Crossref]
  4. R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photonics Rev. 4(2), 311–335 (2010).
    [Crossref]
  5. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
    [Crossref]
  6. J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
    [Crossref]
  7. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
    [Crossref]
  8. R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
    [Crossref]
  9. T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
    [Crossref]
  10. T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
    [Crossref]
  11. J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
    [Crossref]
  12. H. Shen and B. Maes, “Enhanced optical transmission through tapered metallic gratings,” Appl. Phys. Lett. 100(24), 241104 (2012).
    [Crossref]
  13. F. Medina, R. Rodriguez-Berral, and F. Mesa, “Circuit model for metallic gratings with tapered and stepped slits,” Proc. 42nd European Microwave Conference, Oct. 2012.
  14. Y. Liang, W. Peng, R. Hu, and H. Zou, “Extraordinary optical transmission based on subwavelength metallic grating with ellipse walls,” Opt. Express 21(5), 6139–6152 (2013).
    [Crossref]
  15. M. N. M. Kehn, “Modal analysis of metallic screen with finite conductivity perforated by an array of subwavelength rectangular flared holes,” Opt. Express 26(25), 32981–33004 (2018).
    [Crossref]
  16. J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
    [Crossref]
  17. R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
    [Crossref]
  18. H. L. Chen, S. Y. Chuang, W. H. Lee, S. S. Kuo, W. F. Su, S. L. Ku, and Y. F. Chou, “Extraordinary transmittance in three-dimensional crater, pyramid, and hole-array structures prepared through reversal imprinting of metal films,” Opt. Express 17(3), 1636–1645 (2009).
    [Crossref]
  19. Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
    [Crossref]
  20. C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
    [Crossref]
  21. M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
    [Crossref]
  22. P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
    [Crossref]
  23. M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
    [Crossref]
  24. M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
    [Crossref]
  25. L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50(5), 4094–4106 (1994).
    [Crossref]
  26. F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
    [Crossref]
  27. L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
    [Crossref]
  28. B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
    [Crossref]
  29. A. Peer and R. Biswas, “Extraordinary optical transmission in nanopatterned ultrathin metal films without holes,” Nanoscale 8(8), 4657–4666 (2016).
    [Crossref]
  30. Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
    [Crossref]
  31. A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
    [Crossref]
  32. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
    [Crossref]
  33. M. N. M. Kehn, “Extraordinary transmission through subwavelength hole arrays for general oblique incidence - mechanism as related to surface wave dispersion and Floquet lattice diagrams,” Prog. Electromag. Res. (PIER) 82, 49–71 (2018).
    [Crossref]

2019 (1)

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

2018 (4)

M. N. M. Kehn, “Extraordinary transmission through subwavelength hole arrays for general oblique incidence - mechanism as related to surface wave dispersion and Floquet lattice diagrams,” Prog. Electromag. Res. (PIER) 82, 49–71 (2018).
[Crossref]

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
[Crossref]

M. N. M. Kehn, “Modal analysis of metallic screen with finite conductivity perforated by an array of subwavelength rectangular flared holes,” Opt. Express 26(25), 32981–33004 (2018).
[Crossref]

2017 (3)

C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

2016 (3)

A. Peer and R. Biswas, “Extraordinary optical transmission in nanopatterned ultrathin metal films without holes,” Nanoscale 8(8), 4657–4666 (2016).
[Crossref]

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
[Crossref]

2015 (1)

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

2014 (2)

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (2)

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
[Crossref]

2010 (3)

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

2009 (1)

2008 (3)

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

2007 (1)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[Crossref]

2000 (1)

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
[Crossref]

1998 (2)

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(6668), 667–669 (1998).
[Crossref]

J. R. Sambles, “More than transparent,” Nature (London) 391(6668), 641–642 (1998).
[Crossref]

1994 (1)

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50(5), 4094–4106 (1994).
[Crossref]

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[Crossref]

Ai, B.

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Anderton, C. R.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Ayza, M. S.

M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
[Crossref]

Beermann, J.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

Beruete, M.

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
[Crossref]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[Crossref]

Biswas, R.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

A. Peer and R. Biswas, “Extraordinary optical transmission in nanopatterned ultrathin metal films without holes,” Nanoscale 8(8), 4657–4666 (2016).
[Crossref]

Boix, R. R.

M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
[Crossref]

Bozhevolnyi, S. I.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

Camacho, M.

M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
[Crossref]

Chen, H. L.

Chen, Y.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Chen, Z.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Chou, Y. F.

Chuang, S. Y.

Coe, J. V.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

Devaux, E.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

Duan, H.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Ebbesen, T. W.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[Crossref]

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
[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(6668), 667–669 (1998).
[Crossref]

Gao, H.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[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 (London) 391(6668), 667–669 (1998).
[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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

Gray, S. K.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Hafner, C.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50(5), 4094–4106 (1994).
[Crossref]

Heer, J. M.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

Hollingsworth, J. A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

Htoon, H.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

Hu, R.

Hu, Z.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

Kaivola, M.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

Kehn, M. N. M.

M. N. M. Kehn, “Extraordinary transmission through subwavelength hole arrays for general oblique incidence - mechanism as related to surface wave dispersion and Floquet lattice diagrams,” Prog. Electromag. Res. (PIER) 82, 49–71 (2018).
[Crossref]

M. N. M. Kehn, “Modal analysis of metallic screen with finite conductivity perforated by an array of subwavelength rectangular flared holes,” Opt. Express 26(25), 32981–33004 (2018).
[Crossref]

Koskela, J. E.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Kravchenko, A.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Ku, S. L.

Kuo, S. S.

Kuznetsov, S. A.

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

Lee, M. H.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Lee, W. H.

Lezec, H. J.

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
[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(6668), 667–669 (1998).
[Crossref]

Li, P.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Li, X.

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Liang, Y.

Liu, P.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Maes, B.

H. Shen and B. Maes, “Enhanced optical transmission through tapered metallic gratings,” Appl. Phys. Lett. 100(24), 241104 (2012).
[Crossref]

Maria, J.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Medina, F.

F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
[Crossref]

F. Medina, R. Rodriguez-Berral, and F. Mesa, “Circuit model for metallic gratings with tapered and stepped slits,” Proc. 42nd European Microwave Conference, Oct. 2012.

Medsa, F.

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

Mesa, F.

F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
[Crossref]

C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
[Crossref]

F. Medina, R. Rodriguez-Berral, and F. Mesa, “Circuit model for metallic gratings with tapered and stepped slits,” Proc. 42nd European Microwave Conference, Oct. 2012.

Moerland, R. J.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Mohwald, H.

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Molero, C.

C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
[Crossref]

Navarro-Cia, M.

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
[Crossref]

Novikov, S. M.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

Novotny, L.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50(5), 4094–4106 (1994).
[Crossref]

Nuzzo, R. G.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Odom, T. W.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Pacheco-Pena, V.

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

Peer, A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

A. Peer and R. Biswas, “Extraordinary optical transmission in nanopatterned ultrathin metal films without holes,” Nanoscale 8(8), 4657–4666 (2016).
[Crossref]

Peng, W.

Priimagio, A.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Qi, Z.

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Ras, R. H. A.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Rodriguez, K. R.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

Rodriguez-Berral, R.

F. Medina, R. Rodriguez-Berral, and F. Mesa, “Circuit model for metallic gratings with tapered and stepped slits,” Proc. 42nd European Microwave Conference, Oct. 2012.

Rodriquez-Berral, R.

F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
[Crossref]

Rodriquez-Ulibarri, P.

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

Rogers, J. A.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Sambles, J. R.

J. R. Sambles, “More than transparent,” Nature (London) 391(6668), 641–642 (1998).
[Crossref]

Shen, H.

H. Shen and B. Maes, “Enhanced optical transmission through tapered metallic gratings,” Appl. Phys. Lett. 100(24), 241104 (2012).
[Crossref]

Simberg, M.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Singh, A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

Sondergaard, T.

T. Sondergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29(1), 130–137 (2012).
[Crossref]

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

Stewart, M. E.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Su, W. F.

Suh, J. Y.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Teeters-Kennedy, S.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

Thio, T.

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
[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(6668), 667–669 (1998).
[Crossref]

Thompson, L. B.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

Tian, H.

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

van der Vegte, S.

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Wang, L.

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Wang, Q.

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Wolff, P. A.

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

Wu, S.

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Yang, J.-C.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Yu, Y.

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Zhai, Y.

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Zhang, G.

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Zhang, S.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Zhou, W.

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

Zou, H.

Acc. Chem. Res. (1)

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008).
[Crossref]

ACS Nano (1)

B. Ai, Y. Yu, H. Mohwald, L. Wang, and G. Zhang, “Resonant optical transmission through topologically continuous films,” ACS Nano 8(2), 1566–1575 (2014).
[Crossref]

Adv. Opt. Mater. (2)

M. Navarro-Cia, V. Pacheco-Pena, S. A. Kuznetsov, and M. Beruete, “Extraordinary THz transmission with a small beam spot: the leaky wave mechanism,” Adv. Opt. Mater. 6(8), 1701312 (2018).
[Crossref]

L. Wang, B. Ai, H. Mohwald, Y. Yu, and G. Zhang, “Invertible nanocup array supporting hybrid plasmonic resonances,” Adv. Opt. Mater. 4(6), 906–916 (2016).
[Crossref]

Annu. Rev. Phys. Chem. (1)

J. V. Coe, J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, “Extraordinary transmission of metal films with arrays of subwavelength holes,” Annu. Rev. Phys. Chem. 59(1), 179–202 (2008).
[Crossref]

Appl. Phys. Lett. (1)

H. Shen and B. Maes, “Enhanced optical transmission through tapered metallic gratings,” Appl. Phys. Lett. 100(24), 241104 (2012).
[Crossref]

Chem. Rev. (1)

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008).
[Crossref]

IEEE Microw. Mag. (1)

F. Mesa, R. Rodriquez-Berral, and F. Medina, “Unlocking complexity using the ECA,” IEEE Microw. Mag. 19(4), 44–65 (2018).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

M. Beruete, M. Navarro-Cia, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microwave Theory Tech. 59(9), 2180–2188 (2011).
[Crossref]

P. Rodriquez-Ulibarri, M. Navarro-Cia, R. Rodriquez-Berral, F. Medsa, F. Medina, and M. Beruete, “Annular apertures in metallic screens as extraordinary transmission and frequency selective surface structures,” IEEE Trans. Microwave Theory Tech. 65(12), 4933–4946 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics 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 Photonics Rev. 4(2), 311–335 (2010).
[Crossref]

Mater. Horiz. (1)

R. J. Moerland, J. E. Koskela, A. Kravchenko, M. Simberg, S. van der Vegte, M. Kaivola, A. Priimagio, and R. H. A. Ras, “Large-area arrays of three-dimensional plasmonic subwavelength-sized structures from azopolymer surface-relief gratings,” Mater. Horiz. 1(1), 74–80 (2014).
[Crossref]

Nano Lett. (2)

J.-C. Yang, H. Gao, J. Y. Suh, W. Zhou, M. H. Lee, and T. W. Odom, “Enhanced optical transmission mediated by localized Plasmons in anisotropic, 3D nanohole arrays,” Nano Lett. 10(8), 3173–3178 (2010).
[Crossref]

T. Sondergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[Crossref]

Nanoscale (1)

A. Peer and R. Biswas, “Extraordinary optical transmission in nanopatterned ultrathin metal films without holes,” Nanoscale 8(8), 4657–4666 (2016).
[Crossref]

Nanotechnology (1)

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Nature (1)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[Crossref]

Nature (London) (2)

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(6668), 667–669 (1998).
[Crossref]

J. R. Sambles, “More than transparent,” Nature (London) 391(6668), 641–642 (1998).
[Crossref]

New J. Phys. (1)

J. Beermann, T. Sondergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys. 13(6), 063029 (2011).
[Crossref]

Opt. Express (3)

Phys. B (Amsterdam, Neth.) (1)

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Phys. B (Amsterdam, Neth.) 279(1-3), 90–93 (2000).
[Crossref]

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[Crossref]

Phys. Rev. E (3)

C. Molero, R. Rodriquez-Berral, and F. Mesa, “Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays,” Phys. Rev. E 95(2), 023303 (2017).
[Crossref]

M. Camacho, R. R. Boix, and F. Medina, “Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays,” Phys. Rev. E 93(6), 063312 (2016).
[Crossref]

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50(5), 4094–4106 (1994).
[Crossref]

Plasmonics (1)

Q. Wang, Y. Zhai, S. Wu, Z. Qi, L. Wang, and X. Li, “A modified transmission line model for extraordinary optical transmission through sub-wavelength slits,” Plasmonics 10(6), 1545–1549 (2015).
[Crossref]

Prog. Electromag. Res. (PIER) (1)

M. N. M. Kehn, “Extraordinary transmission through subwavelength hole arrays for general oblique incidence - mechanism as related to surface wave dispersion and Floquet lattice diagrams,” Prog. Electromag. Res. (PIER) 82, 49–71 (2018).
[Crossref]

Small (1)

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref]

Other (1)

F. Medina, R. Rodriguez-Berral, and F. Mesa, “Circuit model for metallic gratings with tapered and stepped slits,” Proc. 42nd European Microwave Conference, Oct. 2012.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (26)

Fig. 1.
Fig. 1. Two-dimensional periodic array of generally rectangular (although shown as square ones) flared holes pierced through a metallic sheet of thickness d, with periods along x and y denoted by dx and dy respectively as annotated. Each pyramidal tunnel modeled as a cascaded stepped series of cavity sections, in connection with the modal analysis of [15] from which the herein computed results are obtained. The width a0 and height h0 along x and y of the input smallest section are as indicated, while those of the output largest one are given by aZ and hZ, respectively. Two perspectives showing front and back of the screen are displayed.
Fig. 2.
Fig. 2. Rectangular hole array illuminated by incident plane wave that propagates along direction defined by θinc measured from the z axis and contained within azimuth plane of incidence defined by ϕinc measured from the x axis.
Fig. 3.
Fig. 3. Validation with CST of modal formulation of [15] for zeroth-order transmission coefficient versus frequency for ϕinc = 0 azimuth plane of incidence of arriving plane wave that illuminates array of square holes each divided into two sections (single-step flare), with unit cell period: dx = dy = 5 mm, input square hole sizes: a0 = a1 = h0 = h1 = 2.5 mm, output square hole sizes: aZ = hZ = 4.5 mm, thicknesses of input and output sections = 0.5 mm and 0.75 mm, respectively, total screen thickness d = 1.25 mm: for TMz polarized incidence, θinc = 15°.
Fig. 4.
Fig. 4. Variation of zeroth-modal power transmission coefficient for linearly-flared holes (modeled by 10 cavity sections with numerical tool of [15]) with frequency, for various output hole sizes (at least the size of the input hole) as annotated in each subplot, for input hole size: (a) 1 mm2, (b) 1.52 mm2, (c) 22 mm2, (d) 2.52 mm2, (e) 32 mm2, and (f) 3.52 mm2. All for TMz polarized incidence, ϕinc = 90°, θinc = 0, dx = dy = 5 mm, d = 1.25 mm.
Fig. 5.
Fig. 5. Grating lobe diagram for square cell (dx&y = 5 mm) and with dominant Floquet node at origin (normal incidence); (a) k0-circle intersects the four nodes along the axes, and (b) k0-circle intersects the four diagonal nodes.
Fig. 6.
Fig. 6. Variation of extraordinariness Ψ of linearly-flared square holes (modeled by 10 cavity sections with numerical tool of [15]) with frequency for various output square hole sizes (at least the size of the inputs square hole) as annotated in each subplot, for input square hole size: (a) 1 mm2, (b) 1.52 mm2, (c) 22 mm2, (d) 2.52 mm2, (e) 32 mm2, and (f) 3.52 mm2. All for TMz polarized incidence, ϕinc = 90°, θinc = 0, dx = dy = 5 mm, d = 1.25 mm.
Fig. 7.
Fig. 7. (a) Schematic, and (b) functional representation of quadratic flare profile
Fig. 8.
Fig. 8. Variation of extraordinarity Ψ of quadratically-flared square holes (modeled by 15 cavity sections with numerical tool of [15]) with frequency for various output square hole sizes (larger than the input square hole) as annotated in each subplot, for input square hole size: (a) 1 mm2, (b) 1.52 mm2, (c) 22 mm2, and (d) 2.52 mm2. All for TMz polarized incidence, ϕinc = 90°, θinc = 0, dx = dy = 5 mm, d = 1.25 mm.
Fig. 9.
Fig. 9. (a) Schematic, and (b) functional representation of reverse- quadratic flare profile
Fig. 10.
Fig. 10. Variation of extraordinarity Ψ of reverse-quadratically-flared holes (modeled by 15 cavity sections with numerical tool of [15]) with frequency for various output hole sizes (larger than the input hole) as annotated in each subplot, for input hole size: (a) 1 mm2, (b) 1.52 mm2, (c) 22 mm2, and (d) 2.52 mm2. All for TMz polarized incidence, ϕinc = 90°, θinc = 0, dx = dy = 5 mm, d = 1.25 mm.
Fig. 11.
Fig. 11. Input iris with metallic flange of thickness 5% of 1.25 mm, peering into a single large square cavity-hole (4.52 mm2) near the size of the square unit cell (52 mm2). A perspective view is also furnished.
Fig. 12.
Fig. 12. Variation of extaordinarity Ψ with frequency for flanged-type input iris peering into a single 4.52 mm2 cavity-hole for various input diaphragm sizes as annotated.
Fig. 13.
Fig. 13. Modal field distributions at 60 GHz within an a = 4.5 mm by h = 4.5 mm cavity section of the (a) quadratic, and (b) reverse-quadratic flared hole profile; left plots: |Ey| field, and right plots: |Hx|-field profiles.
Fig. 14.
Fig. 14. Comparison of extraordinarity spectra amongst various topologies as identified in legend, all for fixed input 1 mm2 hole and screen thickness d = 1.25 mm except one case (last item in legend) where it is 0.05 × 1.25 mm2 instead. Output size of 4.52 mm2 except two uniform unflared hole reference cases (first and last items in legend).
Fig. 15.
Fig. 15. Graphs of transmission, conductivity, and total efficiencies versus frequency, for three hole-flare topologies: (a) linear, (b) quadratic, and (c) flanged input iris peering into a single cavity. Copper assumed as the lossy metal, with σ = 5.8 × 107 S/m and μcond = μ0.
Fig. 16.
Fig. 16. Transmission spectra for various θinc as annotated, for two input square hole sizes: upper plots (a) 1 mm2, and lower plots (b) 1.52 mm2; left-side plots of (ai) and (bi) predicted by Bethe theory as of (8), right-side plots of (aii) and (bii) computed by present modal analysis for input square iris with flange thickness 5% of 1.25 mm and peering into a 4.52 mm2 cavity of depth 95% of 1.25 mm.
Fig. 17.
Fig. 17. Grating lobe diagram for square cell (dx&y = 5 mm) and with dominant Floquet node at: (a) (260.2, 0) pertaining to (θinc = 15°, ϕinc = 0), with k0-circle radius of 996.4 rad/m corresponding to 48 GHz, and (b) (419, 0) pertaining to (θinc = 30°, ϕinc = 0), with k0-circle radius of 838 rad/m corresponding to 40 GHz.
Fig. 18.
Fig. 18. Transmission spectra for various θinc as annotated, for two input square hole sizes: upper plots (a) 1 mm2, and lower plots (b) 1.52 mm2; left-side plots of (ai) and (bi) predicted by Bethe theory as of (8), right-side plots of (aii) and (bii) computed by present modal analysis for ordinary unflared square holes pierced through a screen with thickness 5% of 1.25 mm.
Fig. 19.
Fig. 19. Comparison in each panel of extraordinarity spectra amongst various topologies as identified in legend, all for fixed input 1 mm2 and output 4.52 mm2 holes except two uniform 1 mm2 hole reference cases in each subplot, and common screen thickness d = 1.25 mm except one case (where it is 0.05 × 1.25 mm instead) as specified in each legend; for various θinc: (a) 15°, (b) 30°, (c) 45°, and (d) 60°.
Fig. 20.
Fig. 20. Photograph of the three manufactured perforated metallic screens.
Fig. 21.
Fig. 21. Photograph of Sheets 1 and 2 piled on top of each other to create an array of stepped square holes, representing a coarsely discretized form of flared holes made of only two sections.
Fig. 22.
Fig. 22. Photographs of the experimental setup comprising two mutually facing horns both connected to a network analyzer (not shown) and between which the perforated screen is placed, for (a) normal incidence, and (b) θinc = 30°
Fig. 23.
Fig. 23. Graphs of reflection coefficient versus frequency for various hole-array topologies as indicated in the legends, generated by (a) computations of program code based on analysis in [15], and (b) measurements.
Fig. 24.
Fig. 24. Graphs of transmission coefficient of normal incidence versus frequency for various hole-array topologies as indicated in the legends, generated by (a) computations of program code based on analysis in [15], and (b) measurements.
Fig. 25.
Fig. 25. Same type as Fig. 24 but zoomed into range about 23 GHz, for (a) computations, and (b) measurements.
Fig. 26.
Fig. 26. Transmission coefficient versus frequency for various hole-array topologies as indicated in the legends, for TMz polarized oblique (ϕinc = 0, θinc = 30°) incidence generated by (a) computations of program code based on analysis in [15], and (b) measurements.

Equations (17)

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

= a 0 h 0 / d x d y ,
ε T = T / ,
P t r a n s T ζ = { P h o l e s θ = 0 cos θ i n c ; d h o l e > Υ 1 / 4 λ Υ ( d h o l e / d h o l e λ λ ) 4 P h o l e s θ = 0 cos θ i n c ; d h o l e Υ 1 / 4 λ
Λ = { cos θ i n c ; ζ E ( 4 + sin 2 θ i n c ) / ( 4 + sin 2 θ i n c ) ( 4 cos θ i n c ) ;   ζ M ( 4 cos θ i n c ) ; ζ M
P h o l e s θ = 0 = S i n c A h o l e s a l l ;  with  A h o l e s a l l = A t o t a l
P h o l e s = P h o l e s θ = 0 cos θ i n c = P w h o l e s c r e e n S i n c A t o t a l cos θ i n c
T B e t h e T ζ = P t r a n s T ζ / P t r a n s T ζ P w h o l e s c r e e n P w h o l e s c r e e n ,   ζ E  or  M
T B e t h e T ζ / T B e t h e T ζ ε T T ζ B e t h e = { cos θ i n c ; d h o l e > Υ 1 / 4 λ Υ ( d h o l e / d h o l e λ λ ) 4 cos θ i n c ; d h o l e Υ 1 / 4 λ
Ψ = ε T T ζ a c t u a l / ε T T ζ a c t u a l ε T T ζ B e t h e ε T T ζ B e t h e = T a c t u a l T ζ / T a c t u a l T ζ T B e t h e T ζ T B e t h e T ζ
ε T T ζ a c t u a l = T T ζ a c t u a l / T T ζ a c t u a l
k 0 # 1 = 2 π / d x & y = 1256.6  rad/m ,
k 0 # 2 = ( 2 ) ( 2 π / d x & y ) = 1777  rad/m ,
P c o n d = R s 2 S m e t a l | H t | 2 d s ;  where  R s = π f μ c o n d / π f μ c o n d σ σ ,
( k x 00 , k y 00 ) = ( k 0 48 G sin θ i n c cos ϕ i n c = k 0 48 G sin 15 = 260.2 , k 0 48 G sin θ i n c sin ϕ i n c = 0 ) ,
( k x 00 , k y 00 ) = ( k 0 40 G sin θ i n c cos ϕ i n c = k 0 40 G sin 30 = 419 , k 0 40 G sin θ i n c sin ϕ i n c = 0 ) ,
( k x 00 , k y 00 ) = ( k 0 30 G sin θ i n c cos ϕ i n c = k 0 30 G sin 45 = 518 , k 0 30 G sin θ i n c sin ϕ i n c = 0 ) ,
k 0 = | 518 1256.6 | = 738  rad/m f = k 0 c / ( 2 π ) = 35.2 35  GHz indeed .