Abstract

We propose a microscopic surface-mode model for the extraordinary optical transmission (EOT) through subwavelength metallic slit array covered with a thin dielectric layer under illumination of transverse-electric (TE) polarization. Remarkably, surface plasmon polarizations (SPPs) do not exist for this polarization. It is commonly believed that the waveguide mode in the dielectric layer plays a role similar to that of the SPP in classical EOT. To check the intuitive belief, we derive a surface-mode model by considering the multiple scattering process of the fundamental waveguide mode and neglecting all other residual field in the thin dielectric layer. The model captures the main feature of EOT and provides a phase-matching condition to predict the transmission resonance. Quantitative comparison between fully-vectorial calculations and model predictions shows that besides the fundamental waveguide mode, other residual field in the thin dielectric layer also contributes to the EOT without SPP.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2014 (2)

X. Zhang, H. T. Liu, and Y. Zhong, “Microscopic analysis of surface Bloch modes on periodically perforated metallic surfaces and their relation to extraordinary optical transmission,” Phys. Rev. B 89(19), 195431 (2014).
[Crossref]

Z. J. Sun, X. L. Zuo, T. P. Guan, and W. Chen, “Artificial TE-mode surface waves at metal surfaces mimicking surface plasmons,” Opt. Express 22(4), 4714–4722 (2014).
[Crossref] [PubMed]

2013 (2)

H. T. Liu, “Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering system,” Opt. Express 21(20), 24093–24098 (2013).
[Crossref] [PubMed]

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
[Crossref]

2012 (4)

R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa, “Analytical wideband model for strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(12), 3908–3918 (2012).
[Crossref]

R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi analytical modeling of transmission reflection in strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(3), 405–418 (2012).
[Crossref]

I. Schwarz, N. Livneh, and R. Rapaport, “General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations,” Opt. Express 20(1), 426–439 (2012).
[Crossref] [PubMed]

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

2011 (2)

M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett. 98(1), 014106 (2011).
[Crossref]

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

2010 (2)

2009 (5)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λλ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Intercoupling of free-space radiation to s-polarized confined modes via nanocavities,” Appl. Phys. Lett. 94(6), 063119 (2009).
[Crossref]

S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
[Crossref] [PubMed]

A. Yu Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A, Pure Appl. Opt. 11(12), 125702 (2009).
[Crossref]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17(23), 20975–20990 (2009).
[Crossref] [PubMed]

2008 (1)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

2007 (6)

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

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
[Crossref]

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15(3), 1107–1114 (2007).
[Crossref] [PubMed]

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
[Crossref]

2006 (2)

E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006).
[Crossref]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
[Crossref]

2005 (4)

F. García de Abajo and J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005).
[Crossref] [PubMed]

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[Crossref]

C. Genet, P. M. van Exter, and J. P. Woerdman, “Huygens description of resonance phenomena in subwavelength hole arrays,” J. Opt. Soc. Am. A 22(5), 998–1002 (2005).

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).
[Crossref] [PubMed]

2004 (4)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[Crossref] [PubMed]

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

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[Crossref] [PubMed]

2003 (1)

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[Crossref]

2002 (2)

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
[Crossref] [PubMed]

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66(19), 195105 (2002).
[Crossref]

2001 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[Crossref] [PubMed]

2000 (2)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[Crossref]

M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
[Crossref]

1999 (2)

M. M. J. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75(5), 606 (1999).
[Crossref]

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
[Crossref]

1997 (1)

1996 (1)

1995 (1)

1941 (1)

Alexanian, A.

M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
[Crossref]

Atwater, H. A.

Ayza, M. S.

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

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Beruete, M.

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

M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett. 98(1), 014106 (2011).
[Crossref]

S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
[Crossref] [PubMed]

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15(3), 1107–1114 (2007).
[Crossref] [PubMed]

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[Crossref] [PubMed]

Bonn, M.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
[Crossref]

Bravo-Abad, J.

Campillo, I.

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
[Crossref] [PubMed]

Chen, J.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
[Crossref]

Chen, W.

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dolado, J. S.

Du, Q. G.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
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W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
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L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
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Eckert, R.

Enoch, S.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
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E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
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Falcone, F.

Fano, U.

Ferry, V. E.

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J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
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J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
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García-Vidal, F. J.

M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010).
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A. Yu Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A, Pure Appl. Opt. 11(12), 125702 (2009).
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A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Intercoupling of free-space radiation to s-polarized confined modes via nanocavities,” Appl. Phys. Lett. 94(6), 063119 (2009).
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E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006).
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M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
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L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
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García-Vigueras, M.

R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi analytical modeling of transmission reflection in strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(3), 405–418 (2012).
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Gelfand, A. V.

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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
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E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
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M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
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Guan, T. P.

Guillaumée, M.

Guo, L. D.

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
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E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
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P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
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J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).
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Klein, M. J. K.

Koerkamp, K. J.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
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Kubarev, V. V.

Kuipers, L.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
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K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
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Kuznetsov, S. A.

M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett. 98(1), 014106 (2011).
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S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
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Lalanne, P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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H. T. Liu and P. Lalanne, “Comprehensive microscopic model of the extraordinary optical transmission,” J. Opt. Soc. Am. A 27(12), 2542–2550 (2010).
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P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λλ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
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H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
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P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
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J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).
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Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
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Lester, M.

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
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Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
[Crossref]

Li, L. F.

Liu, H. T.

X. Zhang, H. T. Liu, and Y. Zhong, “Microscopic analysis of surface Bloch modes on periodically perforated metallic surfaces and their relation to extraordinary optical transmission,” Phys. Rev. B 89(19), 195431 (2014).
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H. T. Liu, “Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering system,” Opt. Express 21(20), 24093–24098 (2013).
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F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

H. T. Liu and P. Lalanne, “Comprehensive microscopic model of the extraordinary optical transmission,” J. Opt. Soc. Am. A 27(12), 2542–2550 (2010).
[Crossref] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λλ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

Livneh, N.

Lockyear, M. J.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
[Crossref]

Lomakin, V.

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15(3), 1107–1114 (2007).
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V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[Crossref]

MacDonald, M. E.

M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
[Crossref]

Magnusson, R.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[Crossref]

Maldonado, T. A.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
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Martin-Moreno, L.

E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006).
[Crossref]

Martín-Moreno, L.

M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010).
[Crossref] [PubMed]

A. Yu Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A, Pure Appl. Opt. 11(12), 125702 (2009).
[Crossref]

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Intercoupling of free-space radiation to s-polarized confined modes via nanocavities,” Appl. Phys. Lett. 94(6), 063119 (2009).
[Crossref]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[Crossref] [PubMed]

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

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[Crossref] [PubMed]

Medina, F.

R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi analytical modeling of transmission reflection in strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(3), 405–418 (2012).
[Crossref]

R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa, “Analytical wideband model for strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(12), 3908–3918 (2012).
[Crossref]

Mesa, F.

R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa, “Analytical wideband model for strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(12), 3908–3918 (2012).
[Crossref]

R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi analytical modeling of transmission reflection in strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(3), 405–418 (2012).
[Crossref]

Michielssen, E.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[Crossref]

Moharam, M. G.

Molero, C.

R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa, “Analytical wideband model for strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(12), 3908–3918 (2012).
[Crossref]

Moreno, E.

E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006).
[Crossref]

Munday, J. N.

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Navarro-Cía, M.

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

M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett. 98(1), 014106 (2011).
[Crossref]

S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
[Crossref] [PubMed]

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15(3), 1107–1114 (2007).
[Crossref] [PubMed]

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

Nevière, M.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[Crossref]

Nikitin, A. Yu.

Núñez-Manrique, I. J.

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

Pacifici, D.

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[Crossref] [PubMed]

Pendry, J. B.

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

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[Crossref] [PubMed]

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Perea, E.

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

Pommet, D. A.

Popov, E.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[Crossref]

Popovic, Z.

M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
[Crossref]

Porto, J. A.

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Priambodo, P. S.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[Crossref]

Rapaport, R.

Reinisch, R.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[Crossref]

Ren, F. F.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
[Crossref]

Rétif, C.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

Rodríguez-Berral, R.

R. Rodríguez-Berral, F. Medina, F. Mesa, and M. García-Vigueras, “Quasi analytical modeling of transmission reflection in strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(3), 405–418 (2012).
[Crossref]

R. Rodríguez-Berral, C. Molero, F. Medina, and F. Mesa, “Analytical wideband model for strip slit gratings loaded with dielectric slabs,” IEEE Trans. Microw. Theory Tech. 60(12), 3908–3918 (2012).
[Crossref]

Rodríguez-Seco, J. E.

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
[Crossref]

Rosenblatt, D.

Sáenz, J.

F. García de Abajo and J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005).
[Crossref] [PubMed]

Saeta, P. N.

Schwarz, I.

Segerink, F. B.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[Crossref] [PubMed]

Sharon, A.

Shen, N. H.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
[Crossref]

Shieh, H. P. D.

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
[Crossref]

Skigin, D. C.

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

Smiet, C. B.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

Sorolla, M.

Spassov, V.

Stanley, R. P.

Sun, S.

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
[Crossref]

Sun, Z. J.

Tan, B. K.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
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Thio, T.

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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
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M. M. J. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75(5), 606 (1999).
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van Beijnum, F.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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van Exter, P. M.

van Hulst, N. F.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[Crossref] [PubMed]

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λλ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

Wang, H. T.

F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
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Woerdman, J. P.

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 array,” Nature 391(12), 667–669 (1998).
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Ye, Z. C.

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
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M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
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Yu Nikitin, A.

A. Yu Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A, Pure Appl. Opt. 11(12), 125702 (2009).
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Zhang, X.

X. Zhang, H. T. Liu, and Y. Zhong, “Microscopic analysis of surface Bloch modes on periodically perforated metallic surfaces and their relation to extraordinary optical transmission,” Phys. Rev. B 89(19), 195431 (2014).
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Zheng, J.

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
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Zhong, Y.

X. Zhang, H. T. Liu, and Y. Zhong, “Microscopic analysis of surface Bloch modes on periodically perforated metallic surfaces and their relation to extraordinary optical transmission,” Phys. Rev. B 89(19), 195431 (2014).
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Zuo, X. L.

Appl. Phys. Lett. (4)

M. M. J. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75(5), 606 (1999).
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M. Beruete, M. Navarro-Cía, S. A. Kuznetsov, and M. Sorolla, “Circuit approach to the minimal configuration of terahertz anomalous extraordinary transmission,” Appl. Phys. Lett. 98(1), 014106 (2011).
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IEEE J. Sel. Top. Quantum Electron. (1)

Z. C. Ye, J. Zheng, S. Sun, L. D. Guo, and H. P. D. Shieh, “Compact transreflective color filters and polarizers by bilayer metallic nanowire gratings on flexible substrates,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4800205 (2013).
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IEEE Microw. Wirel. Co. (1)

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced gain by double-periodic stacked subwavelength hole array,” IEEE Microw. Wirel. Co. 17(12), 831–833 (2007).
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IEEE Trans. Microw. Theory Tech. (4)

M. Beruete, M. Navarro-Cía, and M. S. Ayza, “Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts,” IEEE Trans. Microw. Theory Tech. 59(9), 2180–2188 (2011).
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M. E. MacDonald, A. Alexanian, R. A. York, Z. Popović, and E. N. Grossman, “Spectral transmittance of lossy printed resonant-grid terahertz bandpass filters,” IEEE Trans. Microw. Theory Tech. 48(4), 712–718 (2000).
[Crossref]

J. Opt. A, Pure Appl. Opt. (3)

A. Yu Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A, Pure Appl. Opt. 11(12), 125702 (2009).
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M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
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E. Moreno, L. Martin-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A, Pure Appl. Opt. 8(4), S94–S97 (2006).
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J. Opt. Soc. Am. (1)

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Nat. Phys. (1)

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
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Nature (4)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature 391(12), 667–669 (1998).
[Crossref]

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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Opt. Express (7)

Z. J. Sun, X. L. Zuo, T. P. Guan, and W. Chen, “Artificial TE-mode surface waves at metal surfaces mimicking surface plasmons,” Opt. Express 22(4), 4714–4722 (2014).
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I. Schwarz, N. Livneh, and R. Rapaport, “General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations,” Opt. Express 20(1), 426–439 (2012).
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M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15(3), 1107–1114 (2007).
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S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
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M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010).
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H. T. Liu, “Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering system,” Opt. Express 21(20), 24093–24098 (2013).
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Opt. Lett. (1)

Phys. Rev. B (6)

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007).
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X. Zhang, H. T. Liu, and Y. Zhong, “Microscopic analysis of surface Bloch modes on periodically perforated metallic surfaces and their relation to extraordinary optical transmission,” Phys. Rev. B 89(19), 195431 (2014).
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M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66(19), 195105 (2002).
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V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
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F. F. Ren, J. Chen, Q. G. Du, N. H. Shen, B. K. Tan, and H. T. Wang, “Electromagnetic transmission through one-dimensional gratings with left-handed materials,” Phys. Rev. B 75(4), 045127 (2007).
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Phys. Rev. Lett. (6)

F. García de Abajo and J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95(23), 233901 (2005).
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L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
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W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
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K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
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Science (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
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Surf. Sci. Rep. (1)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λλ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

Other (4)

E. D. Palik, Handbook of Optical Constants of Solids-Part II (Academic, 1985).

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).

The calculation is performed with an in-house software, H. T. Liu, DIF CODE for modeling light diffraction in nanostructures (Nankai University, 2010).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

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Figures (5)

Fig. 1
Fig. 1 (a) Geometry of the metallic subwavelength slit array covered with a thin dielectric layer. The structure is illuminated by a TE-polarized plane wave (incident angle θ). The zeroth-order power transmittance is given by T = |tF|2 with tF the transmission coefficient. The red and green arrows represent the incident and scattered modes, respectively. (b1)-(b4) Definition of transmission coefficients tA and tB and of reflection coefficients rA and rB at the front and the rear interfaces of the finite-depth slit array, respectively, which appear in the Fabry-Perot Eq. (1) of the model. (c1)-(c5) Definition of elementary scattering coefficients in the model. The coefficients β+, β, t, ρ, τ, α', α and r in (c1)-(c3) are defined for a single infinite-depth slit at the front air-dielectric-gold interface, and the coefficients t0 and r0 in (c4)-(c5) are defined for a single infinite-depth slit at the rear air-gold interface (see their detailed definitions in the main text). (d1)-(d2) Electric field of the fundamental slit mode (for a = 0.4μm) and the fundamental waveguide mode (for h = 0.8μm), which are obtained for wavelength λ = 2.35μm (ng = 1.1040 + 14.7364i for gold, nFM = 0.0239 + 2.4079i, and nWM = 1.1544 + 0.0010i). The fundamental slit mode is normalized to have Ey = 1 at x = 0, and the fundamental waveguide mode is normalized to have Ey = 1 at the air-dielectric interface. The superposed vertical lines show the position of interfaces.
Fig. 2
Fig. 2 Comparison between model predictions and fully-vectorial numerical data for normal incidence. The results are obtained for array period Λ = 2μm, gold film thickness d = 0.16μm, dielectric layer thickness h = 0.8μm, and slit width a = 0.4μm. (a) zeroth-order transmittance T obtained with the fully-vectorial RCWA (blue circles), the surface-mode model (red solid curve), and the Fabry-Perot Eq. (1) (green dashed curve). The inset shows an enlarged view of the transmission peak. (b) Modulus of transmission and reflection coefficients (tB and rB) defined at the rear air-gold interface for the fundamental mode of the slit array. (c)-(d) Modulus and argument of the transmission and reflection coefficients (tA and rA) defined at the front air-dielectric-gold interface for the fundamental mode of the slit array. In (b)-(d), the circles show the RCWA results, and the solid curves show the predictions of the model. The plane wave and the fundamental mode in the slit are normalized to have Ey = 1 at x = 0. (e)-(f) Argument and modulus of phase shift u−1 and of ρ + τ that illustrate the phase-matching condition of Eq. (10).
Fig. 3
Fig. 3 Comparison between model predictions and fully-vectorial numerical data for the case of oblique incidence. (a1)-(b1) Color-scale images showing the zeroth-order transmittance T as a function of the wavelength (vertical axis) and of the in-plane wavevector kx = 2πλ−1sinθ (horizontal axis), which are obtained with fully-vectorial RCWA calculation and the model, respectively. (a2)-(b2) Enlarged views for the resonance peaks in (a1) and (b1). The results are obtained for Λ = 2μm, d = 0.16μm, h = 0.8μm and a = 0.4μm.
Fig. 4
Fig. 4 (a1)-(a5) Zeroth-order transmittance T plotted as a function of array period Λ for normal incidence, where (a2)-(a5) provide enlarged views for the resonance peaks in (a1). The blue circles show the RCWA results and the red solid curve shows the prediction of the model. (b) Electric field Re(Ey) scattered by a single infinite-depth slit under illumination by a normally-incident TE-polarized plane wave (see the inset), from which the background field without slit has been removed. The result is obtained at the central horizontal plane of the dielectric layer, with the incident plane wave normalized to have Ey = 1 at the upper surface of the dielectric layer. The total field, its contained waveguide mode, and the residual field are shown with the blue-dashed curve, the purple-solid curve and the cyan circles, respectively. The results are obtained for λ = 2.35μm, d = 0.16μm, h = 0.8μm and a = 0.4μm.
Fig. 5
Fig. 5 (a1)-(d1) Zeroth-order transmittance T plotted as a function of wavelength λ for period Λ = 0.7, 1, 3 and 10μm, respectively. Other geometrical parameters are d = 0.2Λ, h = 0.4Λ, a = 0.35Λ. The results are obtained for normal illumination with the fully-vectorial RCWA (blue circles) and the model (red-solid curves). (a2)-(d2) Similar to Fig. 4(b), obtained at the resonance wavelengths λ0 of EOT shown in (a1)-(d1). The gold permittivities are εg = ng2 = −31.28 + 2.20i, −65.88 + 5.79i, −484.09 + 96.15i, −3691.30 + 1979.80i for λ0 = 0.851, 1.206, 3.579, 11.880 μm, respectively.

Equations (13)

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t F = t A t B exp(i k 0 n FM d) 1 r A r B exp(i2 k 0 n FM d) .
t A =t+ w 1 u α A+wu α B,
A= β + + w 1 uτA+wuρB,
B= β + w 1 uρA+wuτB,
t A =t+u α β + ( w 1 uτ+uρ)+ β (wuτ+uρ) (1 w 1 uτ)(1wuτ) u 2 ρ 2 .
r A =r+ uα α ( w 1 +w2uτ+2uρ) (1 w 1 uτ)(1wuτ) u 2 ρ 2 .
t A =t+ 2 α β u 1 (ρ+τ) ,
r A =r+ 2 α α u 1 (ρ+τ) .
t B = ψ FM + | ψ FM ψ PW + | ψ PW t B ,
ψ FM + | ψ FM = Λ/2 Λ/2 ( E y,FM + H x,FM E y,FM H x,FM + )dx ,
t B = t 0 ,
r B = r 0 ,
k 0 Re( n WM )Λ+arg(ρ+τ)=2mπ,

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