Abstract

Extraordinary transmission (EOT) through one- and two-dimensional deep metallic grating in the infrared range is explored by numerical electromagnetic (EM) field analysis, such as the finite difference time domain method. The transmittance at normal incidence is greater than the porosity that is defined as a proportion of the gap area to the total cross-section when the gap is much smaller than the wavelength of incident infrared light. The EOT mechanism is investigated using two approaches—the equivalent electrical circuit (EEC) model and the effective medium approximation (EMA). The transmittance and reflectance profiles calculated using the EEC model agree with those obtained by the numerical EM analysis. EMA is applied on the basis of the idea that the deep metallic grating can be regard as hyperbolic metamaterials. Then, the effective refractive index of the deep metallic grating is real with a negligible imaginary part, in infrared range. This means that the metallic grating behaves as a dielectric medium, resulting in the great transmission and existence of a Brewster angle.

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

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2017 (1)

2015 (1)

2014 (1)

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014).
[Crossref]

2013 (3)

X.-J. He, L. Wang, J.-M. Wang, X.-H. Tian, J.-X. Jiang, and Z.-X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D: Appl. Phys. 46(36), 365302 (2013).
[Crossref]

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic Metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

2012 (7)

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S. -H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86(23), 235147 (2012).
[Crossref]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[Crossref]

T. Sondergaard, S. M. Novikov, T. Holmgaard, R. K. Eriksen, J. Beermann, Z. Han, K. Pedersen, and S. I. Bozhevolnyi, “Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves,” Nat. Commun. 3(1), 969 (2012).
[Crossref]

C. Argyropoulos, G. D. Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alù, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85(2), 024304 (2012).
[Crossref]

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D. Aguanno, M. J. Bloemer, and A. Alù, “Broaband Brewster transmission through metallic 2D gratings,” J. Appl. Phys. 112(9), 094317 (2012).
[Crossref]

R.-H. Fan, R.-W. Peng, X.-R. Huang, J. Li, Y. Liu, Q. Hu, M. Wang, and X. Zhang, “Transparent Metals for Ultrabroadband Electromagnetic Waves,” Adv. Mater. 24(15), 1980–1986 (2012).
[Crossref]

M. A. Vincenti, M. Grande, D. de Ceglia, T. Stomeo, V. Petruzzelli, M. De Vittorio, M. Scalora, and A. D. Orazio, “Color control through plasmonic metal gratings,” Appl. Phys. Lett. 100(20), 201107 (2012).
[Crossref]

2011 (4)

L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2), A126–A135 (2011).
[Crossref]

Z. Wang, G. Li, F. Xiao, F. Lu, K. Li, and A. Xu, “Plasmonic critical angle in optical transmission through subwavelength metallic gratings,” Opt. Lett. 36(23), 4584–4586 (2011).
[Crossref]

A. Alù, G. D. Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster Angle: Broadband Extraordinary Transmission through Optical Gratings,” Phys. Rev. Lett. 106(12), 123902 (2011).
[Crossref]

J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angew. Chem., Int. Ed. 50(9), 2085–2089 (2011).
[Crossref]

2010 (4)

X.-R. Huang, R.-W. Peng, and R.-H. Fan, “Making Metals Transparent for White Light by Spoof Surface Plasmons,” Phys. Rev. Lett. 105(24), 243901 (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]

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

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared Perfect Absorber and Its Application As Plasmonic Sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

2009 (3)

2008 (3)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref]

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles,” Langmuir 24(10), 5233–5237 (2008).
[Crossref]

B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
[Crossref]

2007 (5)

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[Crossref]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical Cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref]

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

2006 (5)

U. Leonhardt, “Optical Conformal Mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

A. Alù and N. Engheta, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[Crossref]

H. Gao, J. Henzie, and T. W. Odom, “Direct Evidence for Surface Plasmon-Mediated Enhanced Light Transmission through Metallic Nanohole Arrays,” Nano Lett. 6(9), 2104–2108 (2006).
[Crossref]

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[Crossref]

2005 (5)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref]

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si Nano-Photodiode with a Surface Plasmon Antenna,” Jpn. J. Appl. Phys. 44L364–L366 (2005).
[Crossref]

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[Crossref]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A: Pure Appl. Opt. 7(2), S90–S96 (2005).
[Crossref]

2003 (1)

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

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297(5582), 820–822 (2002).
[Crossref]

Y. Sun and Y. Xia, “Increased Sensitivity of Surface Plasmon Resonance of Gold Nanoshells Compared to That of Gold Solid Colloids in Response to Environmental Changes,” Anal. Chem. 74(20), 5297–5305 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001).
[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 arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1984 (1)

1967 (1)

R. Ulrich, “Far-Infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967).
[Crossref]

1964 (1)

P. Vogel and L. Genzel, “Transmission and Reflection of Metallic Mesh in the Far Infrared,” Infrared Phys. 4(4), 257–262 (1964).
[Crossref]

Aguanno, G. D.

C. Argyropoulos, G. D. Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alù, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85(2), 024304 (2012).
[Crossref]

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D. Aguanno, M. J. Bloemer, and A. Alù, “Broaband Brewster transmission through metallic 2D gratings,” J. Appl. Phys. 112(9), 094317 (2012).
[Crossref]

A. Alù, G. D. Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster Angle: Broadband Extraordinary Transmission through Optical Gratings,” Phys. Rev. Lett. 106(12), 123902 (2011).
[Crossref]

Ahn, S.-W.

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005).
[Crossref]

Akozbek, N.

C. Argyropoulos, G. D. Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alù, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85(2), 024304 (2012).
[Crossref]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Alù, A.

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D. Aguanno, M. J. Bloemer, and A. Alù, “Broaband Brewster transmission through metallic 2D gratings,” J. Appl. Phys. 112(9), 094317 (2012).
[Crossref]

C. Argyropoulos, G. D. Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alù, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85(2), 024304 (2012).
[Crossref]

A. Alù, G. D. Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster Angle: Broadband Extraordinary Transmission through Optical Gratings,” Phys. Rev. Lett. 106(12), 123902 (2011).
[Crossref]

A. Alù and N. Engheta, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[Crossref]

Argyropoulos, C.

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D. Aguanno, M. J. Bloemer, and A. Alù, “Broaband Brewster transmission through metallic 2D gratings,” J. Appl. Phys. 112(9), 094317 (2012).
[Crossref]

C. Argyropoulos, G. D. Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alù, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85(2), 024304 (2012).
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S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005).
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[Crossref]

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H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles,” Langmuir 24(10), 5233–5237 (2008).
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T. Sondergaard, S. M. Novikov, T. Holmgaard, R. K. Eriksen, J. Beermann, Z. Han, K. Pedersen, and S. I. Bozhevolnyi, “Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves,” Nat. Commun. 3(1), 969 (2012).
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T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si Nano-Photodiode with a Surface Plasmon Antenna,” Jpn. J. Appl. Phys. 44L364–L366 (2005).
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R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S. -H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86(23), 235147 (2012).
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M. A. Vincenti, M. Grande, D. de Ceglia, T. Stomeo, V. Petruzzelli, M. De Vittorio, M. Scalora, and A. D. Orazio, “Color control through plasmonic metal gratings,” Appl. Phys. Lett. 100(20), 201107 (2012).
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M. A. Vincenti, M. Grande, D. de Ceglia, T. Stomeo, V. Petruzzelli, M. De Vittorio, M. Scalora, and A. D. Orazio, “Color control through plasmonic metal gratings,” Appl. Phys. Lett. 100(20), 201107 (2012).
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J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angew. Chem., Int. Ed. 50(9), 2085–2089 (2011).
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R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S. -H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86(23), 235147 (2012).
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Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
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T. Sondergaard, S. M. Novikov, T. Holmgaard, R. K. Eriksen, J. Beermann, Z. Han, K. Pedersen, and S. I. Bozhevolnyi, “Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves,” Nat. Commun. 3(1), 969 (2012).
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Stomeo, T.

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Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
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Y. Sun and Y. Xia, “Increased Sensitivity of Surface Plasmon Resonance of Gold Nanoshells Compared to That of Gold Solid Colloids in Response to Environmental Changes,” Anal. Chem. 74(20), 5297–5305 (2002).
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Tao, Y.

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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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 arrays,” Nature 391(6668), 667–669 (1998).
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X.-J. He, L. Wang, J.-M. Wang, X.-H. Tian, J.-X. Jiang, and Z.-X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D: Appl. Phys. 46(36), 365302 (2013).
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M. A. Vincenti, M. Grande, D. de Ceglia, T. Stomeo, V. Petruzzelli, M. De Vittorio, M. Scalora, and A. D. Orazio, “Color control through plasmonic metal gratings,” Appl. Phys. Lett. 100(20), 201107 (2012).
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Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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X.-J. He, L. Wang, J.-M. Wang, X.-H. Tian, J.-X. Jiang, and Z.-X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D: Appl. Phys. 46(36), 365302 (2013).
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X.-J. He, L. Wang, J.-M. Wang, X.-H. Tian, J.-X. Jiang, and Z.-X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D: Appl. Phys. 46(36), 365302 (2013).
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Wang, M.

R.-H. Fan, R.-W. Peng, X.-R. Huang, J. Li, Y. Liu, Q. Hu, M. Wang, and X. Zhang, “Transparent Metals for Ultrabroadband Electromagnetic Waves,” Adv. Mater. 24(15), 1980–1986 (2012).
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Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared Perfect Absorber and Its Application As Plasmonic Sensor,” Nano Lett. 10(7), 2342–2348 (2010).
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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 391(6668), 667–669 (1998).
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Y. Sun and Y. Xia, “Increased Sensitivity of Surface Plasmon Resonance of Gold Nanoshells Compared to That of Gold Solid Colloids in Response to Environmental Changes,” Anal. Chem. 74(20), 5297–5305 (2002).
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Xiao, G.

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
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H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles,” Langmuir 24(10), 5233–5237 (2008).
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S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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Zhang, X.

R.-H. Fan, R.-W. Peng, X.-R. Huang, J. Li, Y. Liu, Q. Hu, M. Wang, and X. Zhang, “Transparent Metals for Ultrabroadband Electromagnetic Waves,” Adv. Mater. 24(15), 1980–1986 (2012).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
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Zhang, Z. M.

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014).
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A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014).
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Zhou, J.

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref]

Zhou, Z.-K.

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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Zhu, J.

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
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Adv. Mater. (1)

R.-H. Fan, R.-W. Peng, X.-R. Huang, J. Li, Y. Liu, Q. Hu, M. Wang, and X. Zhang, “Transparent Metals for Ultrabroadband Electromagnetic Waves,” Adv. Mater. 24(15), 1980–1986 (2012).
[Crossref]

Anal. Chem. (1)

Y. Sun and Y. Xia, “Increased Sensitivity of Surface Plasmon Resonance of Gold Nanoshells Compared to That of Gold Solid Colloids in Response to Environmental Changes,” Anal. Chem. 74(20), 5297–5305 (2002).
[Crossref]

Angew. Chem., Int. Ed. (1)

J. A. Hutchison, D. M. O’Carroll, T. Schwartz, C. Genet, and T. W. Ebbesen, “Absorption-Induced Transparency,” Angew. Chem., Int. Ed. 50(9), 2085–2089 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. A. Vincenti, M. Grande, D. de Ceglia, T. Stomeo, V. Petruzzelli, M. De Vittorio, M. Scalora, and A. D. Orazio, “Color control through plasmonic metal gratings,” Appl. Phys. Lett. 100(20), 201107 (2012).
[Crossref]

L. P. Wang and Z. M. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009).
[Crossref]

Infrared Phys. (2)

P. Vogel and L. Genzel, “Transmission and Reflection of Metallic Mesh in the Far Infrared,” Infrared Phys. 4(4), 257–262 (1964).
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R. Ulrich, “Far-Infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967).
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J. Appl. Phys. (1)

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D. Aguanno, M. J. Bloemer, and A. Alù, “Broaband Brewster transmission through metallic 2D gratings,” J. Appl. Phys. 112(9), 094317 (2012).
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J. Opt. A: Pure Appl. Opt. (1)

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

J. Phys. D: Appl. Phys. (1)

X.-J. He, L. Wang, J.-M. Wang, X.-H. Tian, J.-X. Jiang, and Z.-X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D: Appl. Phys. 46(36), 365302 (2013).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si Nano-Photodiode with a Surface Plasmon Antenna,” Jpn. J. Appl. Phys. 44L364–L366 (2005).
[Crossref]

Langmuir (1)

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles,” Langmuir 24(10), 5233–5237 (2008).
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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]

Nano Lett. (2)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared Perfect Absorber and Its Application As Plasmonic Sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

H. Gao, J. Henzie, and T. W. Odom, “Direct Evidence for Surface Plasmon-Mediated Enhanced Light Transmission through Metallic Nanohole Arrays,” Nano Lett. 6(9), 2104–2108 (2006).
[Crossref]

Nanotechnology (1)

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S. H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005).
[Crossref]

Nat. Commun. (2)

Y. Shen, J. Zhou, T. Liu, Y. Tao, R. Jiang, M. Liu, G. Xiao, J. Zhu, Z.-K. Zhou, X. Wang, C. Jin, and J. Wang, “Plasmonic gold mushroom arrays with refractive index sensing figures of merit approaching the theoretical limit,” Nat. Commun. 4(1), 2381 (2013).
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Figures (16)

Fig. 1.
Fig. 1. Geometry of the deep metallic gratings of interest: (a) 1-dimension and (b) 2-dimension.
Fig. 2.
Fig. 2. Comparison of transmission spectra of 1D and 2D gratings.
Fig. 3.
Fig. 3. Transmittance $T$, reflectivity $R$ and absorbance $A$ spectra of the 2D gold gratings at $w =$ 0.03 $\mu$m, length $l =$ 0.2 $\mu$m, and $g =$ 0.005, 0.01 and 0.03 $\mu$m. The dotted line corresponds to the porosity $p$.
Fig. 4.
Fig. 4. $T$, $R$ and $A$ spectra for the 2-D gold gratings at constant gap $g =$ 0.01 $\mu$m, length $l =$ 0.2 $\mu$m, and different width $w =$ 0.01, 0.03 and 0.06 $\mu$m. The dotted line corresponds to the porosity $p$.
Fig. 5.
Fig. 5. $T$, $R$ and $A$ spectra for the 2D gold gratings at constant gap $g =$ 0.01 $\mu$m and width $w = 0.03$ $\mu$m, and different length $l =$ 0.1, 0.2, 0.3 and 0.5 and 1 $\mu$m. The dotted line corresponds to the porosity $p$.
Fig. 6.
Fig. 6. Transmittance $T$, reflectivity $R$ and absorbance $A$ spectra calculated for the 2-D gold gratings at constant porosity $p =$ 0.438 ($w/g =$ 3) and different size (the periodicity is $\Lambda =$ (a) 0.04, (b) 0.2, (c) 0.8, (d) 2.0, (e) 4.0 and (f) 10 $\mu$m). The dotted line corresponds to the porosity $p$.
Fig. 7.
Fig. 7. (a) Transmittance $T$, reflectivity $R$ and absorbance $A$ calculated for the 2D gold gratings at constant porosity $p =$ 0.438 ($w/g =$ 3) and different cross-sectional shape: square, octagon and circle. The dotted line corresponds to the porosity $p$.
Fig. 8.
Fig. 8. Change in the transmittance $T$ and reflectivity $R$ spectra of the 2D grating in different ambient RI, $n =$ 1, 1.3 and 1.5. The grating with (a) small periodicity ($\Lambda =$ 0.04 $\mu$m) and (b) large periodicity ($\Lambda =$ 3 $\mu$m). Porosity of both gratings are $p =$ 0.438 ($w/g =$ 3). The dotted line corresponds to the porosity $p$.
Fig. 9.
Fig. 9. Equivalent circuit of the 2D grating. (a) the original circuit and (b) the reduced circuit.
Fig. 10.
Fig. 10. Effective RI $\beta /k_0$ as a function of wavelength.
Fig. 11.
Fig. 11. The transmittance $T$ (a) and reflectivity $R$ (b) spectra calculated with the equivalent circuit. The calculated results of $T$ and $R$ by the FDTD method are also shown for comparison.
Fig. 12.
Fig. 12. The impedance ${Z_\textrm {i}}$ and ${Z_\textrm {L}}$ as a function of $\Lambda$ at $\lambda = 3\ \mu$m.
Fig. 13.
Fig. 13. Transmittance $T$ and reflectivity $R$ calculated under the EMA, for the 2-D gold gratings at constant gap $g =$ 0.01 $\mu$m and width $w =$ 0.03 $\mu$m, and different length (a) $l =$ 0.2 $\mu$m and (b) 1 $\mu$m. Those calculated by FDTD is also plotted with dotted line for comparison.
Fig. 14.
Fig. 14. Transmittance $T$ and reflectivity $R$ as a function of the angle of incidence, calculated based on the EMA, for the 2-D gold gratings at (a) p-polarization and (b) s-polarization. The gap, width and length are $g =$ 0.01 $\mu$m, $w = 0.03$ $\mu$m, and $l =$ 0.2 $\mu$m, respectively.
Fig. 15.
Fig. 15. Real and imaginary part of the effective RI of the grating, in (a) $x$-direction and (b) $y$-direction. The gap, width and length are $g =$ 0.01 $\mu$m, $w = 0.03$ $\mu$m, and $l =$ 0.2$\mu$m, respectively.
Fig. 16.
Fig. 16. Schematic of a four-terminal circuit.

Tables (1)

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Table 1. Comparison of the sensitivity and FOM at the peak wavelength.

Equations (22)

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C i = 1 ω Z 0 Λ g tan π l λ + ϵ 0 Λ 2 π ln [ 1 α 2 4 α 2 ( 1 + α 1 α ) α ] ,
C p = ϵ 0 w l g + ϵ 0 g l Λ .
L m = 1 2 μ 0 g l w ,
L k = l 2 ϵ 0 ω p 2 S .
S = { δ w           ( δ < w ) w 2           ( δ w )
Z s = 4 Z i 2 Z L ( Z L + Z p ) ( Z i + 2 Z L + 2 Z p ) ( Z i + 2 Z L ) .
β = 1 l arctan Z in,sh Z in,op ,
Z in,op = 2 Z i ( Z L + Z p ) 2 Z L + 2 Z p + Z i
Z in,sh = 2 Z i Z L 2 Z L + Z i .
R = | ( Z s 2 Z in Z out ) tan ( β l ) j ( Z in Z out ) Z s ( Z s 2 + Z in Z out ) tan ( β l ) + j ( Z in + Z out ) Z s | 2
T = | 2 Z out Z s sec ( β l ) ( Z in + Z out ) Z s 2 + j ( Z s 2 + Z in Z out ) tan ( β l ) | 2 .
n eff, e 2 = w Λ n m 2 + g Λ n 0 2
n eff, o 2 = w Λ n m 2 + g Λ n 0 2 ,
n eff, e 2 = ( w Λ ) 2 n m 2 + ( g Λ ) 2 n 0 2
n eff, o 2 = w Λ n A 2 + g Λ n 0 2 ,
n A 2 = w Λ n m 2 + g Λ n 0 2 .
n eff,o 2 = f oct n A 2 + ( 1 f oct ) n o 2 ,
n A 2 = a s + a s + + g ( 1 s log s n m 2 + 1 log ( 2 a + g g + a s ) n 0 2 ) ,
n eff, e 2 = ( a s + a s + + g ) 2 n m 2 + ( g a s + + g ) 2 n 0 2 .
Z s = F 11 F 12 F 21 F 22 .
( V 1 I 1 ) = F ( V 2 I 2 ) ,
F = ( 1 0 1 / Z i 1 ) ( 1 2 Z L 0 1 ) ( 1 0 1 / 2 Z p 1 ) . = ( 1 + Z L Z p 2 Z L ( 1 + Z L Z p ) 1 Z i + 1 2 Z p 1 + 2 Z L Z i )