Ultrasensitive molecular absorption detection using metal slot antenna arrays

Kwang Jun Ahn; Young-Mi Bahk; Dai-Sik Kim; Jisoo Kyoung; Fabian Rotermund

doi:10.1364/OE.23.019047

Ultrasensitive molecular absorption detection using metal slot antenna arrays

Kwang Jun Ahn, Young-Mi Bahk, Dai-Sik Kim, Jisoo Kyoung, and Fabian Rotermund

Optics Express
Vol. 23,
Issue 15,
pp. 19047-19055
(2015)
•https://doi.org/10.1364/OE.23.019047

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Kwang Jun Ahn, Young-Mi Bahk, Dai-Sik Kim, Jisoo Kyoung, and Fabian Rotermund, "Ultrasensitive molecular absorption detection using metal slot antenna arrays," Opt. Express 23, 19047-19055 (2015)

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Related Topics
Table of Contents Category
- Sensors
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction and gratings (050.0050)
- Plasmonics (250.5403)
- Optical sensing and sensors (280.4788)
- Absorption (300.1030)

About this Article
History
- Original Manuscript: May 18, 2015
- Revised Manuscript: July 7, 2015
- Manuscript Accepted: July 7, 2015
- Published: July 15, 2015

Accessible

Open Access

Abstract

We theoretically study the transmission reduction of light passing through absorptive molecules embedded in a periodic metal slot array in a near infrared wavelength regime. From the analytically solved transmitted light, we present a simple relation given by the attenuation length of light at the resonance wavelength of the slot antennas with respect to the spectral width of the resonant transmission peak. This relation clearly explains that the control of the transmission reduction even with very low absorptive materials is possible. We investigate also the transmission reduction by absorptive molecules in a real metallic slot antenna array on a dielectric substrate and compare the results with finite difference time domain calculations. In numerical calculations, we demonstrate that the same amount of transmission reduction by a bulk absorptive material can be achieved only with one-hundredth thickness of the same material when it is embedded in an optimized Fano-resonant slot antenna array. Our relation presented in this study can contribute to label-free chemical and biological sensing as an efficient design and performance criterion for periodic slot antenna arrays.

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References

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|
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|
Author
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Publication

C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, 2005).
L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]
J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]
J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[Crossref] [PubMed]
Y. Binfeng, H. Guohua, Z. Ruohu, and C. Yiping, “Design of a compact and high sensitive refractive index sensor base on metal-insulator-metal plasmonic Bragg grating,” Opt. Express 22, 28662–28670 (2014).
[Crossref] [PubMed]
G. D. Osowiecki, E. Barakat, A. Naqavi, and H. P. Herzig, “Vertically coupled plasmonic slot waveguide cavity for localized biosensing applications,” Opt. Express 22, 20871–20880 (2014).
[Crossref] [PubMed]
B. You, J.-Y. Lu, T.-A. Liu, and J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21, 21087–21096 (2013).
[Crossref] [PubMed]
H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]
D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. Garcia-Parajo, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotech. 8, 512–516 (2013).
[Crossref]
T. Sannomiya, O. Scholder, K. Jefimovs, C. Hafner, and A. B. Dahlin, “Investigation of plasmon resonances in metal films with nanohole arrays for biosensing applications,” Small 7, 1653–1663 (2011).
[Crossref] [PubMed]
R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]
J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule-surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical wwitching,” Adv. Mater. 18, 1267–1270 (2006).
[Crossref]
M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]
L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).
[Crossref] [PubMed]
B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[Crossref]
S. Savoia, A. Ricciardi, A. Crescitelli, C. Granata, E. Esposito, V. Galdi, and A. Cusano, “Surface sensitivity of Rayleigh anomalies in metallic nanogratings,” Opt. Express 21, 23531–23542 (2013).
[Crossref] [PubMed]
A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]
A. Taflove and S. C. Hagness, Computational Electrodynamics : The Finite-Difference Time-Domain Method (Artech House, 2005).
J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]
F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[Crossref] [PubMed]
J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]
J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
S. V. Yuferev and N. Ida, Surface Impedance Boundary Conditions : A Comprehensive Approach (CRC Press/Taylor & Francis, 2010).
F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[Crossref]
H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51, 1729–1741 (2012).
[Crossref] [PubMed]
K. Jun Ahn and A. Knorr, “Radiative lifetime of quantum confined excitons near interfaces,” Phys. Rev. B 68, 161307 (2003).
[Crossref]
A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]
Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/fdtd/ .

2014 (2)

Y. Binfeng, H. Guohua, Z. Ruohu, and C. Yiping, “Design of a compact and high sensitive refractive index sensor base on metal-insulator-metal plasmonic Bragg grating,” Opt. Express 22, 28662–28670 (2014).
[Crossref] [PubMed]

G. D. Osowiecki, E. Barakat, A. Naqavi, and H. P. Herzig, “Vertically coupled plasmonic slot waveguide cavity for localized biosensing applications,” Opt. Express 22, 20871–20880 (2014).
[Crossref] [PubMed]

2013 (4)

B. You, J.-Y. Lu, T.-A. Liu, and J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21, 21087–21096 (2013).
[Crossref] [PubMed]

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. Garcia-Parajo, and J. Wenger, “A plasmonic ’antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotech. 8, 512–516 (2013).
[Crossref]

S. Savoia, A. Ricciardi, A. Crescitelli, C. Granata, E. Esposito, V. Galdi, and A. Cusano, “Surface sensitivity of Rayleigh anomalies in metallic nanogratings,” Opt. Express 21, 23531–23542 (2013).
[Crossref] [PubMed]

2012 (1)

H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51, 1729–1741 (2012).
[Crossref] [PubMed]

2011 (2)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

T. Sannomiya, O. Scholder, K. Jefimovs, C. Hafner, and A. B. Dahlin, “Investigation of plasmon resonances in metal films with nanohole arrays for biosensing applications,” Small 7, 1653–1663 (2011).
[Crossref] [PubMed]

2010 (4)

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[Crossref]

2009 (1)

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]

2007 (1)

A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]

2006 (3)

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[Crossref] [PubMed]

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule-surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical wwitching,” Adv. Mater. 18, 1267–1270 (2006).
[Crossref]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[Crossref]

2005 (2)

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

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).
[Crossref] [PubMed]

2004 (1)

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

2003 (2)

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

K. Jun Ahn and A. Knorr, “Radiative lifetime of quantum confined excitons near interfaces,” Phys. Rev. B 68, 161307 (2003).
[Crossref]

1998 (1)

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Ahn, K.

Ahn, K. J.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Ahn, Y. H.

Ameling, R.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Bahk, Y.-M.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Balanis, C. A.

C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, 2005).

Barakat, E.

Barnard, E. S.

Barnes, W. L.

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

Bernien, H.

Binfeng, Y.

Braun, P. V.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Bravo-Abad, J.

Brongersma, M. L.

Cai, W.

Chang, S.-H.

Choe, J. H.

Choe, J.-H.

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]

Chong, C. T.

Crescitelli, A.

Cusano, A.

Dahlin, A. B.

Depine, R. A.

H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51, 1729–1741 (2012).
[Crossref] [PubMed]

Dereux, A.

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

Dintinger, J.

Djurišic, A. B.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Ebbesen, T. W.

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

Elazar, J. M.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Enoch, S.

Esposito, E.

Galdi, V.

Garcia-Parajo, M. F.

García-Vidal, F. J.

A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]

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

Giessen, H.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Gordon, R.

Granata, C.

Guohua, H.

Hafner, C.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics : The Finite-Difference Time-Domain Method (Artech House, 2005).

Halas, N. J.

Han, S.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Harmsen, R. H.

Hentschel, M.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Herzig, H. P.

Ida, N.

S. V. Yuferev and N. Ida, Surface Impedance Boundary Conditions : A Comprehensive Approach (CRC Press/Taylor & Francis, 2010).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Jefimovs, K.

Jun, Y. C.

Jun Ahn, K.

K. Jun Ahn and A. Knorr, “Radiative lifetime of quantum confined excitons near interfaces,” Phys. Rev. B 68, 161307 (2003).
[Crossref]

Kang, J. H.

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]

Kim, B. J.

Kim, D. S.

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]

Kim, D.-S.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Kim, H.-s.

Kim, H.-T.

Klein, S.

Knorr, A.

K. Jun Ahn and A. Knorr, “Radiative lifetime of quantum confined excitons near interfaces,” Phys. Rev. B 68, 161307 (2003).
[Crossref]

Koo, S.

Kuipers, L.

Kumar, L. K. S.

Kyoung, J.

Langguth, L.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Luk’yanchuk, B.

Maier, S. A.

Majewski, M. L.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Martín-Moreno, L.

A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]

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

Mary, A.

A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]

Mesch, M.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97, 253116 (2010).
[Crossref]

Mivelle, M.

Moparthi, S. B.

Moreno, E.

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

Naqavi, A.

Nordlander, P.

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

Osowiecki, G. D.

Park, H.

Park, H.-R.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Park, N.

H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13, 1782–1786 (2013).
[PubMed]

Park, Q. H.

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17, 15652–15658 (2009).
[Crossref] [PubMed]

Peng, J.-L.

B. You, J.-Y. Lu, T.-A. Liu, and J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21, 21087–21096 (2013).
[Crossref] [PubMed]

Porto, J. A.

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

Prangsma, J. C.

Punj, D.

Rakic, A. D.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Ricciardi, A.

Rigneault, H.

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[Crossref]

Ruohu, Z.

Sandtke, M.

Sannomiya, T.

Savoia, S.

Schatz, G. C.

Scholder, O.

Schuller, J. A.

Segerink, F. B.

Seo, M.

Sherry, L. J.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics : The Finite-Difference Time-Domain Method (Artech House, 2005).

Van Duyne, R. P.

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

van Hulst, N. F.

van Nieuwstadt, J. A. H.

van Zanten, T. S.

Wenger, J.

White, J. S.

Wiley, B. J.

Xia, Y.

Yiping, C.

You, B.

B. You, J.-Y. Lu, T.-A. Liu, and J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21, 21087–21096 (2013).
[Crossref] [PubMed]

Yuferev, S. V.

S. V. Yuferev and N. Ida, Surface Impedance Boundary Conditions : A Comprehensive Approach (CRC Press/Taylor & Francis, 2010).

Zheludev, N. I.

Adv. Mater. (1)

Appl. Opt. (2)

H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51, 1729–1741 (2012).
[Crossref] [PubMed]

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Fig. 1

The sample geometry considered in this study. A periodic array of rectangular apertures perforated in a thin metal film is attached on a dielectric substrate. Each aperture has a same dimension of l × w × h (length × width × height) and the array has periods L_x and L_y along the x- and the y-axis. The dielectric constants of the substrate, the metal, molecules in the metal cavity, and the incident region are denoted as ε₃, ε_m, ε₂, and ε₁, in respective.

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Fig. 2

Transmission spectra of (a) the PEC and (b) the Au slot antenna (l = 350nm, w = 50nm, h = 100nm) array (L_x = 850nmLy = 600nm) for ε₂ = 1 (red solid line), ε₂ = 1 + 0.01i (blue dashed lines), and their ratio (T/T₀) (black solid line), calculated for ε₁ = ε₃ = 1 by the Rayleigh expansion model (REM). For a comparison, the transmission of the same size of a single PEC slot antenna is displayed in Fig. 2(a).

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Fig. 3

Transmission spectra of (a) the PEC and (b) the Au slot antenna array with the same dimensions and periods of Fig. 2 for ε₂ = 1 (red solid line), ε₂ = 1 + 0.01i (blue dashed lines), and their ratio (T/T₀) (black solid line), calculated by the REM with considering an dielectric substrate (ε₃ = 2.25).

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Fig. 4

Transmission spectra of (a) the PEC and (b) the Au slit array with the same dimensions and periods of Fig. 2 for ε₂ = 1 (red solid line), ε₂ = 1 + 0.01i (blue dashed lines), and their ratio (T/T₀) (black solid line), calculated for ε₃ = 2.25 by FDTD.

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Fig. 5

Transmission spectra of the Au slot antenna array with the same dimensions and periods of Fig. 2 for ε₂ = 1 (red solid line) and a dispersive ε₂(w) (blue dashed lines), and their ratio (T/T₀) (black solid line), calculated by (a) the REM and (b) the FDTD method.

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Equations (17)

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E_{x}^{I} = \frac{i}{k_{0} ε_{1}} \sum_{k_{x}, k_{y}} {- i k_{1 z} e^{- i k_{1 z} (z - h / 2)} δ_{k_{x,} 0} δ_{k_{y,} 0} + (i k_{1 z} g_{y} - i k_{x} g_{z}) e^{i Θ} e^{i k_{1 z} (z - h / 2)}},

H_{y}^{I} = \frac{1}{Z_{0}} \sum_{k_{x}, k_{y}} {e^{- i k_{1 z} (z - h / 2)} δ_{k_{x}, 0} δ_{k_{y,} 0} + g_{y} e^{i Θ} e^{i k_{1 z} (z - h / 2)}} for z > h / 2,

E_{x}^{II} = sin (\frac{π y}{l}) (A e^{- i β z} + B e^{i β z}),

H_{y}^{II} = \frac{β}{k_{0} Z_{0}} sin (\frac{π y}{l}) (A e^{- i β z} - B e^{i β z}),

H_{z}^{II} = - \frac{π}{k_{0} l Z_{0}} cos (\frac{π y}{l}) (A e^{- i β z} + B e^{i β z}) for - h / 2 \leq z \leq h / 2,

E_{x}^{III} = \frac{1}{k_{0} ε_{3}} \sum_{k_{x}, k_{y}} {(k_{3 z} f_{y} + k_{x} f_{z}) e^{i Θ} e^{- i k_{3 z} (z + h / 2)}},

H_{y}^{III} = \frac{1}{Z_{0}} \sum_{k_{x}, k_{y}} f_{y} e^{i Θ} e^{- i k_{3 z} (z + h / 2)} for z < - h / 2,

T = \frac{1}{2} Re [E_{x}^{III} H_{y}^{III *}] = \frac{32 I_{0}}{π^{2} | D |^{2}} {| \frac{β}{k_{0}} |}^{2} Re [W_{3}],

I_{0} = \frac{1}{2 Z_{0}} \frac{l w}{L_{x} L_{y}},

W_{j} = \frac{l w}{2 L_{x} L y} \sum_{k_{x}, k_{y}} \frac{k_{j z}^{2} + k_{x}^{2}}{k_{0} k_{j z}} {| J (k_{x}, k_{y}) |}^{2},

J (k_{x}, k_{y}) = sinc (\frac{k_{x} w}{2}) {sinc (\frac{k_{y} l + π}{2}) + sinc (\frac{k_{y} l - π}{2})},

D = - i sin (β h) ({| \frac{β}{k_{0}} |}^{2} + W_{1} W_{3}) + cos (β h) \frac{β}{k_{0}} (W_{1} + W_{3}) .

\begin{array}{l} R = \frac{1}{2} Re [E_{x}^{I} H_{y}^{I *}] = \frac{8 I_{0}}{π} Re [\frac{1}{D} {\frac{β}{k_{0}} cos (β h) - i W_{3} sin (β h)} \sum_{k_{x}, k_{y}} J (k_{x}, k_{y})] \\ - \frac{32 I_{0}}{π^{2} {| D |}^{2}} {| \frac{β}{k_{0}} cos (β h) - i W_{3} sin (β h) |}^{2} Re [W_{1}] . \end{array}

tan (\frac{l}{2} \sqrt{k_{0}^{2} ε_{2} - β^{2}}) = \sqrt{\frac{β^{2} - k_{0}^{2} ε_{m}}{k_{0}^{2} ε_{2} - β^{2}},}

T \propto {| \frac{β}{k_{0}} |}^{2} \frac{G_{r}}{{| D |}^{2}} \approx G_{r} / {| i (2 G_{i} - \frac{h}{k_{0}} β^{2}) + 2 G_{r} |}^{2} .

T \propto G_{r} / {| i (2 G_{i} - \frac{h}{k_{0}} (ε_{r} k_{0}^{2} - k_{ρ}^{2})) + (ε_{i} h k_{0} + 2 G_{r}) |}^{2} .

T / T_{0} = 1 / {| \frac{k_{0} h}{2 G_{r}} ε_{i} + 1 |}^{2} .

Abstract

References

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