Abstract

We investigate coupling in arrays of nanoparticles resonating as half-wave antennas on both silicon and sapphire, and find a universal behavior when scaled by antenna length and substrate index. Three distinct coupling regimes are identified and characterized by rigorous finite-difference time domain simulations. As interparticle pitch is reduced below the oft-described radiative to evanescent transition, resonances blue shift and narrow and exhibit an asymmetric band consistent with a Fano lineshape. Upon further pitch reduction, a transition to a third regime, termed here as near-field coupling, is observed in which the resonance shifts red, becomes more symmetric, and broadens dramatically. This latter regime occurs when the extension of the resonant mode beyond the physical antenna end overlaps that of its neighbor. Simulations identify a clear rearrangement of field intensity accompanying this regime, illustrating that longitudinal modal fields localize in the air gap rather than in the higher index substrate at a pitch consistent with the experimentally observed transition.

© 2012 OSA

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2012

F. López-Tejeira, R. Paniagua-Dominguez, R. Rodriguez-Oliveros, and J. A. Sanchez-Gil, “Fano-like interference of plasmon resonances at a single rod-shaped Nanoantenna,” New J. Phys.14(2), 023035 (2012).
[CrossRef]

P. Biagioni, J. S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

2011

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

S. M. R. Z. Bajestani, M. Shabadi, and N. Talebi, “Analysis of plasmon propagation along a chain of metal nanospheres using the generalized multipole technique,” J. Opt. Soc. Am. B28(4), 937–943 (2011).
[CrossRef]

L. B. Sagle, L. K. Ruvuna, J. A. Ruemmele, and R. P. Van Duyne, “Advances in localized surface plasmon resonance spectroscopy biosensing,” Nanomedicine (Lond)6(8), 1447–1462 (2011).
[CrossRef] [PubMed]

J. D. Caldwell, O. J. Glembocki, F. J. Bezares, M. I. Kariniemi, J. T. Niinistö, T. T. Hatanpää, R. W. Rendell, M. Ukaegbu, M. K. Ritala, S. M. Prokes, C. M. Hosten, M. A. Leskelä, and R. Kasica, “Large-area plasmonic hot-spot arrays: Sub-2 nm interparticle separations with plasma-enhanced atomic layer deposition of Ag on periodic arrays of Si nanopillars,” Opt. Express19(27), 26056–26064 (2011).
[CrossRef] [PubMed]

J. D. Caldwell, O. J. Glembocki, F. J. Bezares, N. D. Bassim, R. W. Rendell, M. Feygelson, M. Ukaegbu, R. Kasica, L. Shirey, and C. Hosten, “Plasmonic nanopillar arrays for large-area, high-enhancement surface-enhanced Raman scattering sensors,” ACS Nano5(5), 4046–4055 (2011).
[CrossRef] [PubMed]

K. Ueno and H. Misawa, “Photochemical reaction fields with strong coupling between a photon and a molecule,” J. Photochem. Photobiol. Chem.221(2-3), 130–137 (2011).
[CrossRef]

D. Weber, P. Albella, P. Alonso-González, F. Neubrech, H. Gui, T. Nagao, R. Hillenbrand, J. Aizpurua, and A. Pucci, “Longitudinal and transverse coupling in infrared gold nanoantenna arrays: long range versus short range interaction regimes,” Opt. Express19(16), 15047–15061 (2011).
[CrossRef] [PubMed]

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111(6), 3888–3912 (2011).
[CrossRef] [PubMed]

2010

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(9), 707–715 (2010).
[CrossRef] [PubMed]

B. Augié, X. M. Bendaña, W. L. Barnes, and F. J. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: critical role of the substrate,” Phys. Rev. B82(15), 155447 (2010).
[CrossRef]

R. Adato, A. A. Yanik, C. H. Wu, G. Shvets, and H. Altug, “Radiative engineering of plasmon lifetimes in embedded nanoantenna arrays,” Opt. Express18(5), 4526–4537 (2010).
[CrossRef] [PubMed]

H. Im, K. C. Bantz, N. C. Lindquist, C. L. Haynes, and S. H. Oh, “Vertically oriented sub-10-nm plasmonic nanogap arrays,” Nano Lett.10(6), 2231–2236 (2010).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

M. J. Kofke, D. H. Waldeck, and G. C. Walker, “Composite nanoparticle nanoslit arrays: A novel platform for LSPR mediated subwavelength optical transmission,” Opt. Express18(8), 7705–7713 (2010).
[CrossRef] [PubMed]

R. A. Flynn, I. Vurgaftman, K. L. Bussmann, B. S. Simpkins, C. S. Kim, and J. P. Long, “Transmission efficiency of surface plasmon polaritons across gaps in gold waveguides,” Appl. Phys. Lett.96(11), 111101 (2010).
[CrossRef]

2009

J. Parsons, E. Hendry, C. P. Burrows, B. Auguiě, J. R. Sambles, and W. L. Barnes, “Localized surface-plasmon resonances in periodic nondiffracting metallic nanoparticle and nanohole arrays,” Phys. Rev. B79(7), 073412 (2009).
[CrossRef]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett.9(4), 1663–1667 (2009).
[CrossRef] [PubMed]

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonators for surface plasmons,” Appl. Phys. Lett.95(20), 201101 (2009).
[CrossRef]

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A.106(46), 19227–19232 (2009).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett.102(14), 146807 (2009).
[CrossRef] [PubMed]

2008

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8(12), 4391–4397 (2008).
[CrossRef] [PubMed]

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008).
[CrossRef] [PubMed]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

L. Brus, “Noble metal nanocrystals: plasmon electron transfer photochemistry and single-molecule Raman spectroscopy,” Acc. Chem. Res.41(12), 1742–1749 (2008).
[CrossRef] [PubMed]

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8(2), 631–636 (2008).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

R. L. Olmon, P. M. Krenz, A. C. Jones, G. D. Boreman, and M. B. Raschke, “Near-field imaging of optical antenna modes in the mid-infrared,” Opt. Express16(25), 20295–20305 (2008).
[CrossRef] [PubMed]

A. O. Pinchuk and G. C. Schatz, “Nanoparticle optical properties: Far- and near-field electrodynamic coupling in a chain of silver spherical nanoparticles,” Mater. Sci. Eng. B149(3), 251–258 (2008).
[CrossRef]

2007

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett.98(26), 266802 (2007).
[CrossRef] [PubMed]

2006

F. Neubrech, T. Kolb, R. Lovrincic, G. Fahsold, A. Pucci, J. Aizpurua, T. W. Cornelius, M. E. Toimil-Molares, R. Neumann, and S. Karim, “Resonances of individual metal nanowires in the infrared,” Appl. Phys. Lett.89(25), 253104 (2006).
[CrossRef]

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: Optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B110(37), 18243–18253 (2006).
[CrossRef] [PubMed]

Z. Chen, X. Li, A. Taflove, and V. Backman, “Backscattering enhancement of light by nanoparticles positioned in localized optical intensity peaks,” Appl. Opt.45(4), 633–638 (2006).
[CrossRef] [PubMed]

2005

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005).
[CrossRef]

2004

S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. D. Stafford, S. R. Bishop, U. K. Lincoln, and J. V. Coe, “Use of the extraordinary infrared transmission of metallic subwavelength arrays to study the catalyzed reaction of methanol to formaldehyde on copper oxide,” J. Phys. Chem. B108(31), 11833–11837 (2004).
[CrossRef]

N. Félidj, S. L. Truong, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, A. Leitner, and F. R. Aussenegg, “Gold particle interaction in regular arrays probed by surface enhanced Raman scattering,” J. Chem. Phys.120(15), 7141–7146 (2004).
[CrossRef] [PubMed]

T. Atay, J. H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: From dipole-dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B70(12), 125429 (2004).
[CrossRef]

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M. I. Stockman, L. N. Pandey, L. S. Muratove, and T. F. George, “Optical-absorption and localization of eignenmodes in disordered clusters,” Phys. Rev. B51(1), 185–195 (1995).
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R. Adato, A. A. Yanik, C. H. Wu, G. Shvets, and H. Altug, “Radiative engineering of plasmon lifetimes in embedded nanoantenna arrays,” Opt. Express18(5), 4526–4537 (2010).
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R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A.106(46), 19227–19232 (2009).
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V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
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R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A.106(46), 19227–19232 (2009).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
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Ashraf El-Bayoumi, M.

M. Kasha, H. R. Rawls, and M. Ashraf El-Bayoumi, “The exciton model in molecular spectroscopy,” Pure Appl. Chem.11(3-4), 371–392 (1965).
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N. Félidj, S. L. Truong, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, A. Leitner, and F. R. Aussenegg, “Gold particle interaction in regular arrays probed by surface enhanced Raman scattering,” J. Chem. Phys.120(15), 7141–7146 (2004).
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[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett.84(20), 4721–4724 (2000).
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Bajestani, S. M. R. Z.

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B. Augié, X. M. Bendaña, W. L. Barnes, and F. J. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: critical role of the substrate,” Phys. Rev. B82(15), 155447 (2010).
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J. Parsons, E. Hendry, C. P. Burrows, B. Auguiě, J. R. Sambles, and W. L. Barnes, “Localized surface-plasmon resonances in periodic nondiffracting metallic nanoparticle and nanohole arrays,” Phys. Rev. B79(7), 073412 (2009).
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B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008).
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J. D. Caldwell, O. J. Glembocki, F. J. Bezares, N. D. Bassim, R. W. Rendell, M. Feygelson, M. Ukaegbu, R. Kasica, L. Shirey, and C. Hosten, “Plasmonic nanopillar arrays for large-area, high-enhancement surface-enhanced Raman scattering sensors,” ACS Nano5(5), 4046–4055 (2011).
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B. Augié, X. M. Bendaña, W. L. Barnes, and F. J. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: critical role of the substrate,” Phys. Rev. B82(15), 155447 (2010).
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Bezares, F. J.

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P. Biagioni, J. S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
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J. H. Van Vleck, F. Bloch, and M. Hamermesh, “theory of radar reflection from wires or thin metallic strips,” J. Appl. Phys.18(3), 274–294 (1947).
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Boreman, G. D.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
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M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B62(24), R16356–R16359 (2000).
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L. Brus, “Noble metal nanocrystals: plasmon electron transfer photochemistry and single-molecule Raman spectroscopy,” Acc. Chem. Res.41(12), 1742–1749 (2008).
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G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8(2), 631–636 (2008).
[CrossRef] [PubMed]

Burrows, C. P.

J. Parsons, E. Hendry, C. P. Burrows, B. Auguiě, J. R. Sambles, and W. L. Barnes, “Localized surface-plasmon resonances in periodic nondiffracting metallic nanoparticle and nanohole arrays,” Phys. Rev. B79(7), 073412 (2009).
[CrossRef]

Bussmann, K. L.

R. A. Flynn, I. Vurgaftman, K. L. Bussmann, B. S. Simpkins, C. S. Kim, and J. P. Long, “Transmission efficiency of surface plasmon polaritons across gaps in gold waveguides,” Appl. Phys. Lett.96(11), 111101 (2010).
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Caldwell, J. D.

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E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonators for surface plasmons,” Appl. Phys. Lett.95(20), 201101 (2009).
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Chen, Z.

Chong, C. T.

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(9), 707–715 (2010).
[CrossRef] [PubMed]

Coe, J. V.

S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. D. Stafford, S. R. Bishop, U. K. Lincoln, and J. V. Coe, “Use of the extraordinary infrared transmission of metallic subwavelength arrays to study the catalyzed reaction of methanol to formaldehyde on copper oxide,” J. Phys. Chem. B108(31), 11833–11837 (2004).
[CrossRef]

Cornelius, T. W.

F. Neubrech, T. Kolb, R. Lovrincic, G. Fahsold, A. Pucci, J. Aizpurua, T. W. Cornelius, M. E. Toimil-Molares, R. Neumann, and S. Karim, “Resonances of individual metal nanowires in the infrared,” Appl. Phys. Lett.89(25), 253104 (2006).
[CrossRef]

Cubukcu, E.

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonators for surface plasmons,” Appl. Phys. Lett.95(20), 201101 (2009).
[CrossRef]

Ditlbacher, H.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett.84(20), 4721–4724 (2000).
[CrossRef] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
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El-Sayed, M. A.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: Optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B110(37), 18243–18253 (2006).
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Erramilli, S.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A.106(46), 19227–19232 (2009).
[CrossRef] [PubMed]

Eustis, S.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: Optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B110(37), 18243–18253 (2006).
[CrossRef] [PubMed]

Fahsold, G.

F. Neubrech, T. Kolb, R. Lovrincic, G. Fahsold, A. Pucci, J. Aizpurua, T. W. Cornelius, M. E. Toimil-Molares, R. Neumann, and S. Karim, “Resonances of individual metal nanowires in the infrared,” Appl. Phys. Lett.89(25), 253104 (2006).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961).
[CrossRef]

Félidj, N.

N. Félidj, S. L. Truong, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, A. Leitner, and F. R. Aussenegg, “Gold particle interaction in regular arrays probed by surface enhanced Raman scattering,” J. Chem. Phys.120(15), 7141–7146 (2004).
[CrossRef] [PubMed]

Fernández-Domínguez, A. I.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111(6), 3888–3912 (2011).
[CrossRef] [PubMed]

Ferry, V. E.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8(12), 4391–4397 (2008).
[CrossRef] [PubMed]

Feygelson, M.

J. D. Caldwell, O. J. Glembocki, F. J. Bezares, N. D. Bassim, R. W. Rendell, M. Feygelson, M. Ukaegbu, R. Kasica, L. Shirey, and C. Hosten, “Plasmonic nanopillar arrays for large-area, high-enhancement surface-enhanced Raman scattering sensors,” ACS Nano5(5), 4046–4055 (2011).
[CrossRef] [PubMed]

Fluhr, W.

Flynn, R. A.

R. A. Flynn, I. Vurgaftman, K. L. Bussmann, B. S. Simpkins, C. S. Kim, and J. P. Long, “Transmission efficiency of surface plasmon polaritons across gaps in gold waveguides,” Appl. Phys. Lett.96(11), 111101 (2010).
[CrossRef]

Ford, G. W.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B70(12), 125429 (2004).
[CrossRef]

Francescato, Y.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Fritz, S.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances - Bulk dielectric functions and chemical interface damping,” Phys. Rev. B Condens. Matter48(24), 18178–18188 (1993).
[CrossRef] [PubMed]

García de Abajo, F. J.

B. Augié, X. M. Bendaña, W. L. Barnes, and F. J. García de Abajo, “Diffractive arrays of gold nanoparticles near an interface: critical role of the substrate,” Phys. Rev. B82(15), 155447 (2010).
[CrossRef]

G. W. Bryant, F. J. García de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8(2), 631–636 (2008).
[CrossRef] [PubMed]

Genet, C.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

George, T. F.

M. I. Stockman, L. N. Pandey, L. S. Muratove, and T. F. George, “Optical-absorption and localization of eignenmodes in disordered clusters,” Phys. Rev. B51(1), 185–195 (1995).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Giannini, V.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111(6), 3888–3912 (2011).
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G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett.102(14), 146807 (2009).
[CrossRef] [PubMed]

Giessen, H.

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(9), 707–715 (2010).
[CrossRef] [PubMed]

Glembocki, O. J.

Gómez Rivas, J.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett.102(14), 146807 (2009).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Gui, H.

Gunnarsson, L.

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B107(30), 7337–7342 (2003).
[CrossRef]

Halas, N. J.

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(9), 707–715 (2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Hamermesh, M.

J. H. Van Vleck, F. Bloch, and M. Hamermesh, “theory of radar reflection from wires or thin metallic strips,” J. Appl. Phys.18(3), 274–294 (1947).
[CrossRef]

Hao, F.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett.9(4), 1663–1667 (2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B62(24), R16356–R16359 (2000).
[CrossRef]

Hatanpää, T. T.

Haynes, C. L.

H. Im, K. C. Bantz, N. C. Lindquist, C. L. Haynes, and S. H. Oh, “Vertically oriented sub-10-nm plasmonic nanogap arrays,” Nano Lett.10(6), 2231–2236 (2010).
[CrossRef] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B107(30), 7337–7342 (2003).
[CrossRef]

Hecht, B.

P. Biagioni, J. S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Heck, S. C.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111(6), 3888–3912 (2011).
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[CrossRef]

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N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett.9(4), 1663–1667 (2009).
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[CrossRef] [PubMed]

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S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. D. Stafford, S. R. Bishop, U. K. Lincoln, and J. V. Coe, “Use of the extraordinary infrared transmission of metallic subwavelength arrays to study the catalyzed reaction of methanol to formaldehyde on copper oxide,” J. Phys. Chem. B108(31), 11833–11837 (2004).
[CrossRef]

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T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

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M. I. Stockman, L. N. Pandey, L. S. Muratove, and T. F. George, “Optical-absorption and localization of eignenmodes in disordered clusters,” Phys. Rev. B51(1), 185–195 (1995).
[CrossRef]

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S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B69(12), 125418 (2004).
[CrossRef]

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V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8(12), 4391–4397 (2008).
[CrossRef] [PubMed]

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Talebi, N.

Taminiau, T. H.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

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S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. D. Stafford, S. R. Bishop, U. K. Lincoln, and J. V. Coe, “Use of the extraordinary infrared transmission of metallic subwavelength arrays to study the catalyzed reaction of methanol to formaldehyde on copper oxide,” J. Phys. Chem. B108(31), 11833–11837 (2004).
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Figures (10)

Fig. 1
Fig. 1

(a) Reflection spectra (red) and Fano fits (blue) for random arrays of 130 nm wide antennas on sapphire. Each curve is labeled with its corresponding nanorod antenna length. Blue arrows indicate higher order antenna modes for the 1.58 μm long antenna. Dashed black curve corresponds to the normalized scattering cross-section computed with microwave scattering theory for a single, isolated antenna with an effective length and diameter of 1.3 and 0.06 μm, respectively. (b) Resonance position via Fano fits for 65, 130, and 260 nm wide antennas on sapphire as a function of antenna length. As antenna length is increased, resonance shifts to longer wavelengths. Linear fits (solid lines) indicate antennas are well-behaved half-wavelength resonators, with λres = 2neff(L + 2δ) as defined in text. neff decreases for wider antennas as shown in inset of (b).

Fig. 2
Fig. 2

Typical reflection spectra (red) and Fano fits (blue) for square arrays of 1100 nm long antennas on (a) sapphire and (b) silicon. The subset of data presented includes pitches, p, of 1.2, 1.275, 1.35, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, and 2.8 μm for both substrates. (Insets) SEM images of 1100 nm antenna array with p = 1.6 μm and 550 nm antenna array with p = 0.8 μm. In addition to the blue shift and reduced linewidth which typically accompany the transition from radiative to evanescent coupling, a substantial line broadening, red shift and loss of asymmetry is observed at very small pitches.

Fig. 3
Fig. 3

Summary of spectral properties for square arrays of 550 and 1100 nm antennas on sapphire and Si. All systems exhibit comparable behavior. The relevant features associated with the radiative to evanescent transition with decreasing pitch (indicated by slanted dashed lines for the m = + 1 and −1 diffractive orders) are a relative blue shifting of the peak and increased oscillator quality factor Q. Our results demonstrate additional significant modifications to line shape when pitch is further reduced, which consist of line broadening (reduced Q), loss of asymmetry (increased Fano parameter q), and a relative red shift. Note that the most widely-spaced arrays studied have a resonance red-shifted relative to that of non-interacting antennas as predicted by the results of Fig. 1 (horizontal dashed line). Blue arrows indicate pitch at which longitudinal current extension (δ) of adjacent antennas overlaps.

Fig. 4
Fig. 4

Summary of (a) resonance position and (b) quality factor plotted with a universal scaling to enable direct comparison of arrays of different lengths and on different substrates.

Fig. 5
Fig. 5

Finite-difference time-domain simulated lineshapes for arrays of 1100 nm long antennas on (a) sapphire and (b) silicon at pitches of 1.2, 1.3, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, and 3.0 μm. Note the different frequency scales. All of the pertinent features exhibited by the data (Fig. 2) are reproduced by the simulations, namely the pitch-dependent trends in linewidth, asymmetry, and spectral shifts.

Fig. 6
Fig. 6

Peak positions extracted from FTDT results (open dots) compare very well with those from the experimental results (solid dots) for 1100 nm antenna arrays on (a) sapphire and (b) silicon. This agreement demonstrates that simulations provide an accurate description of the real system.

Fig. 7
Fig. 7

Contour plots of |Ex|2 for 1100 nm long antennas calculated for a plan view section taken 1 nm below the substrate surface. Values are plotted on a common logarithmic scale relative to incident intensity (0.01-1200 E0). Position of a single antenna is indicated by a dotted rectangle and periodic boundary conditions were used to generate infinite array. Plots correspond to array pitches of (a) 2.8, (b) 2.4, (c) 2.0, (d) 1.6, (e) 1.3, and (f) 1.2 μm.

Fig. 8
Fig. 8

Comparison of field intensity at the longitudinal and transverse mid-gap positions (marked by red dots labeled L and T in Fig. 7(a)) for arrays of (a) 1100 nm antennas and (b) 550 nm antennas on sapphire. Vertical dashed lines indicate array with greatest oscillator quality factor, Q.

Fig. 9
Fig. 9

(a) Vertical field profiles taken at longitudinal mid gap for 1100 nm antennas on sapphire for pitches from 1.2 to 3 μm. Dashed black line indicates air-substrate boundary. Red box indicates height of antennas. As pitch is reduced, the field maximum moves up from the substrate eventually reaching a peaked value in the air between antennas. (b) Pitch-dependent position of maximum field for arrays of 1100 (black) and 550 nm antennas (red) on sapphire. The maximum-field transitions from substrate to air at p~1.5 and p~0.86 μm for arrays of 1100 and 550 nm antennas, respectively (indicated by vertical black dashed line). These pitches correlate well with the onset of red-shifting observed in Fig. 3 which we attribute to longitudinal coupling.

Fig. 10
Fig. 10

(a) Experimental data (black dots) and exponential fit (red line) to 1100 nm antennas on sapphire with smallest spacings. This fit is used in (b) to predict line broadening due to possible gap modulation from lithographic variability. As shown in (b), gap variability of ~5 nm would only reduce Q to experimentally-observed values at much smaller spacings and therefore is not responsible for the observed broadening.

Equations (1)

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I( ω )= I 0 + A q ( 2Δ+qγ ) 2 4 Δ 2 + γ 2

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