Abstract

We report results of second harmonic generation calculations performed on Silver coupled 2D-nanoresonators. Coupling is responsible for the creation of resonant modes that can be localized on small portions of the structure or distributed over the whole structure. Different field profiles can be obtained by varying the parameters of the input field (i.e. the wavelength). The second harmonic generation nonlinear process is enhanced by the excitation of coupled surface plasmon polaritons. The emitted field is strongly affected by the linear properties of the structure behaving as a nano antenna. We note that different configurations of the pump field lead to different second harmonic far-field emission patterns. Also, we show that the angular emission of the second harmonic field contains information about the spatial location of the pump field hot spots at different frequencies. Applications to a new class of nano sources for single molecule fluorescence and sensors are proposed.

© 2011 OSA

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2010

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[CrossRef] [PubMed]

Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[CrossRef] [PubMed]

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

A. Nevet, N. Berkovitch, A. Hayat, P. Ginzburg, S. Ginzach, O. Sorias, and M. Orenstein, “Plasmonic nanoantennas for broad-band enhancement of two-photon emission from semiconductors,” Nano Lett. 10(5), 1848–1852 (2010).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[CrossRef] [PubMed]

A. Benedetti, M. Centini, C. Sibilia, and M. Bertolotti, “Engineering the second harmonic generation pattern from coupled gold nanowires,” J. Opt. Soc. Am. B 27(3), 408–416 (2010).
[CrossRef]

C. G. Biris and N. C. Panoiu, “Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires,” Phys. Rev. B 81(19), 195102 (2010).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

2009

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9(10), 3608–3611 (2009).
[CrossRef] [PubMed]

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[CrossRef]

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103(25), 257404 (2009).
[CrossRef]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express 17(5), 3603–3609 (2009).
[CrossRef] [PubMed]

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[CrossRef] [PubMed]

J. I. Dadap, H. B. de Aguiar, and S. Roke, “Nonlinear light scattering from clusters and single particles,” J. Chem. Phys. 130(21), 214710 (2009).
[CrossRef] [PubMed]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[CrossRef]

2008

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
[CrossRef]

W. L. Schaich, “Second harmonic generation by periodically-structured metal surfaces,” Phys. Rev. B 78(19), 195416 (2008).
[CrossRef]

2007

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007).
[CrossRef]

2006

W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

2005

K. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72(15), 153401 (2005).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef]

E. Centeno, “Second-harmonic superprism effect in photonic crystals,” Opt. Lett. 30(9), 1054–1056 (2005).
[CrossRef] [PubMed]

2004

R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69(8), 085407 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

B. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

C. I. Valencia, E. R. Mendez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” J. Opt. Soc. Am. B 21(1), 36–44 (2004).
[CrossRef]

2003

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

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

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A 18(4), 854–861 (2001).
[CrossRef]

1999

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
[CrossRef]

1998

1985

J. C. Quail and H. J. Simon, “Second-harmonic generation from silver and aluminum films in total internal reflection,” Phys. Rev. B Condens. Matter 31(8), 4900–4905 (1985).
[CrossRef] [PubMed]

1984

G. A. Farias and A. A. Maradudin, “Second harmonic generation in reflection from a metallic grating,” Phys. Rev. B 30(6), 3002–3015 (1984).
[CrossRef]

1983

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects,” Phys. Rev. B 28(4), 1870–1885 (1983).
[CrossRef]

1968

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Abdenour, A.

W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Acimovic, S. S.

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[CrossRef] [PubMed]

Adam, P.-M.

M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
[CrossRef]

Akozbek, N.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

Aktsipetrov, O. A.

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

Allegrini, M.

M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
[CrossRef]

Atkinson, R.

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007).
[CrossRef]

Atwater, H. A.

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

Aussenegg, F. R.

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A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
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T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103(25), 257404 (2009).
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J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
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W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
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Butet, J.

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M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
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Centini, M.

Cerullo, G.

M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
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N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
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Dereux, A.

R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69(8), 085407 (2004).
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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
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J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
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M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
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S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005).
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S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
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M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
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S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005).
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A. Nevet, N. Berkovitch, A. Hayat, P. Ginzburg, S. Ginzach, O. Sorias, and M. Orenstein, “Plasmonic nanoantennas for broad-band enhancement of two-photon emission from semiconductors,” Nano Lett. 10(5), 1848–1852 (2010).
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R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69(8), 085407 (2004).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
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S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
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M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
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Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
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T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103(25), 257404 (2009).
[CrossRef]

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A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
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A. Nevet, N. Berkovitch, A. Hayat, P. Ginzburg, S. Ginzach, O. Sorias, and M. Orenstein, “Plasmonic nanoantennas for broad-band enhancement of two-photon emission from semiconductors,” Nano Lett. 10(5), 1848–1852 (2010).
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J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
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Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
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Husu, H.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
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Jefimovs, K.

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
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Jonin, C.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[CrossRef] [PubMed]

Juanola Parramon, R.

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9(10), 3608–3611 (2009).
[CrossRef] [PubMed]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

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B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
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B. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
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Kildishev, A. V.

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[CrossRef]

Klein, M. W.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Koch, S. W.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[CrossRef]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Krauss, G.

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103(25), 257404 (2009).
[CrossRef]

Krenn, J. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[CrossRef]

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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
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S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[CrossRef] [PubMed]

Krishna, S.

W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Kuittinen, M.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[CrossRef] [PubMed]

Kujala, S.

Labardi, M.

M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P.-M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92(9), 093119 (2008).
[CrossRef]

Lacroute, Y.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[CrossRef]

Larciprete, M. C.

Laukkanen, J.

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S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
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M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[CrossRef] [PubMed]

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9(10), 3608–3611 (2009).
[CrossRef] [PubMed]

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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[CrossRef]

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R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69(8), 085407 (2004).
[CrossRef]

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[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

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T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103(25), 257404 (2009).
[CrossRef]

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W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007).
[CrossRef]

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[CrossRef]

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W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007).
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Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[CrossRef]

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W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
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S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005).
[CrossRef] [PubMed]

Zheludev, N. I.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

ACS Nano

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
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Appl. Opt.

Appl. Phys. Lett.

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Figures (11)

Fig. 2
Fig. 2

(a) Sketch of the considered geometry (not in scale); (b) Absorption coefficient as a function of the wavelength for the 4-rod structure.

Fig. 1
Fig. 1

Single nanoresonator composed by two silver rods: a) modulus of the y component of the fundamental frequency electric field normalized with respect to the amplitude of the x-polarized, upward propagating, incident field with a wavelength of 950 nm; The white boxes represent the sections of the rods b) Absorption coefficient as a function of the wavelength for the fundamental frequency field. White lines have been used to identify the boundaries of the rods.

Fig. 3
Fig. 3

modulus of the y component of the fundamental frequency electric field normalized with respect to the amplitude of the x polarized, upward propagating, incident field with a wavelength of (a) 940 nm; (b) 990 nm.

Fig. 4
Fig. 4

Nonlinear scattering cross section as a function of the pump wavelength calculated for the single rod (blue dashed line) and for the nanoresonator composed by two coupled rods separated by 28 nm air gap.

Fig. 5
Fig. 5

(a) Log10 of the modulus of the y component of the generated SH electric field normalized with respect to the amplitude of the x polarized, upward propagating, incident field with a wavelength of 950 nm; (b) differential nonlinear scattering cross section for a SH field wavelength of 475 nm. White lines have been used to identify the boundaries of the rods.

Fig. 6
Fig. 6

Nonlinear scattering cross section as a function of the pump wavelength calculated for the 4-rod structure.

Fig. 7
Fig. 7

differential nonlinear scattering cross section calculate for the 4-rod structure considering a pump wavelength of 940 nm (SH @ 470nm- blue dashed line) and 990 nm (SH @ 495 nm –red solid line).

Fig. 8
Fig. 8

Nonlinear scattering cross section as a function of the pump wavelength calculated for the 8-rod structure.

Fig. 9
Fig. 9

(a) modulus of the y component of the fundamental frequency field normalized with respect to the amplitude of the x polarized, upward propagating, incident field with a wavelength of 920 nm (a) and 960 nm (c); differential nonlinear scattering cross section for the SH field wavelength of 460 nm (b) and 480 nm (d).

Fig. 10
Fig. 10

(a) modulus of the y component of the fundamental frequency field normalized with respect to the amplitude of the x polarized, upward propagating, incident field with a wavelength of 980 nm (a) and 1030 nm (c); differential nonlinear scattering cross section for the SH field wavelength of 490 nm (b) and 515 nm (d).

Fig. 11
Fig. 11

Log10 of the modulus of the y component of the SH frequency field normalized with respect to the amplitude of the x-polarized incident field of wavelength of: (a) 920 nm (SH @ 460 nm); (b) 960 nm (SH @ 480 nm); (c) 980 nm (SH @ 490 nm) and (d) 1030 nm (SH at 515 nm). White lines have been used to identify the boundaries of the rods.

Equations (7)

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ε r ( ω ) = 1 G 0 ω P 2 ω ( ω + i γ 0 ) + k = 1 5 G k ω P 2 ω 0 , k 2 ω 2 i ω γ k ,
Q a b s = 2 P i n Re S ( E × H * ) n ^ d S = 2 R I i n L Re 0 2 π ( E × H * ) n ^ d θ ,
J N L B u l k = i 2 ω ε 0 β ( ε D , 1 1 ) 2 b [ ( a 1 ) ( E 1 · ) E 1 + 1 2 [ E 1 · E 1 ] ] ,
X ^ J N L S u r f a c e = i 2 ω ε 0 a b E 1 , X ( ) E 1 , Y ( ) β ( 1 ε D , 1 ) δ ( Y ) , Y ^ J N L S u r f a c e = i 2 ω ε 0 a b [ E 1 , Y ( ) ] 2 β 4 [ ( 1 ε D , 1 ) ( ε r , 1 + 3 ) ] δ ( Y ) ,
a = ω ω + i γ 0 ;     b = 2 ω 2 ω + i γ 0 ;     β = e 2 m ω 2 ,
(         ( 2 ω ) 2 c 2 I ¯ ¯ ) E 2 ( r ) = i ( 2 ω ) μ 0 [ i ( ε r , 2 1 ) 2 ω ε 0 E 2 + J N L B u l k + J N L S u r f a c e ] ,
Q n l ( 2 ω ) = L P ( 2 ω ) s c [ P i n ] 2 = 0 2 π q ( θ | 2 ω ) d θ ,

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