Abstract

We propose a strategy for active control of second harmonic generation (SHG) in a plasmonic Fano structure by electrically doping its underlying monolayer graphene. A detailed theoretical model for the proposed scheme is developed and numerical simulations are carried out to demonstrate the operation. Specifically, we show that a merely 30 meV change in graphene Fermi level can result in 45 times increase in SHG peak intensity, accompanied by a resonance wavelength shift spanning 220 nm. Further analysis uncovers that such tunability in SHG arises from the Fermi-level-modulated graphene permittivity, the real and imaginary parts of which dominate the resonance wavelength and the intensity of SHG, respectively.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
  2. 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]
  3. M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
    [Crossref] [PubMed]
  4. 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] [PubMed]
  5. S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
    [Crossref] [PubMed]
  6. Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
    [Crossref] [PubMed]
  7. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
    [Crossref] [PubMed]
  8. V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
    [Crossref] [PubMed]
  9. G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
    [Crossref] [PubMed]
  10. W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
    [Crossref] [PubMed]
  11. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
    [Crossref] [PubMed]
  12. T. D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7(3), 557–564 (2007).
    [Crossref] [PubMed]
  13. 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] [PubMed]
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    [PubMed]
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    [Crossref] [PubMed]
  17. H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
    [Crossref] [PubMed]
  18. B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
    [PubMed]
  19. S. Tang, D. J. Cho, H. Xu, W. Wu, Y. R. Shen, and L. Zhou, “Nonlinear responses in optical metamaterials: theory and experiment,” Opt. Express 19(19), 18283–18293 (2011).
    [Crossref] [PubMed]
  20. L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
    [Crossref] [PubMed]
  21. G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
    [Crossref] [PubMed]
  22. J. J. Zhang, S. S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18(16), 17187–17192 (2010).
    [Crossref] [PubMed]
  23. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
    [Crossref] [PubMed]
  24. A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
    [Crossref] [PubMed]
  25. R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
    [Crossref]
  26. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
    [Crossref] [PubMed]
  27. N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
    [Crossref] [PubMed]
  28. F. Xiao, W. Zhu, M. Premaratne, and J. Zhao, “Controlling Fano resonance of ring/crescent-ring plasmonic nanostructure with Bessel beam,” Opt. Express 22(2), 2132–2140 (2014).
    [Crossref] [PubMed]
  29. E. J. Osley, C. G. Biris, P. G. Thompson, R. R. F. Jahromi, P. A. Warburton, and N. C. Panoiu, “Fano resonance resulting from a tunable interaction between molecular vibrational modes and a double continuum of a plasmonic metamolecule,” Phys. Rev. Lett. 110(8), 087402 (2013).
    [Crossref] [PubMed]
  30. J. Sancho-Parramon and S. Bosch, “Dark modes and Fano resonances in plasmonic clusters excited by cylindrical vector beams,” ACS Nano 6(9), 8415–8423 (2012).
    [Crossref] [PubMed]
  31. X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
    [Crossref] [PubMed]
  32. J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
    [Crossref] [PubMed]
  33. S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
    [Crossref] [PubMed]
  34. N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
    [Crossref] [PubMed]
  35. Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
    [Crossref] [PubMed]
  36. W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
    [Crossref]
  37. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
    [Crossref] [PubMed]
  38. D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96(7), 3626–3634 (2004).
    [Crossref]
  39. Y. Zeng, W. Hoyer, J. 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]

2014 (3)

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
[Crossref] [PubMed]

F. Xiao, W. Zhu, M. Premaratne, and J. Zhao, “Controlling Fano resonance of ring/crescent-ring plasmonic nanostructure with Bessel beam,” Opt. Express 22(2), 2132–2140 (2014).
[Crossref] [PubMed]

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
[Crossref] [PubMed]

2013 (11)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
[Crossref]

E. J. Osley, C. G. Biris, P. G. Thompson, R. R. F. Jahromi, P. A. Warburton, and N. C. Panoiu, “Fano resonance resulting from a tunable interaction between molecular vibrational modes and a double continuum of a plasmonic metamolecule,” Phys. Rev. Lett. 110(8), 087402 (2013).
[Crossref] [PubMed]

X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
[Crossref] [PubMed]

G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
[Crossref] [PubMed]

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
[Crossref] [PubMed]

Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
[Crossref] [PubMed]

K. Thyagarajan, J. Butet, and O. J. F. Martin, “Augmenting second harmonic generation using Fano resonances in plasmonic systems,” Nano Lett. 13(4), 1847–1851 (2013).
[PubMed]

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

2012 (5)

A. Capretti, G. F. Walsh, S. Minissale, J. Trevino, C. Forestiere, G. Miano, and L. Dal Negro, “Multipolar second harmonic generation from planar arrays of Au nanoparticles,” Opt. Express 20(14), 15797–15806 (2012).
[Crossref] [PubMed]

H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

J. Sancho-Parramon and S. Bosch, “Dark modes and Fano resonances in plasmonic clusters excited by cylindrical vector beams,” ACS Nano 6(9), 8415–8423 (2012).
[Crossref] [PubMed]

2011 (7)

R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
[Crossref] [PubMed]

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
[Crossref] [PubMed]

S. Tang, D. J. Cho, H. Xu, W. Wu, Y. R. Shen, and L. Zhou, “Nonlinear responses in optical metamaterials: theory and experiment,” Opt. Express 19(19), 18283–18293 (2011).
[Crossref] [PubMed]

S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
[Crossref] [PubMed]

W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[Crossref] [PubMed]

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

2010 (6)

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] [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]

J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref] [PubMed]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[Crossref] [PubMed]

J. J. Zhang, S. S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18(16), 17187–17192 (2010).
[Crossref] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

2009 (2)

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] [PubMed]

Y. Zeng, W. Hoyer, J. 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]

2007 (2)

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]

T. D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7(3), 557–564 (2007).
[Crossref] [PubMed]

2006 (1)

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

2004 (1)

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96(7), 3626–3634 (2004).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Aktsipetrov, O. A.

Alici, K. B.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

Al-Naib, I. A. I.

R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Ameloot, M.

Arju, N.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

Bachelier, G.

J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (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]

Bai, B.

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]

Bao, K.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
[Crossref] [PubMed]

Bartal, G.

S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
[Crossref] [PubMed]

Bautista, G.

Benichou, E.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (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]

Biris, C. G.

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X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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J. Sancho-Parramon and S. Bosch, “Dark modes and Fano resonances in plasmonic clusters excited by cylindrical vector beams,” ACS Nano 6(9), 8415–8423 (2012).
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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, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
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J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
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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. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
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L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
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K. Thyagarajan, J. Butet, and O. J. F. Martin, “Augmenting second harmonic generation using Fano resonances in plasmonic systems,” Nano Lett. 13(4), 1847–1851 (2013).
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J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
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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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J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
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L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
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W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
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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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J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
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Castro-Lopez, M.

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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
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S. Tang, D. J. Cho, H. Xu, W. Wu, Y. R. Shen, and L. Zhou, “Nonlinear responses in optical metamaterials: theory and experiment,” Opt. Express 19(19), 18283–18293 (2011).
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R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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Cui, Y. H.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
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G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
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Dragnea, B.

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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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T. D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7(3), 557–564 (2007).
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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
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J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
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Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
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Fozdar, D. Y.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
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A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Geng, B. S.

J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
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Gillijns, W.

Halas, N. J.

Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
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S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
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J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

Hanke, T.

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] [PubMed]

Hansen, O.

X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
[Crossref] [PubMed]

Hao, Y. F.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

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Y. Zeng, W. Hoyer, J. 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).
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N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
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H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

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]

Huttunen, M. J.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Jahromi, R. R. F.

E. J. Osley, C. G. Biris, P. G. Thompson, R. R. F. Jahromi, P. A. Warburton, and N. C. Panoiu, “Fano resonance resulting from a tunable interaction between molecular vibrational modes and a double continuum of a plasmonic metamolecule,” Phys. Rev. Lett. 110(8), 087402 (2013).
[Crossref] [PubMed]

Jeppesen, C.

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Jonin, C.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[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]

J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref] [PubMed]

Kang, L.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
[Crossref] [PubMed]

Kats, M. A.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Kauranen, M.

G. Bautista, M. J. Huttunen, J. M. Kontio, J. Simonen, and M. Kauranen, “Third- and second-harmonic generation microscopy of individual metal nanocones using cylindrical vector beams,” Opt. Express 21(19), 21918–21923 (2013).
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H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

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]

Khanikaev, A. B.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

Kholmanov, I.

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

Kildishev, A. V.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
[Crossref] [PubMed]

Kim, J.

J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

Kim, K.

J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

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. 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]

Kong, J.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Kontio, J. M.

Krause, D.

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96(7), 3626–3634 (2004).
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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] [PubMed]

Kristensen, A.

Kuittinen, M.

H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

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]

Kundu, J.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

Lagae, L.

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
[Crossref] [PubMed]

Lan, S. F.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
[Crossref] [PubMed]

Lascoux, N.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P. F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Lassiter, J. B.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

Laukkanen, J.

H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

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]

Lehtolahti, J.

H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

Leitenstorfer, A.

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] [PubMed]

Li, Z. Y.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Linden, S.

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

Liu, J. J.

Y. Zeng, W. Hoyer, J. 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]

Liu, R. J.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
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S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
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J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
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Zhang, J. J.

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S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
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S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
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R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
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Zhang, X.

S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
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Zhang, Y.

Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
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Zhao, J.

Zhao, J. M.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
[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).
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Zhen, Y. R.

Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
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Zhou, L.

Zhu, W.

F. Xiao, W. Zhu, M. Premaratne, and J. Zhao, “Controlling Fano resonance of ring/crescent-ring plasmonic nanostructure with Bessel beam,” Opt. Express 22(2), 2132–2140 (2014).
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W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
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X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
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Zi, J.

X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
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ACS Nano (2)

J. Sancho-Parramon and S. Bosch, “Dark modes and Fano resonances in plasmonic clusters excited by cylindrical vector beams,” ACS Nano 6(9), 8415–8423 (2012).
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A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
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Appl. Phys. Lett. (2)

R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
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W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
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Nano Lett. (16)

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011).
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J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
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N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
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G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
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X. Zhu, L. Shi, M. S. Schmidt, A. Boisen, O. Hansen, J. Zi, S. Xiao, and N. A. Mortensen, “Enhanced light-matter interactions in graphene-covered gold nanovoid arrays,” Nano Lett. 13(10), 4690–4696 (2013).
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J. Kim, H. Son, D. J. Cho, B. S. Geng, W. Regan, S. F. Shi, K. Kim, A. Zettl, Y. R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
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S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. F. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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K. Thyagarajan, J. Butet, and O. J. F. Martin, “Augmenting second harmonic generation using Fano resonances in plasmonic systems,” Nano Lett. 13(4), 1847–1851 (2013).
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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. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
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Nat Commun (1)

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat Commun 5, 4680 (2014).
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Nat. Mater. (1)

S. Palomba, S. Zhang, Y. Park, G. Bartal, X. B. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. 11(1), 34–38 (2011).
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Opt. Express (6)

Phys. Rev. B (1)

Y. Zeng, W. Hoyer, J. 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).
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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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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).
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J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
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Proc. Natl. Acad. Sci. U.S.A. (1)

Y. Zhang, F. Wen, Y. R. Zhen, P. Nordlander, and N. J. Halas, “Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9215–9219 (2013).
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Sci Rep (1)

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of shape resonance in second-harmonic generation from metallic nanohole arrays,” Sci Rep 3, 2358 (2013).
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Figures (4)

Fig. 1
Fig. 1 (a) Schematic view of the monolayer graphene-based dolmen structure. The geometry parameters l1, l2, s, w, and g are 2, 1.4, 1, 0.2, and 0.1 μm, respectively. The periods in both x and y direction are 2.3 μm. (b) Illustration of Fano resonance as an interference between a narrow state of dark mode and a broad state of bright mode. (c) Extinction spectra of the dolmen structure excited by plane waves with horizontal (red) and vertical (blue) polarization as indicated in (d). (d) Normalized surface charge distributions of the dipolar mode and Fano extinction dip as labeled in (c).
Fig. 2
Fig. 2 (a) Graphene permittivities at Fermi levels of 75, 80, 85, 90, and 95 meV, where the upper and lower panels are the real and imaginary parts of the permittivity, respectively. (b) Extinction spectra of the dolmen structure as a dependence of graphene Fermi level. (c) Representative extinction spectra of the dolmen structure with graphene Fermi levels EF = 70, 80 and 95 meV, where the dots and lines correspond to the simulation and fitting results, respectively. (d) Resonance wavelengths of dark (upper panel) and bright modes (lower panel) versus graphene Fermi level. Here, the dots and triangles are the resonance wavelengths of the modes and the corresponding real parts of graphene permittivity, respectively.
Fig. 3
Fig. 3 (a) Spectra of SHG (blue solid curve) and local field intensity (red dashed curve) of the dolmen structure excited by a vertical polarization beam at graphene Fermi level EF = 0 meV. (b) Polarization of the SHG emission represented as a polar diagram at the wavelength indicated in (a). (c) Normalized SHG intensity (upper panels) and the 4th power of fundamental field distributions (lower panels) at the dolmen and air interface with the excitation wavelength as labeled in (a).
Fig. 4
Fig. 4 (a) SHG spectra of the dolmen structure as a function of graphene Fermi level. (b) Representative SHG spectra at the graphene Fermi levels EF = 70, 80 and 95 meV. The dots and lines are the simulation and fitting results, respectively. (c) Dependence of the resonance wavelength of SHG on graphene Fermi level. The upper and lower panels correspond to the SHG peaks of the dark and bright modes, respectively. (d) ISHG (top panel), integral |Eloc|4 (middle panel), and imaginary part of graphene permittivity (bottom panel) versus the graphene Fermi level at the fundamental wavelength for maximum SHG.

Equations (7)

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ε g ' ( ω )=1+ e 2 8πω ε 0 d ln ( ω+2| E F | ) 2 + Γ 2 ( ω2| E F | ) 2 + Γ 2 e 2 π ε 0 d | E F | ( ω ) 2 + ( 1/τ ) 2 ε g '' ( ω )= e 2 4ω ε 0 d [ 1+ 1 π ( tan 1 ω2| E F | Γ tan 1 ω+2| E F | Γ ) ] + e 2 πτω ε 0 d | E F | ( ω ) 2 + ( 1/τ ) 2 .
d 2 x d d t 2 + γ d d x d dt + ω d 2 x d +g x b = 1 2 ( η d d 3 x d d t 3 + η b d 3 x b d t 3 )+ η d E d 2 x b d t 2 + γ b d x b dt + ω b 2 x b +g x d = 1 2 ( η d d 3 x d d t 3 + η b d 3 x b d t 3 )+ η b E .
C d ( ω )= η b E 0 ( g+ i 2 η b ω 3 ) η d E 0 ( ω 2 i γ b ω ω b 2 i 2 η b ω 3 ) ( ω 2 i γ d ω ω d 2 i 2 η d ω 3 )( ω 2 i γ b ω ω b 2 i 2 η b ω 3 )( g+ i 2 η d ω 3 )( g+ i 2 η b ω 3 ) C b ( ω )= ( g+ i 2 η d ω 3 ) C d ( ω ) η b E 0 ω 2 i γ b ω ω b 2 i 2 η b ω 3 .
Δ λ R λ R = 1 2 E d( b ) | Δ ε g | E d( b ) E d( b ) | ε g | E d( b ) ,
p ( 2 ) ( r,2ω )= χ s ( 2 ) :E( r,ω )E( r,ω ),
I SHG ( ω )= s χ s ( 2 ) :E( x,y,ω )E( x,y,ω ) dxdy.
I SHG ( ω )= | A+ B e i φ 1 ω ω 1 +i ξ 1 + C e i φ 2 ω ω 2 +i ξ 2 | 4 .

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