Abstract

Surface second-harmonic generation (SHG) in plasmonic metal nanostructures provides a promising approach to design compact and ultrafast nonlinear nanophotonics devices. However, typical plasmonic nanostructures, such as those with tiny gaps that provide strong near-field-amplified nonlinear sources, often suffer from the cancellation of nonlinear fields in the gaps, which results in the so-called silenced SHG and consequently attenuates the overall nonlinear conversion efficiency. In this study, we propose and demonstrate that the silenced SHG in a gold split-ring resonator can be effectively restored by carefully tailoring its gap geometry to avoid the cancellation of nonlinear fields in the gap and simultaneously achieve both spatial and frequency mode matching between the magnetic and the electric dipolar resonances. As a result, the effective nonlinear sources in the gap can be dramatically amplified and the surface second-harmonic emissions can be efficiently coupled out, leading to an SHG intensity enhancement of 7 times compared to a conventional split-ring resonator. The overall SHG conversion efficiency can thus be enlarged to about 1.49 × 10−8 in the near-infrared excitation region. Importantly, the restored surface second-harmonic emission exhibits the scattering characteristics of an ideal electric dipole, which can be very useful for nonlinear far-field manipulation such as beam steering and holograms.

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

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2019 (3)

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium niobate nanocubes as linear and nonlinear ultraviolet Mie resonators,” ACS Photonics 6(2), 545–552 (2019).
[Crossref]

D. C. Hooper, C. Kuppe, D. Wang, W. Wang, J. Guan, T. W. Odom, and V. K. Valev, “Second harmonic spectroscopy of surface lattice resonances,” Nano Lett. 19(1), 165–172 (2019).
[Crossref]

C. Renaut, L. Lang, K. Frizyuk, M. Timofeeva, F. E. Komissarenko, I. S. Mukhin, D. Smirnova, F. Timpu, M. Petrov, Y. Kivshar, and R. Grange, “Reshaping the second-order polar response of hybrid metal-dielectric nanodimers,” Nano Lett. 19(2), 877–884 (2019).
[Crossref]

2018 (7)

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second harmonic light manipulation with vertical split ring resonators,” Adv. Mater. 31, 1806479 (2018).
[Crossref]

B. N. Carnio and A. Y. Elezzabi, “Second harmonic generation in metal-LiNbO3-metal and LiNbO3 hybrid-plasmonic waveguides,” Opt. Express 26(20), 26283–26291 (2018).
[Crossref]

G. Bautista, C. Dreser, X. R. Zang, D. P. Kern, M. Kauranen, and M. Fleischer, “Collective effects in second-harmonic generation from plasmonic oligomers,” Nano Lett. 18(4), 2571–2580 (2018).
[Crossref]

G. D. Bernasconi, J. Butet, and O. J. F. Martin, “Dynamics of second-harmonic generation in a plasmonic silver nanorod,” ACS Photonics 5(8), 3246–3254 (2018).
[Crossref]

R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less is more: Enhancement of second-harmonic generation from metasurfaces by reduced nanoparticle density,” Nano Lett. 18(12), 7709–7714 (2018).
[Crossref]

Q. Ai, L. L. Gui, D. Paone, B. Metzger, M. Mayer, K. Weber, A. Fery, and H. Giessen, “Ultranarrow second-harmonic resonances in hybrid plasmon-fiber cavities,” Nano Lett. 18(9), 5576–5582 (2018).
[Crossref]

A. Gomez-Tornero, C. Tserkezis, J. R. Moreno, L. E. Bausa, and M. O. Ramirez, “Field enhancement and spectral features of hexagonal necklaces of silver nanoparticles for enhanced nonlinear optical processes,” Opt. Express 26(17), 22394–22404 (2018).
[Crossref]

2017 (9)

S. V. Makarov, M. I. Petrov, U. Zywietz, V. Milichko, D. Zuev, N. Lopanitsyna, A. Kuksin, I. Mukhin, G. Zograf, E. Ubyivovk, D. A. Smirnova, S. Starikov, B. N. Chichkov, and Y. S. Kivshar, “Efficient second-harmonic generation in nanocrystalline silicon nanoparticles,” Nano Lett. 17(5), 3047–3053 (2017).
[Crossref]

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

D. J. Yang, S. J. Im, G. M. Pan, S. J. Ding, Z. J. Yang, Z. H. Hao, L. Zhou, and Q. Q. Wang, “Magnetic Fano resonance-induced second-harmonic generation enhancement in plasmonic metamolecule rings,” Nanoscale 9(18), 6068–6075 (2017).
[Crossref]

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
[Crossref]

G. X. Li, L. Wu, K. F. Li, S. M. Chen, C. Schlickriede, Z. J. Xu, S. Y. Huang, W. D. Li, Y. J. Liu, E. Y. B. Pun, T. Zentgraf, K. W. Cheah, Y. Luo, and S. Zhang, “Nonlinear metasurface for simultaneous control of spin and orbital angular momentum in second harmonic generation,” Nano Lett. 17(12), 7974–7979 (2017).
[Crossref]

F. Walter, G. X. Li, C. Meier, S. Zhang, and T. Zentgraf, “Ultrathin nonlinear metasurface for optical image encoding,” Nano Lett. 17(5), 3171–3175 (2017).
[Crossref]

F. Timpu, N. R. Hendricks, M. Petrov, S. B. Ni, C. Renaut, H. Wolf, L. Isa, Y. Kivshar, and R. Grange, “Enhanced second-harmonic generation from sequential capillarity-assisted particle assembly of hybrid nanodimers,” Nano Lett. 17(9), 5381–5388 (2017).
[Crossref]

Y. Li, M. Kang, J. J. Shi, K. Wu, S. P. Zhang, and H. Xu, “Transversely divergent second harmonic generation by surface plasmon polaritons on single metallic nanowires,” Nano Lett. 17(12), 7803–7808 (2017).
[Crossref]

J. Butet, G. D. Bernasconi, M. Petit, A. Bouhelier, C. Yan, O. J. F. Martin, B. Cluzel, and O. Demichel, “Revealing a mode interplay that controls second-harmonic radiation in gold nanoantennas,” ACS Photonics 4(11), 2923–2929 (2017).
[Crossref]

2016 (6)

G. Sartorello, N. Olivier, J. J. Zhang, W. S. Yue, D. J. Gosztola, G. P. Wiederrecht, G. Wurtz, and A. V. Zayats, “Ultrafast optical modulation of second- and third-harmonic generation from cut-disk-based metasurfaces,” ACS Photonics 3(8), 1517–1522 (2016).
[Crossref]

A. B. Evlyukhin, T. Fischer, C. Reinhardt, and B. N. Chichkov, “Optical theorem and multipole scattering of light by arbitrarily shaped nanoparticles,” Phys. Rev. B 94(20), 205434 (2016).
[Crossref]

W. M. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. T. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7(1), 11930 (2016).
[Crossref]

S. D. Liu, E. S. P. Leong, G. C. Li, Y. D. Hou, J. Deng, J. H. Teng, H. C. Ong, and D. Y. Lei, “Polarization-independent multiple Fano resonances in plasmonic nonamers for multimode-matching enhanced multiband second-harmonic generation,” ACS Nano 10(1), 1442–1453 (2016).
[Crossref]

S. Zhang, G. C. Li, Y. Q. Chen, X. P. Zhu, S. D. Liu, D. Y. Lei, and H. G. Duan, “Pronounced Fano resonance in single gold split nanodisks with 15 nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
[Crossref]

2015 (10)

G. X. Li, S. M. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alu, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref]

S. X. Shen, L. Y. Meng, Y. J. Zhang, J. B. Han, Z. W. Ma, S. Hu, Y. H. He, J. F. Li, B. Ren, T. M. Shih, Z. H. Wang, Z. L. Yang, and Z. Q. Tian, “Plasmon-enhanced second-harmonic generation nanorulers with ultrahigh sensitivities,” Nano Lett. 15(10), 6716–6721 (2015).
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J. Butet, P. F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
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D. Lehr, J. Reinhold, I. Thiele, H. Hartung, K. Dietrich, C. Menzel, T. Pertsch, E. B. Kley, and A. Tunnermann, “Enhancing second harmonic generation in gold nanoring resonators filled with lithium niobate,” Nano Lett. 15(2), 1025–1030 (2015).
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B. Metzger, L. L. Gui, J. Fuchs, D. Floess, M. Hentschel, and H. Giessen, “Strong enhancement of second harmonic emission by plasmonic resonances at the second harmonic wavelength,” Nano Lett. 15(6), 3917–3922 (2015).
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M. Celebrano, X. F. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
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L. J. Black, P. R. Wiecha, Y. D. Wang, C. H. de Groot, V. Paillard, C. Girard, O. L. Muskens, and A. Arbouet, “Tailoring second harmonic generation in single L-shaped plasmonic nanoantennas from the capacitive to conductive coupling regime,” ACS Photonics 2(11), 1592–1601 (2015).
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D. de Ceglia, M. A. Vincenti, C. de Angelis, A. Locatelli, J. W. Haus, and M. Scalora, “Role of antenna modes and field enhancement in second harmonic generation from dipole nanoantenna,” Opt. Express 23(2), 1715–1729 (2015).
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2014 (4)

R. Sanatinia, S. Anand, and M. Swillo, “Modal engineering of second-harmonic generation in single GaP nanopillars,” Nano Lett. 14(9), 5376–5381 (2014).
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G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14(11), 6660–6665 (2014).
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J. Butet and O. J. F. Martin, “Nonlinear plasmonic nanorulers,” ACS Nano 8(5), 4931–4939 (2014).
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J. Butet and O. J. F. Martin, “Refractive index sensing with Fano resonant plasmonic nanostructures: a symmetry based nonlinear approach,” Nanoscale 6(24), 15262–15270 (2014).
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2013 (2)

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
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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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2012 (10)

G. Bautista, M. J. Huttunen, J. Makitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
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H. Aouani, M. Navarro-Cia, M. Rahmani, T. P. H. Sidiropoulos, M. H. Hong, R. F. Oulton, and S. A. Maier, “Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light,” Nano Lett. 12(9), 4997–5002 (2012).
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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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M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
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C. Ciraci, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
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K. Thyagarajan, S. Rivier, A. Lovera, and O. J. F. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
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J. Berthelot, G. Bachelier, M. X. Song, P. Rai, G. C. des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
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A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J. F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20(1), 220–227 (2012).
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C. Ciraci, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86(11), 115451 (2012).
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2011 (1)

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
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2010 (3)

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 nanoparticle,” Phys. Rev. Lett. 105(7), 077401 (2010).
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G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
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2009 (1)

F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
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2007 (2)

T. Xu, X. Jiao, G. P. Zhang, and S. Blair, “Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement,” Opt. Express 15(21), 13894–13906 (2007).
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B. K. Canfield, H. Husu, J. Laukkanen, B. F. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
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2006 (1)

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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1984 (1)

O. A. Aktsipetrov, I. M. Baranova, E. D. Mishina, and A. V. Petukhov, “Lightning rod effect in surface-enhanced second harmonic generation,” JETP Lett. 40, 1012–1015 (1984).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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Ahorinta, R.

F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
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Ai, Q.

Q. Ai, L. L. Gui, D. Paone, B. Metzger, M. Mayer, K. Weber, A. Fery, and H. Giessen, “Ultranarrow second-harmonic resonances in hybrid plasmon-fiber cavities,” Nano Lett. 18(9), 5576–5582 (2018).
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Aktsipetrov, O. A.

O. A. Aktsipetrov, I. M. Baranova, E. D. Mishina, and A. V. Petukhov, “Lightning rod effect in surface-enhanced second harmonic generation,” JETP Lett. 40, 1012–1015 (1984).

Albers, W. M.

F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
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Alu, A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alu, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
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Anand, S.

R. Sanatinia, S. Anand, and M. Swillo, “Modal engineering of second-harmonic generation in single GaP nanopillars,” Nano Lett. 14(9), 5376–5381 (2014).
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Aouani, H.

H. Aouani, M. Navarro-Cia, M. Rahmani, T. P. H. Sidiropoulos, M. H. Hong, R. F. Oulton, and S. A. Maier, “Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light,” Nano Lett. 12(9), 4997–5002 (2012).
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Arbouet, A.

L. J. Black, P. R. Wiecha, Y. D. Wang, C. H. de Groot, V. Paillard, C. Girard, O. L. Muskens, and A. Arbouet, “Tailoring second harmonic generation in single L-shaped plasmonic nanoantennas from the capacitive to conductive coupling regime,” ACS Photonics 2(11), 1592–1601 (2015).
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Avayu, O.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
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S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
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Ayala-Orozco, C.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref]

Bachelier, G.

J. Berthelot, G. Bachelier, M. X. Song, P. Rai, G. C. des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
[Crossref]

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 nanoparticle,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref]

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]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

Bai, B. F.

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

Baranova, I. M.

O. A. Aktsipetrov, I. M. Baranova, E. D. Mishina, and A. V. Petukhov, “Lightning rod effect in surface-enhanced second harmonic generation,” JETP Lett. 40, 1012–1015 (1984).

Baselli, M.

M. Celebrano, X. F. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
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Bausa, L. E.

Bautista, G.

G. Bautista, C. Dreser, X. R. Zang, D. P. Kern, M. Kauranen, and M. Fleischer, “Collective effects in second-harmonic generation from plasmonic oligomers,” Nano Lett. 18(4), 2571–2580 (2018).
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G. Bautista, M. J. Huttunen, J. Makitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref]

Belkin, M. A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alu, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref]

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]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

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]

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 nanoparticle,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref]

Bernasconi, G. D.

G. D. Bernasconi, J. Butet, and O. J. F. Martin, “Dynamics of second-harmonic generation in a plasmonic silver nanorod,” ACS Photonics 5(8), 3246–3254 (2018).
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J. Butet, G. D. Bernasconi, M. Petit, A. Bouhelier, C. Yan, O. J. F. Martin, B. Cluzel, and O. Demichel, “Revealing a mode interplay that controls second-harmonic radiation in gold nanoantennas,” ACS Photonics 4(11), 2923–2929 (2017).
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Berthelot, J.

Biagioni, P.

M. Celebrano, X. F. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
[Crossref]

Black, L. J.

L. J. Black, P. R. Wiecha, Y. D. Wang, C. H. de Groot, V. Paillard, C. Girard, O. L. Muskens, and A. Arbouet, “Tailoring second harmonic generation in single L-shaped plasmonic nanoantennas from the capacitive to conductive coupling regime,” ACS Photonics 2(11), 1592–1601 (2015).
[Crossref]

Blair, S.

Bouhelier, A.

J. Butet, G. D. Bernasconi, M. Petit, A. Bouhelier, C. Yan, O. J. F. Martin, B. Cluzel, and O. Demichel, “Revealing a mode interplay that controls second-harmonic radiation in gold nanoantennas,” ACS Photonics 4(11), 2923–2929 (2017).
[Crossref]

J. Berthelot, G. Bachelier, M. X. Song, P. Rai, G. C. des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
[Crossref]

Bragas, A. V.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14(11), 6660–6665 (2014).
[Crossref]

Brevet, P. F.

J. Butet, P. F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref]

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]

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]

Brevet, P.-F.

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 nanoparticle,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
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Buscaglia, M. T.

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium niobate nanocubes as linear and nonlinear ultraviolet Mie resonators,” ACS Photonics 6(2), 545–552 (2019).
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Buscaglia, V.

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium niobate nanocubes as linear and nonlinear ultraviolet Mie resonators,” ACS Photonics 6(2), 545–552 (2019).
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Butet, J.

G. D. Bernasconi, J. Butet, and O. J. F. Martin, “Dynamics of second-harmonic generation in a plasmonic silver nanorod,” ACS Photonics 5(8), 3246–3254 (2018).
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R. Czaplicki, A. Kiviniemi, M. J. Huttunen, X. Zang, T. Stolt, I. Vartiainen, J. Butet, M. Kuittinen, O. J. F. Martin, and M. Kauranen, “Less is more: Enhancement of second-harmonic generation from metasurfaces by reduced nanoparticle density,” Nano Lett. 18(12), 7709–7714 (2018).
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J. Butet, G. D. Bernasconi, M. Petit, A. Bouhelier, C. Yan, O. J. F. Martin, B. Cluzel, and O. Demichel, “Revealing a mode interplay that controls second-harmonic radiation in gold nanoantennas,” ACS Photonics 4(11), 2923–2929 (2017).
[Crossref]

J. Butet, P. F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref]

J. Butet and O. J. F. Martin, “Nonlinear plasmonic nanorulers,” ACS Nano 8(5), 4931–4939 (2014).
[Crossref]

J. Butet and O. J. F. Martin, “Refractive index sensing with Fano resonant plasmonic nanostructures: a symmetry based nonlinear approach,” Nanoscale 6(24), 15262–15270 (2014).
[Crossref]

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation,” Nano Lett. 13(4), 1787–1792 (2013).
[Crossref]

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).
[Crossref]

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]

G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82(23), 235403 (2010).
[Crossref]

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]

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 nanoparticle,” Phys. Rev. Lett. 105(7), 077401 (2010).
[Crossref]

Caldarola, M.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14(11), 6660–6665 (2014).
[Crossref]

Canfield, B. K.

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

Celebrano, M.

M. Celebrano, X. F. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
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Cerullo, G.

M. Celebrano, X. F. Wu, M. Baselli, S. Grossmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duo, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10(5), 412–417 (2015).
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Chauvat, D.

Cheah, K. W.

G. X. Li, L. Wu, K. F. Li, S. M. Chen, C. Schlickriede, Z. J. Xu, S. Y. Huang, W. D. Li, Y. J. Liu, E. Y. B. Pun, T. Zentgraf, K. W. Cheah, Y. Luo, and S. Zhang, “Nonlinear metasurface for simultaneous control of spin and orbital angular momentum in second harmonic generation,” Nano Lett. 17(12), 7974–7979 (2017).
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G. X. Li, S. M. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
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Chen, J. W.

W. Y. Tsai, T. L. Chung, H. H. Hsiao, J. W. Chen, R. J. Lin, P. C. Wu, G. Sun, C. M. Wang, H. Misawa, and D. P. Tsai, “Second harmonic light manipulation with vertical split ring resonators,” Adv. Mater. 31, 1806479 (2018).
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Chen, S. M.

G. X. Li, L. Wu, K. F. Li, S. M. Chen, C. Schlickriede, Z. J. Xu, S. Y. Huang, W. D. Li, Y. J. Liu, E. Y. B. Pun, T. Zentgraf, K. W. Cheah, Y. Luo, and S. Zhang, “Nonlinear metasurface for simultaneous control of spin and orbital angular momentum in second harmonic generation,” Nano Lett. 17(12), 7974–7979 (2017).
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G. X. Li, S. M. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
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Chen, Y. Q.

S. Zhang, G. C. Li, Y. Q. Chen, X. P. Zhu, S. D. Liu, D. Y. Lei, and H. G. Duan, “Pronounced Fano resonance in single gold split nanodisks with 15 nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016).
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Figures (8)

Fig. 1.
Fig. 1. SHG in conventional SRRs of a rectangular gap, with an outer radius R = 80 nm and an inner radius r = 40 nm. The thickness of each SRR is 30 nm, and G in the inset of (a) denotes the SRR gap width. (a, b) Scattering (solid circular points) and absorption (open circular points) spectra for an SRR with G = 30 nm under (a) x- and (b) y-polarized incidence. The green dashed and the orange dotted lines represent, respectively, the electric dipole (p) and the magnetic dipole (m) contributions obtained from multipolar decomposition of the scattering spectra. The m contribution is scaled by a factor of 3 for better visualization. The corners of the SRR structure are rounded by 3 nm to avoid unphysical singularities. (c) SHG scattering spectrum under y-polarized incidence. (d-h) Electric near-field amplitude distribution profiles (the left panels), three-dimensional far-field radiation patterns (the middle panels), and cross-sectional views of far-field scattering patterns under x-polarized incidence at λinc = 900 nm (d), under y-polarized incidence at λinc = 1800 nm (e), and SHG electric near-field amplitude distribution profiles under y-polarized incidence at λinc = 1760 nm (f), 1800 nm (g), and 1840 nm (h). The SHG near-field amplitudes in (f-g) are scaled by a factor of 2. (i-k) Fundamental (i, j) and SH (k) scattering cross-sections as functions of gap width G and incident wavelength under x- (i) and y-polarized (j, k) incidence. The SH scattering cross sections in (k) are scaled by a factor of 3. The blue and the red dashed lines denote the spectral positions of the ED and the MD modes, respectively.
Fig. 2.
Fig. 2. Schematics of silenced SHG in a conventional SRR (a) and restoring the silenced SHG in the SRR of a V-shaped gap (b). (I): Surface charge distribution associated with the MD mode at the fundamental wavelength; (II) Overall and (III) effective nonlinear source distributions in the gap region; and (IV) Surface charge distribution associated with the ED mode at the SH wavelength.
Fig. 3.
Fig. 3. Similar results as Fig. 1 for tailored SRRs of a V-shaped gap. The gap geometry is characterized by the tip-to-tip separation s and the apex angle θ as sketched in the inset of (a). In (a-h), R = 80 nm, r = 40 nm, s = 20 nm, θ = 65°; in (i-k), R = 80 nm, r = 40 nm, s = 20 nm. In (a-c), the gray points show the spectra for a conventional SRR with G = 20 nm and other parameters the same as above.
Fig. 4.
Fig. 4. Tuning SHG in tailored SRRs by adjusting the tip-to-tip gap separation s. Here the SRRs have R = 80 nm, r = 40 nm, θ = 65°, and a thickness of 30 nm. (a-c) Fundamental (a, b) and SHG (c) scattering spectra for s-varied SRR under (a) x- and (b, c) y-polarized incidence. (d-f) Fundamental (d, e) and SHG scattering cross sections as functions of the tip-to-tip gap separation s and incident wavelength under x- (d) and y-polarized incidence (e, f). The blue and red dashed lines denote the spectral positions of the ED and MD modes, respectively.
Fig. 5.
Fig. 5. The amplitude of the electric field distributions along the dashed line of the conventional SRR for the MD mode, where the geometry parameters and excitation conditions are identical with that of Fig. 1(b).
Fig. 6.
Fig. 6. The amplitude of near-field distributions (the left panels), the three dimensional far-field scattering patterns (the middle panels), and the cross section views of the far-field scattering patterns with x-polarized incidence and λinc = 975 nm (a), y-polarized incidence and λinc = 1950 nm (b), and SHG of the SRR with y-polarized incidence and λinc = 1890 nm (c), 1950 nm (d), and 1980 nm (e), where the SHG near-field distributions have been scaled by a factor of 2, the gap width G = 20 nm, and the rest geometry parameters for the conventional SRR are identical with that of Fig. 1.
Fig. 7.
Fig. 7. The amplitude of the electric field distributions along the dashed line of the conventional SRR for the MD mode when the gap width G = 30 nm (the black line) and 20 nm (the red line), where the rest geometry parameters are identical with that of Fig. 1.
Fig. 8.
Fig. 8. (a) Near-field distributions of the MD mode for the modified SRRs with s = 3 nm and (b) 9 nm. (c) The comparison of the amplitude of the electric field distributions along the dashed line of the modified SRRs with different gap separations. (d-f) The corresponding SHG near-field distributions. The rest geometry parameters of the SRRs are identical with that of Fig. 3.

Equations (9)

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S N L = e m e E 1 ( P 1 ) + i ω e m e P 1 × B 1 ω 2 n 0 e [ ( P 1 ) P 1 + ( P 1 ) P 1 ]
P 2 S = 1 2 n 0 e [ ( P 1 ) P 1 + ω 2 ω + i γ ( P 1 ) P 1 ]
K N L = i ω n 0 e [ t ^ ( P 1 P 1 ) + n ^ 1 2 3 ω + i γ 2 ω + i γ ( P 1 ) 2 ]
P = ε 0 ( ε p ε d ) E
P ( r ) = P ( r ) δ ( r r ) d r
p = P ( r ) d r
T = i ω 10 { 2 r 2 P ( r ) [ r P ( r ) ] r } d r
m = i ω 2 [ r × P ( r ) ] d r
P sca = k 0 4 12 π ε 0 2 v d μ 0 | p + i k d v d T | 2 + k 0 4 ε d 12 π ε 0 v d | m | 2

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