Abstract

We theoretically investigate the properties of second-harmonic generation (SHG) in gold–silicon core–shell nanostructures. We first study a concentric structure. This structure exhibits strong electric field enhancement in the silicon shell due to the combined toroidal dipole mode and electric dipole mode. Efficient SHG can be obtained and the SHG signal is about 5 times as strong as that of the individual Si shell. Further calculations show that the contribution from a surface nonlinear susceptibility at the inner surface of the silicon shell dominates the SHG signal of the core–shell structure. The SHG as a function of wavelength is considered and it shows a resonance behavior. The cases of nonconcentric core–shell structures have also been considered. The SHG is further enhanced in this kind of configuration and the SHG signal can reach about 10 times as strong as that of the concentric case. Our results reveal the strong modification of the SHGs in dielectric nanostructures by using the metal–dielectric hybrid configurations, and could find applications in nanoscale nonlinear devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

Q. Zhao, Z.-J. Yang, and J. He, “Fano resonances in heterogeneous dimers ofvsilicon and gold nanospheres,” Front. Phys. 13(3), 137801 (2018).
[Crossref]

A. Rudenko, K. Ladutenko, S. Makarov, and T. E. Itina, “Photogenerated Free Carrier-Induced Symmetry Breaking in Spherical Silicon Nanoparticle,” Adv. Opt. Mat. 6, 1701153 (2018).
[Crossref]

2017 (9)

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal Magnetic Dipole Scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Z.-J. Yang, R. Jiang, X. Zhuo, Y.-M. Xie, J. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), 8100 (2017).
[Crossref] [PubMed]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref] [PubMed]

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

Z.-J. Yang, Q. Zhao, and J. He, “Boosting magnetic field enhancement with radiative couplings of magnetic modes in dielectric nanostructures,” Opt. Express 25(14), 15927–15937 (2017).
[Crossref] [PubMed]

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] [PubMed]

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref] [PubMed]

I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophotonics,” Nat. Photonics 11(5), 274–284 (2017).
[Crossref]

2016 (16)

W.-C. Zhai, T.-Z. Qiao, D.-J. Cai, W.-J. Wang, J.-D. Chen, Z.-H. Chen, and S.-D. Liu, “Anticrossing double Fano resonances generated in metallic/dielectric hybrid nanostructures using nonradiative anapole modes for enhanced nonlinear optical effects,” Opt. Express 24(24), 27858–27869 (2016).
[Crossref] [PubMed]

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
[Crossref]

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III-V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), 2472 (2016).
[Crossref] [PubMed]

C. Ma, J. Yan, P. Liu, Y. Wei, and G. Yang, “Second harmonic generation from an individual all-dielectric nanoparticle: resonance enhancement versus particle geometry,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(25), 6063–6069 (2016).
[Crossref]

D. Smirnova and Y. S. Kivshar, “Multipolar nonlinear nanophotonics,” Optica 3(11), 1241–1255 (2016).
[Crossref]

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
[Crossref] [PubMed]

X. Zambrana-Puyalto and N. Bonod, “Tailoring the chirality of light emission with spherical Si-based antennas,” Nanoscale 8(19), 10441–10452 (2016).
[Crossref] [PubMed]

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
[Crossref]

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref] [PubMed]

W. Fan, B. Yan, Z. Wang, and L. Wu, “Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies,” Sci. Adv. 2(8), e1600901 (2016).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

M. Cazzanelli and J. Schilling, “Second order optical nonlinearity in silicon by symmetry breaking,” Appl. Phys. Rev. 3(1), 011104 (2016).
[Crossref]

D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016).
[Crossref] [PubMed]

2015 (10)

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] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole‐induced transparency in core–shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
[Crossref] [PubMed]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
[Crossref]

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

2014 (6)

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
[Crossref] [PubMed]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

R. Sanatinia, S. Anand, and M. Swillo, “Modal Engineering of Second-Harmonic Generation in Single GaP Nanopillars,” Nano Lett. 14(9), 5376–5381 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

2013 (2)

Z.-J. Yang, Q.-Q. Wang, and H.-Q. Lin, “Tunable two types of Fano resonances in metal–dielectric core–shell nanoparticle clusters,” Appl. Phys. Lett. 103(11), 111115 (2013).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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2012 (1)

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband Unidirectional Scattering by Magneto-Electric Core-Shell Nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
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2011 (1)

2010 (1)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
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2005 (1)

B. Liu and H. C. Zeng, “Symmetric and asymmetric Ostwald ripening in the fabrication of homogeneous core-shell semiconductors,” Small 1(5), 566–571 (2005).
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2004 (1)

2001 (1)

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
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1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
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Aizpurua, J.

Albella, P.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
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M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (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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Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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Andreani, L. C.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
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Aouani, H.

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
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Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Arbouet, A.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
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P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
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Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Bakker, R. M.

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
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Baron, T.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
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P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
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Belov, P. A.

D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016).
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Bonod, N.

X. Zambrana-Puyalto and N. Bonod, “Tailoring the chirality of light emission with spherical Si-based antennas,” Nanoscale 8(19), 10441–10452 (2016).
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Boulesbaa, A.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
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Bragas, A. V.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
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Brener, I.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III-V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
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R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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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).
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Briggs, D. P.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), 2472 (2016).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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Buse, K.

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
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Butet, J.

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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Cai, D.-J.

Caldarola, M.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
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Capasso, F.

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), 8100 (2017).
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Cazzanelli, M.

M. Cazzanelli and J. Schilling, “Second order optical nonlinearity in silicon by symmetry breaking,” Appl. Phys. Rev. 3(1), 011104 (2016).
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Chantada, L.

Chen, H.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
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Chen, J.-D.

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
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Chen, Z.-H.

Chichkov, B. N.

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).
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Choi, D.-Y.

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
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Chong, K. E.

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
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Cortés, E.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
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Cui, Y.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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Dadap, J. I.

Decker, M.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
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M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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Deng, S.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
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Dominguez, J.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
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Duan, Z.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
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Ezhov, A. A.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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Falasconi, M.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
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Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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Fan, S.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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W. Fan, B. Yan, Z. Wang, and L. Wu, “Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies,” Sci. Adv. 2(8), e1600901 (2016).
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Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
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A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal Magnetic Dipole Scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
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J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
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Gao, Y.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
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García-Etxarri, A.

Geohegan, D.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

Giessen, H.

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
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Girard, C.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
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Gómez-Medina, R.

Gonzaga, L.

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
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Gregorkiewicz, T.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
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Grinblat, G.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
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Guo, R.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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Q. Zhao, Z.-J. Yang, and J. He, “Fano resonances in heterogeneous dimers ofvsilicon and gold nanospheres,” Front. Phys. 13(3), 137801 (2018).
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M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
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A. Rudenko, K. Ladutenko, S. Makarov, and T. E. Itina, “Photogenerated Free Carrier-Induced Symmetry Breaking in Spherical Silicon Nanoparticle,” Adv. Opt. Mat. 6, 1701153 (2018).
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S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
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Kallel, H.

P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
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Ke, Y.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
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Figures (5)

Fig. 1
Fig. 1 Linear optical responses. (a) Schematic of a core–shell nanostructure. The origin of the coordinate system is located at the center of the structure. (b) Extinction spectra of a core–shell structure, an Au sphere and an individual Si shell. The radius of the Au core is 50 nm. The outer radius of the Si shell is 73 nm. (c) Absorption and scattering spectra of the core–shell structure. The absorption of the individual Si shell and Au core are also shown (dashed lines). (d) Electric field enhancement of the core–shell structure on the y-z plane at λ = 800 nm. (e) Magnetic field enhancement of the core–shell structure on the x-z plane at λ = 800 nm. (f) Electric field enhancement of the individual Si nanoshell on the y-z plane at λ = 800 nm.
Fig. 2
Fig. 2 The SHG near field and far field properties of the core-shell structure and a solid Si sphere at λ = 400 nm. The radius of the solid Si sphere is 103 nm. The SH near fields (Log(|E(2ω)|/|E0|)) for core-shell (a), individual shell (b), core-shell with only χ Au,  ( 2 ) source (c) and solid sphere (d). The SH far field Efar(2ω) for core-shell (e), individual shell (f), core-shell with only χ Au,  ( 2 ) source (g) and solid sphere (h).
Fig. 3
Fig. 3 (a) The Efar(2ω) distributions on the y-z plane of the core–shell structure, which are calculated based on different nonlinear source terms. The angle 0 corresponds to the + y-axis direction. The results for the χ || || (2) , σ, γ have been multiplied by 5, respectively, for clearer demonstration. (b) The Efar(2ω) calculated with only the χ ( 2 ) source on the outer (black) and inner surface (red) of the core–shell structure. The results are shown on the same plane as that in (a). (c) The same contents as that in (b) for the individual Si nanoshell. The result of the inner surface has been multiplied by 10 for clearer demonstration.
Fig. 4
Fig. 4 (a) The maximal Efar(2ω) of the core–shell structure as a function of fundamental wavelength. The size of the structure is the same as above. The insets show the E(ω) / E0 at λ = 700 and 900 nm. The color bar for them is the same. (b) The resonant maximal Efar(2ω) of the core–shell structures with varying inner radius. The resonance for each case is kept at λ = 800 nm. The insets show the E(ω) / E0 of Rin = 45 and 55 nm.
Fig. 5
Fig. 5 SHG of nonconcentric core-shell nanostructures. (a) Schematic of a nonconcentric core-shell nanostructure excited by a plane wave. The size of the Au core and Si shell are the same as that in Fig. 1. (b) Absorption, scattering and extinction spectra of the core–shell structure. (c) Electric field enhancement of the core-shell structure on the y-z plane at λ = 820 nm. The distance between the centers of the core and shell is 15 nm. (d) The 3D Efar(2ω) distribution for the core-shell at λ = 410 nm. The distance between the centers of the core and shell is 15 nm. (e) The maximal SH far field as a function of the distance between the centers of the core and shell. The resonance wavelengths for the distances 0, 5, 10, 15 and 20 nm are λ = 400, 400, 405, 410, 410 nm, respectively, which are slightly different.

Equations (4)

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P surf (2ω) = P surf (2ω) + P bulk (2ω) ,
P surf (2ω) = ε 0 χ s (2) : E ( ω ) (r) E ( ω ) ( r )δ( r r s ),
P bulk (2ω) = ε 0 [β E ( ω ) ( E ( ω ) )+γ( E ( ω ) E ( ω ) )+ δ ( E ( ω ) ) E ( ω ) ],
P surf ( 2ω ) = ε 0 δ( r r s )[ χ ( 2 ) ( E r (ω) ) 2 r ^ + χ || || (2) ( E θ (ω) ) 2 r ^ + χ || || (2) ( E φ (ω) ) 2 r ^ + 2 χ |||| (2) E r (ω) E θ (ω) + θ ^ +2 χ |||| (2) E r (ω) E φ (ω) φ ^ ],

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