Abstract

We demonstrate that the nonlocal dielectric response of metal, comparing with the traditional local model, will significantly boost the third-order harmonic generation (THG) from gold nanowires of rough surface by a factor of several orders of magnitude. The enhancement is probably due to the penetrated field into the fine nanostructures on the metal surface in nonlocal model. The anisotropy THG efficiency versus the angle of incidence is also demonstrated due to the inhomogeneous surface morphology. The possible ways to verify the nonlocal effect to the THG are demonstrated. The results have a general significance in explaining the experimental observations.

© 2017 Optical Society of America

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2016 (3)

M. Mesch, B. Metzger, M. Hentschel, and H. Giessen, “Nonlinear plasmonic sensing,” Nano Lett. 16(5), 3155–3159 (2016).
[Crossref] [PubMed]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

T. Ning, Y. Huo, S. Jiang, J. Li, and B. Man, “Second harmonic generation from ultrathin Gold nanotubes,” Plasmonics 11(6), 1629–1636 (2016).
[Crossref]

2015 (11)

C. Lumdee, B. Yun, and P. G. Kik, “Effect of surface roughness on substrate-tuned gold nanoparticle gap plasmon resonances,” Nanoscale 7(9), 4250–4255 (2015).
[Crossref] [PubMed]

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

C. Ciracì, M. Scalora, and D. R. Smith, “Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures,” Phys. Rev. B 91(20), 205403 (2015).
[Crossref]

S. Shen, L. Meng, Y. Zhang, J. Han, Z. Ma, S. Hu, Y. He, J. Li, B. Ren, T. M. Shih, Z. Wang, Z. Yang, and Z. Tian, “Plasmon-enhanced second-harmonic generation nanorulers with ultrahigh sensitivities,” Nano Lett. 15(10), 6716–6721 (2015).
[Crossref] [PubMed]

R. Czaplicki, J. Mäkitalo, R. Siikanen, H. Husu, J. Lehtolahti, M. Kuittinen, and M. Kauranen, “Second-harmonic generation from metal nanoparticles: resonance enhancement versus particle geometry,” Nano Lett. 15(1), 530–534 (2015).
[Crossref] [PubMed]

L.-J. Black, P. R. Wiecha, Y. 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]

L. Leandro, R. Malureanu, N. Rozlosnik, and A. Lavrinenko, “Ultrathin, ultrasmooth gold layer on dielectrics without the use of additional metallic adhesion layers,” ACS Appl. Mater. Interfaces 7(10), 5797–5802 (2015).
[Crossref] [PubMed]

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

M. Scalora, M. A. Vincenti, D. De Ceglia, C. M. Cojocaru, M. Grande, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
[Crossref]

R. Chandrasekar, N. K. Emani, A. Lagutchev, V. M. Shalaev, C. Ciracì, D. R. Smith, and A. V. Kildishev, “Second harmonic generation with plasmonic metasurfaces: direct comparison of electric and magnetic resonances,” Opt. Mater. Express 5(11), 2682–2691 (2015).
[Crossref]

Z. Huang, A. Baron, S. Larouche, C. Argyropoulos, and D. R. Smith, “Optical bistability with film-coupled metasurfaces,” Opt. Lett. 40(23), 5638–5641 (2015).
[Crossref] [PubMed]

2014 (8)

G. Hajisalem, Q. Min, R. Gelfand, and R. Gordon, “Effect of surface roughness on self-assembled monolayer plasmonic ruler in nonlocal regime,” Opt. Express 22(8), 9604–9610 (2014).
[Crossref] [PubMed]

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] [PubMed]

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

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2014).
[Crossref]

J. B. Lassiter, X. Chen, X. Liu, C. Ciracì, T. B. Hoang, S. Larouche, S. H. Oh, M. H. Mikkelsen, and D. R. Smith, “Third-harmonic generation enhancement by film-coupled plasmonic stripe resonators,” ACS Photonics 1(11), 1212–1217 (2014).
[Crossref]

Y. Zhao, X. Liu, D. Y. Lei, and Y. Chai, “Effects of surface roughness of Ag thin films on surface-enhanced Raman spectroscopy of graphene: spatial nonlocality and physisorption strain,” Nanoscale 6(3), 1311–1317 (2014).
[Crossref] [PubMed]

G. Hajisalem, M. S. Nezami, and R. Gordon, “Probing the quantum tunneling limit of plasmonic enhancement by third harmonic generation,” Nano Lett. 14(11), 6651–6654 (2014).
[Crossref] [PubMed]

P. Zhang, J. Feist, A. Rubio, P. G. González, and F. J. G. Vidal, “Ab initio nanoplasmonics: The impact of atomic structure,” Phys. Rev. B 90(16), 161470 (2014).

2013 (4)

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]

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] [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]

X. Liu, A. Rose, E. Poutrina, C. Ciracì, S. Larouche, and D. R. Smith, “Surfaces, films, and multilayers for compact nonlinear plasmonics,” J. Opt. Soc. Am. B 30(11), 2999 (2013).
[Crossref]

2012 (8)

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, 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] [PubMed]

N. Vogel, J. Zieleniecki, and I. Köper, “As flat as it gets: ultrasmooth surfaces from template-stripping procedures,” Nanoscale 4(13), 3820–3832 (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]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

C. Ciracì, 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).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12(6), 3308–3314 (2012).
[Crossref] [PubMed]

T. Dong, X. Ma, and R. Mittra, “Optical response in subnanometer gaps due to nonlocal response and quantum tunneling,” Appl. Phys. Lett. 101(23), 233111 (2012).
[Crossref]

2011 (3)

2010 (2)

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010).
[Crossref] [PubMed]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82(3), 035423 (2010).
[Crossref]

2009 (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (1)

A. Halder and N. Ravishankar, “Ultrafine single-crystalline gold nanowire arrays by oriented attachment,” Adv. Mater. 19(14), 1854–1858 (2007).
[Crossref]

2006 (1)

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

2004 (1)

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

2002 (1)

A. Bietsch and B. Michel, “Size and grain-boundary effects of a gold nanowire measured by conducting atomic force microscopy,” Appl. Phys. Lett. 80(18), 3346–3348 (2002).
[Crossref]

1998 (1)

1981 (1)

C. K. Chen, A. R. B. De Castro, and Y. R. Shen, “Surface-Enchanced Second-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

1971 (1)

W. K. Burns and N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4(10), 4389–4402 (1971).
[Crossref]

Aizpurua, J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Anceau, C.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

Arbouet, A.

L.-J. Black, P. R. Wiecha, Y. 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]

Argyropoulos, C.

Asger Mortensen, N.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

Baron, A.

Baumberg, J. J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Bautista, G.

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]

G. Bautista, M. J. Huttunen, J. Mäkitalo, 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] [PubMed]

Bergman, D. J.

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[Crossref] [PubMed]

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S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
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N. Vogel, J. Zieleniecki, and I. Köper, “As flat as it gets: ultrasmooth surfaces from template-stripping procedures,” Nanoscale 4(13), 3820–3832 (2012).
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ACS Appl. Mater. Interfaces (1)

L. Leandro, R. Malureanu, N. Rozlosnik, and A. Lavrinenko, “Ultrathin, ultrasmooth gold layer on dielectrics without the use of additional metallic adhesion layers,” ACS Appl. Mater. Interfaces 7(10), 5797–5802 (2015).
[Crossref] [PubMed]

ACS Nano (1)

J. Butet and O. J. F. Martin, “Nonlinear plasmonic nanorulers,” ACS Nano 8(5), 4931–4939 (2014).
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ACS Photonics (2)

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Figures (6)

Fig. 1
Fig. 1 The schematic configuration of cross section of Au nanowires of radius 10 nm with an ideal surface (a) and rough surface within ± 0.5 nm fluctuation with the maximum number of knots 100 (b), 200 (c) and 300 (d). The configuration of light incidence is shown in the middle.
Fig. 2
Fig. 2 (a) The THG power from the perfect nanowire versus the value of β at the angle of incidence 0°. The inset shows the induced charge density beneath the metal surface under different values of β. (b) Schematic configuration of metal-air interface with a cut-line. (c) The induced charge density and (d) electric field along the cut line in (b). The local field distributions near the top-part of nanowire in local (e) and nonlocal (f) models of free-electron are calculated with the typical value of β = 1.26 × 106 m/s of Au. All calculations are conducted under the fundamental wavelength of 1064 nm and the incident electric field E0 = 1 × 107 V/m.
Fig. 3
Fig. 3 Calculated THG power from Au nanowires dependence on the angle of incidence under (a) local and (b) nonlocal model, respectively. The parameters: the fundamental wavelength of 1064 nm, the incident electric field E0 = 1 × 107 V/m and β = 1.26 × 106 m/s.
Fig. 4
Fig. 4 Extinction from Au nanowires calculated using the (a) local and (b) nonlocal model under the angle of incidence 0°. In order to compare the differences of the two models, the nanowire of ideal surface (Perfect) and rough surface with maximum knots 300 (Rough300) are simultaneously plotted in (c). Extinction spectra from the sample Rough300 versus angle of incidence 0° to 180° are plotted in (d) considering the nonlocal model. The insets in Figs. 4(a)-4(c) show the extinction around the surface plasmon resonance wavelength.
Fig. 5
Fig. 5 (a) The distributions of fundamental and THG electric field from Au nanowires of rough surface (Rough300) considering local and nonlocal model at angle of incidence 0° and 90°, respectively. In order to observe the local field distribution clearly, we enlarge the top-part of sample at the angle of incidence 0°. The parameters: the fundamental wavelength of 1064 nm, the incident electric field E0 = 1 × 107 V/m and β = 1.26 × 106 m/s.
Fig. 6
Fig. 6 The dependence of THG power on the angle of incidence from Au nanowires of roughness within ± 0.5 nm, ± 1 nm, ± 1.5 nm and ± 2 nm fluctuations with the fixed maximum number of knots 300 using (a) local and (b) nonlocal model, respectively. The electric field distribution on the top-part of Au nanowire of roughness within ± 1 nm at angle of incidence 0° using (c) local and (d) nonlocal model, respectively. The parameters: the fundamental wavelength of 1064 nm, the incident electric field E0 = 1 × 107 V/m and β = 1.26 × 106 m/s.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

×× E ω k ω 2 E ω = μ 0 ω 2 P ω
ε(ω)= ε ω p 2 ω 2 +iωγ
P ωf = ε 0 ω p 2 ω 2 +iωγ E ω
ε( k ω ,ω)= ε ω p 2 ω 2 +iωγ β 2 k ω 2
β 2 ( P ωf )+( ω 2 +iωγ) P ωf = n 0 e 2 m e * E ω
P ωb = j ε 0 ω p 2 ω 2 ω 0,j 2 +iω γ j E ω
×× E 3ω k 3ω 2 E 3ω = μ 0 (3ω) 2 P 3ω + μ 0 (3ω) 2 P NL
P i NL = ε 0 jkl χ ijkl (3) (3ω;ω,ω,ω) E ωj E ωk E ωl

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