Abstract

We systematically study the contribution of local-field distribution to second-harmonic generation (SHG) in cross-shaped Ag nanohole arrays, which is usually covered by resonance enhancement effect. By increasing one arm-length of the centrosymmetric cross-shaped Ag nanohole, the local-field distribution varies from centrosymmetric to non-centrosymmetric, while the localized surface plasmon resonance peak is red-shifted to the wavelength of the pumping laser accordingly. Both experimental and stimulated results indicate that the contribution of the asymmetric local-field distribution to SHG is quantitatively separated from a strong resonance enhancement effect. It shows that the pure effective second-order nonlinear susceptibility increases as the asymmetric degree of local-field distribution increases, and the largest effective second-order nonlinear susceptibility is ~2.5 times to that in a centrosymmetric local-field distribution. Our results provide evidence for optimizing the design of nonlinear plasmonic nanoantennas and metasurfaces.

© 2017 Optical Society of America

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2016 (5)

S. D. Liu, E. S. Leong, G. C. Li, Y. 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] [PubMed]

J. M. Yi, V. Smirnov, X. Piao, J. Hong, H. Kollmann, M. Silies, W. Wang, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Suppression of radiative damping and enhancement of second harmonic generation in bull’s eye nanoresonators,” ACS Nano 10(1), 475–483 (2016).
[Crossref] [PubMed]

J. Butet and O. J. Martin, “Evaluation of the nonlinear response of plasmonic metasurfaces: Miller’s rule, nonlinear effective susceptibility method, and full-wave computation,” J. Opt. Soc. Am. B 33(2), A8–A15 (2016).
[Crossref]

C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “nonreciprocal phase shift and mode modulation in dynamic graphene waveguides,” J. Lightwave Technol. 34(16), 3877–3883 (2016).

S. Ke, B. Wang, C. Qin, H. Long, K. Wang, and P. Lu, “Exceptional points and asymmetric mode switching in plasmonic waveguides,” J. Lightwave Technol. 34(22), 5258–5262 (2016).
[Crossref]

2015 (9)

S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015).
[Crossref] [PubMed]

H. Linnenbank and S. Linden, “Second harmonic generation spectroscopy on second harmonic resonant plasmonic metamaterials,” Optica 2(8), 698–701 (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]

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

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

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (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]

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]

2014 (3)

X. Wen, G. Li, J. Zhang, Q. Zhang, B. Peng, L. M. Wong, S. Wang, and Q. Xiong, “Transparent free-standing metamaterials and their applications in surface-enhanced Raman scattering,” Nanoscale 6(1), 132–139 (2014).
[Crossref] [PubMed]

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]

K. Konishi, T. Higuchi, J. Li, J. Larsson, S. Ishii, and M. Kuwata-Gonokami, “Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry,” Phys. Rev. Lett. 112(13), 135502 (2014).
[Crossref] [PubMed]

2013 (4)

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

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

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

W. Liu, K. Wang, Z. Liu, G. Shen, and P. Lu, “Laterally emitted surface second harmonic generation in a single ZnTe nanowire,” Nano Lett. 13(9), 4224–4229 (2013).
[Crossref] [PubMed]

2012 (5)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

J. Berthelot, G. Bachelier, M. Song, P. Rai, G. Colas 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] [PubMed]

H. Aouani, M. Navarro-Cia, M. Rahmani, T. P. Sidiropoulos, M. 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).
[Crossref] [PubMed]

2011 (2)

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] [PubMed]

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

2010 (4)

J. F. Li, Y. F. Huang, Y. Ding, Z. L. Yang, S. B. Li, X. S. Zhou, F. R. Fan, W. Zhang, Z. Y. Zhou, D. Y. Wu, B. Ren, Z. L. Wang, and Z. Q. Tian, “Shell-isolated nanoparticle-enhanced Raman spectroscopy,” Nature 464(7287), 392–395 (2010).
[Crossref] [PubMed]

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

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

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

2008 (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

2007 (1)

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]

2006 (1)

J. A. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

P. Mühlschlegel, H. J. Eisler, O. J. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

2004 (2)

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004).
[Crossref]

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[Crossref]

1988 (1)

Aktsipetrov, O. A.

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

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Ansell, D.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

H. Aouani, M. Navarro-Cia, M. Rahmani, T. P. Sidiropoulos, M. 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).
[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]

Atwater, H. A.

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

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] [PubMed]

Bachelier, G.

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]

Baselli, M.

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

Berthelot, J.

Biagioni, P.

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

Black, L. J.

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]

Bonn, M.

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004).
[Crossref]

Bouhelier, A.

Brevet, P. F.

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Figures (8)

Fig. 1
Fig. 1 (a) Illustration of the SHG in the cross-shaped Ag nanohole arrays. Note that the sample is placed in the xy plane with a normal incident laser pumping along z-axis; (b) Geometrical parameters of a single cross-shaped Ag nanohole with the arm-direction along x- and y-axis. The bottom arm-length, l, increases from 55 nm to 115 nm at 10 nm, while the other three arm-length (l0 = 55 nm) and the arm-width (w = 50 nm) are kept as constants for all samples; (c) SEM images of four typical cross-shaped Ag nanohole arrays at l = 55 nm, 75 nm, 95 nm and 115 nm. The scale bar is 400 nm.
Fig. 2
Fig. 2 (a) Measured and (b) simulated transmission spectra for the cross-shaped Ag nanohole arrays at l = 105 nm under x- (red curve) and y-polarized (black curve) illuminations, respectively. The LSPR peaks for x- and y-polarizations are located at 790 nm and 680 nm respectively. The insets show corresponding SEM image of single cross-shaped Ag nanohole as well as a modeled profile. The scale bar is 100 nm; (c) Calculated local-field distribution (|E|) under the resonance conditions of x- and y-polarized illuminations by the finite-element solver COMSOL.
Fig. 3
Fig. 3 (a) and (b) Measured transmission spectra with the increased arm-length, l, from 55 nm to 115 nm (increased at 10 nm) under x- and y-polarized illuminations, respectively. The fundamental wavelength of the pumping laser (790 nm) is marked as a vertical dark red bar; (c) Contour plot of the calculated transmission spectra as a function of l under x-polarized light illumination; (d) Corresponding local-field distribution (|E|) of four typical samples at l = 55 nm, 75 nm, 95 nm and 115 nm (mentioned in Fig. 1(c)) under x-polarized illumination.
Fig. 4
Fig. 4 (a) Measured nonlinear emission spectra of the cross-shaped nanohole arrays with an increased arm-length, l, from 55 nm to 115 nm (increased at 10 nm) under x-polarized laser pumping; (b) The extracted WLC spectra by high-order polynomial-fitting from the results in Fig. 4(a); (c) Acquired SHG signals by deducting the fitting results of WLC signals from the nonlinear emission spectra. The inset shows the SHG intensity as a function of the arm-length l; (d) The normalized effective values of χ(2) as a function of the arm-length l according to the value of χ(2) at l = 55 nm.
Fig. 5
Fig. 5 Calculated (a) SH electric field intensity E(2ω), (b) fundamental field enhancement factor L(ω) and (c) effective second-order susceptibility χ(2) as a function of the arm-length l. They are normalized by the values of E(2ω), L(ω) and χ(2) at l = 55 nm, respectively.
Fig. 6
Fig. 6 (a) The schematic sketch of the experiment setup for micro-area transmission and SHG measurements on cross-shaped nanohole arrays. H1, H2: half-wave plates at 800 nm; H3: linear film polarizer; H4: Glan-laser polarizer; S: polarizing beam splitter; LP: 600-nm long pass filter; SP: 720-nm short pass filter. (b) The nonlinear emission spectra of cross-shaped nanohole array with a broad measurement range from 350 to 700 nm. (c) Measured SHG signal intensity ISHG as a function of the square of the pumping power P2. (d) Measured WLC signal intensity IWLC as a function of the fourth power of the pumping power P4.
Fig. 7
Fig. 7 (a) Experimental polar plot for the measured SHG intensity at l = 95 nm as a function of the polarization angle of the pumping laser, where 0°represents x-polarized pumping; (b) The polarimetric analysis of the SH emissions in the nanohole arrays at l = 95 nm under a fixed pumping polarization along x-axis.
Fig. 8
Fig. 8 Calculated fundamental mode and SH mode of three featured nanoholes with (a) l = 55 nm, (b) l = 95 nm and (c) l = 115 nm.

Equations (5)

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I SHG [ χ ( 2 ) L 2 ( ω ) E 2 ( ω ) ] 2 ,
I WLC [ L 4 ( ω ) E 4 ( ω ) ] 2 ,
χ ( 2 ) I SHG / ( I WLC ) 1 / 2 ,
E nl ( 2 ω ) χ nnn E n 2 ( ω ) E n ( 2 ω ) d S ,
E ( 2 ω ) = χ ( 2 ) L 2 ( ω ) E 2 ( ω ) .

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