Abstract

We demonstrate optical Second Harmonic Generation (SHG) in planar arrays of cylindrical Au nanoparticles arranged in periodic and deterministic aperiodic geometries. In order to understand the respective roles of near-field plasmonic coupling and long-range photonic interactions on the SHG signal, we systematically vary the interparticle separation from 60 nm to distances comparable to the incident pump wavelength. Using polarization-resolved measurements under femtosecond pumping, we demonstrate multipolar SHG signal largely tunable by the array geometry. Moreover, we show that the SHG signal intensity is maximized by arranging Au nanoparticles in aperiodic spiral arrays. The possibility to engineer multipolar SHG in planar arrays of metallic nanoparticles paves the way to the development of novel optical elements for nanophotonics, such as nonlinear optical sensors, compact frequency converters, optical mixers, and broadband harmonic generators on a chip.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
    [CrossRef]
  34. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
    [CrossRef] [PubMed]
  35. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
    [CrossRef] [PubMed]
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2012 (3)

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser. Photon. Rev. 6(2), 178–218 (2012).
[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] [PubMed]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, “Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals,” Opt. Express 20(3), 3015–3033 (2012).
[CrossRef] [PubMed]

2011 (5)

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alù, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28(2), 253–264 (2011).
[CrossRef]

S. F. Liew, H. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic bandedge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 23631–23642 (2011).
[CrossRef] [PubMed]

J. Trevino, H. Cao, and L. Dal Negro, “Circularly symmetric light scattering from nanoplasmonic spirals,” Nano Lett. 11(5), 2008–2016 (2011).
[CrossRef] [PubMed]

C. Forestiere, G. Iadarola, L. Dal Negro, and G. Miano, “Near field calculation based on the T-matrix method with discrete sources,” J. Quant. Spectrosc. Radiat. Transf. 112(14), 2384–2394 (2011).
[CrossRef]

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

2010 (1)

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

2008 (6)

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef] [PubMed]

E. Fort and S. Gresillon, “Surface enhanced fluorescence,” J. Phys. D Appl. Phys. 41(1), 013001 (2008).
[CrossRef]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
[CrossRef] [PubMed]

2007 (3)

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]

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
[CrossRef]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

2006 (1)

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

2005 (2)

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2001 (1)

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

1999 (2)

B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68(3), 419–423 (1999).
[CrossRef]

isJ. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
[CrossRef]

1995 (1)

1988 (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
[CrossRef]

1987 (1)

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[CrossRef] [PubMed]

1986 (2)

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]

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B Condens. Matter 33(12), 7923–7936 (1986).
[CrossRef] [PubMed]

1983 (1)

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27(4), 1965–1979 (1983).
[CrossRef]

1982 (1)

G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982).
[CrossRef]

1981 (1)

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[CrossRef]

Adam, P. M.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982).
[CrossRef]

Alù, A.

Aussenegg, F. R.

B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68(3), 419–423 (1999).
[CrossRef]

Awada, C.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Bachelier, G.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[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 nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

Bachelot, R.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

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]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Benichou, E.

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

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[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 nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

Bloemer, M. J.

Boriskina, S. V.

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser. Photon. Rev. 6(2), 178–218 (2012).
[CrossRef]

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef] [PubMed]

Bowie, C. T.

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
[CrossRef]

Boyd, G. T.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B Condens. Matter 33(12), 7923–7936 (1986).
[CrossRef] [PubMed]

Breit, M.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Brevet, P.-F.

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

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[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 nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

Bunton, P. H.

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

Butet, J.

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

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

Canfield, B. K.

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]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

Cao, H.

Chen, C. K.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27(4), 1965–1979 (1983).
[CrossRef]

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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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Dadap, J. I.

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J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, “Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals,” Opt. Express 20(3), 3015–3033 (2012).
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J. Trevino, H. Cao, and L. Dal Negro, “Circularly symmetric light scattering from nanoplasmonic spirals,” Nano Lett. 11(5), 2008–2016 (2011).
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A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
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R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
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L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Dallapiccola, R.

de Castro, A. R. B.

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
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de Ceglia, D.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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Dieringer, J. A.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
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Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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Eisenthal, K. B.

isJ. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
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Feldmann, J.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Feng, N.-N.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
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L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
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Ferrara, D.

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
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Flytzanis, C.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
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Forestiere, C.

C. Forestiere, G. Iadarola, L. Dal Negro, and G. Miano, “Near field calculation based on the T-matrix method with discrete sources,” J. Quant. Spectrosc. Radiat. Transf. 112(14), 2384–2394 (2011).
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E. Fort and S. Gresillon, “Surface enhanced fluorescence,” J. Phys. D Appl. Phys. 41(1), 013001 (2008).
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Gadenne, P.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Gopinath, A.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef] [PubMed]

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
[CrossRef] [PubMed]

L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Gresillon, S.

E. Fort and S. Gresillon, “Surface enhanced fluorescence,” J. Phys. D Appl. Phys. 41(1), 013001 (2008).
[CrossRef]

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[CrossRef] [PubMed]

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]

Hache, F.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
[CrossRef]

Haglund, E. A.

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

Haglund, R. F.

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
[CrossRef]

Heinz, T. F.

isJ. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27(4), 1965–1979 (1983).
[CrossRef]

Husu, H.

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]

Iadarola, G.

C. Forestiere, G. Iadarola, L. Dal Negro, and G. Miano, “Near field calculation based on the T-matrix method with discrete sources,” J. Quant. Spectrosc. Radiat. Transf. 112(14), 2384–2394 (2011).
[CrossRef]

Jefimovs, K.

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
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G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982).
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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).
[CrossRef] [PubMed]

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

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
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Jonin, Ch.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Jr, R. F.

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
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Kauranen, M.

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]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

Kessi, F.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Kostcheev, S.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Kreibig, U.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
[CrossRef]

Kuittinen, M.

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]

Kujala, S.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

Lamprecht, B.

B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68(3), 419–423 (1999).
[CrossRef]

Lascoux, N.

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

Laukkanen, J.

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]

Leitner, A.

B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68(3), 419–423 (1999).
[CrossRef]

Liew, S. F.

Lopez, R.

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
[CrossRef]

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

Mattiucci, N.

McMahon, M. D.

M. D. McMahon, D. Ferrara, C. T. Bowie, R. Lopez, and R. F. Haglund, “Second harmonic generation from resonantly excited arrays of gold nanoparticles,” Appl. Phys. B 87(2), 259–265 (2007).
[CrossRef]

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

Miano, G.

C. Forestiere, G. Iadarola, L. Dal Negro, and G. Miano, “Near field calculation based on the T-matrix method with discrete sources,” J. Quant. Spectrosc. Radiat. Transf. 112(14), 2384–2394 (2011).
[CrossRef]

Nappa, J.

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

Negro, L. D.

Noh, H.

Podolskiy, V. A.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Ray,

M. D. McMahon, R. Lopez, R. F. Jr, E. A. Haglund, Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73(4), 041401 (2006).
[CrossRef]

Reinhard, B. M.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef] [PubMed]

Revillod, G.

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

Ricard, D.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27(4), 1965–1979 (1983).
[CrossRef]

Rivoal, J. C.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Royer, P.

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[CrossRef]

Russier-Antoine, I.

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

C. Awada, F. Kessi, Ch. Jonin, P. M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, and P.-F. Brevet, “On- and off-axis second harmonic generation from an array of gold metallic nanocylinders,” J. Appl. Phys. 110(2), 023109 (2011).
[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 nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25(6), 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
[CrossRef]

Sarychev, A. K.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Shah, N. C.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
[CrossRef] [PubMed]

Shalaev, V. M.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Shan, J.

isJ. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
[CrossRef]

Shen, Y. R.

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[CrossRef] [PubMed]

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]

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B Condens. Matter 33(12), 7923–7936 (1986).
[CrossRef] [PubMed]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27(4), 1965–1979 (1983).
[CrossRef]

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[CrossRef]

Stellacci, F.

Stiles, P. L.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
[CrossRef] [PubMed]

Svirko, Y.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

Trevino, J.

Turunen, J.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

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

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

Vallius, T.

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A, Pure Appl. Opt. 7(2), S110–S117 (2005).
[CrossRef]

Van Duyne, R. P.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
[CrossRef] [PubMed]

Vincenti, M. A.

von Plessen, G.

M. Breit, V. A. Podolskiy, S. Gresillon, G. von Plessen, J. Feldmann, J. C. Rivoal, P. Gadenne, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of percolation-enhanced nonlinear light scattering from semicontinuous metal films,” Phys. Rev. B 64(12), 125106 (2001).
[CrossRef]

Xu, Y. L.

Yu, Z. H.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B Condens. Matter 33(12), 7923–7936 (1986).
[CrossRef] [PubMed]

Annu Rev Anal Chem (Palo Alto Calif) (1)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 601–626 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (2)

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Figures (6)

Fig. 1
Fig. 1

SEM micrographs of periodic (a), Fibonacci (b) and GA spiral (c) arrays of 200nm-diameter cylindrical gold nanoparticles with a particle separation of 60 nm.

Fig. 2
Fig. 2

Dark-field scattering intensity spectra for periodic (a), Fibonacci (b) and GA spiral (c) arrays with different interparticle separation L: 60 nm (red), 200 nm (green), 436 nm (blue), 523 nm (magenta), 567 nm (cyan), 653 nm (yellow). (d) Dark-field scattering intensity at λ = 780 nm for periodic (red squares), Fibonacci (green triangles) and GA Spiral (blue circles) arrays versus L.

Fig. 3
Fig. 3

(a) Schematics of the excitation-collection configuration; (b) spectra of SHG signals from arrays with interparticle separation of 60 nm, for several pump power densities W/Wmax: 1 (red), 0.821 (green), 0.654 (blue), 0.525 (magenta), 0.402 (cyan), 0.290 (yellow), 0.213 (black); (c) collected signals at pump wavelength (λ = 780 nm) and (d) SHG wavelength (λ = 390 nm) versus pump power intensity for periodic (red squares), Fibonacci (green triangles) and GA spiral (blue circles) arrays with interparticle separation of 60 nm. Scales are logarithmic.

Fig. 4
Fig. 4

Intensity of the radiated SHG parallel (a) and orthogonal (b) components for periodic (red) and spiral (blue) arrays; intensity of the radiated SHG parallel (c) and orthogonal (d) components for the Fibonacci array (green). Experimental data is with scattered symbols, least-squares fit is with continuous lines. The intensities in the plots of panel (a) have been reduced of the factor 11/4 for the sake of clearness.

Fig. 5
Fig. 5

(a) Intensity of the collected SHG signal as a function of the interparticle separation L, for periodic (red squares), Fibonacci (green triangles) and GA Spiral (blue circles) arrays; (a inset) Filling fraction of gold for periodic (red squares), Fibonacci (green triangles) and GA Spiral (blue circles) arrays; (b) correlation diagram between SHG and pump collected signals.

Fig. 6
Fig. 6

Near-field distribution at the pump frequency over periodic (a) and GA spiral (b) arrays with interparticle separation L = 60 nm. Near-field distribution at the fundamental frequency over periodic (c) and GA spiral (d) arrays with interparticle separation L = 611 nm. All the near-field maps are plotted in logscale.

Tables (1)

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Table 1 Fitting Parameters

Equations (2)

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I(γ)=a cos 4 (γ)+b cos 2 (γ) sin 2 (γ)+c sin 4 (γ)
I(γ)=a cos 4 (γ)+b cos 2 (γ) sin 2 (γ)+c sin 4 (γ)+d cos 3 (γ)sin(γ)+ecos(γ) sin 3 (γ).

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