Abstract

The coupling between metallic nanostructures is a common and easy way to control the optical properties of plasmonic systems. Even though the coupling between plasmonic oscillators has been widely studied in the linear regime, its influence on the nonlinear optical response of metallic nanostructures has been sparsely considered. Using a surface integral equation method, we investigate the second order nonlinear optical response of plasmonic metamolecules supporting Fano resonances revealing that the typical lineshape of Fano resonances is also clearly observable in the nonlinear regime. The physical mechanisms leading to nonlinear Fano resonances are revealed by the coupled oscillator model and the symmetry subgroup decomposition. It is found that the origin of the nonlinear scattered wave, i. e. the active plasmonic oscillator, can be selectively chosen. Furthermore, interferences between nonlinear emissions are clearly observed in specific configurations. The results presented in this article pave the way for the design of efficient nonlinear plasmonic metamolecules with controlled nonlinear radiation.

© 2014 Optical Society of America

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2014 (4)

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

Y. Zhang, Y.-R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat Commun 5, 4424 (2014).
[PubMed]

B. Metzger, T. Schumacher, M. Hentschel, M. Lippitz, and H. Giessen, “Third harmonic generation in complex plasmonic Fano structures,” ACS Photon. 1(6), 471–476 (2014).
[Crossref]

J. Butet, S. Dutta-Gupta, and O. J. F. Martin, “Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties,” Phys. Rev. B 89(24), 245449 (2014).
[Crossref]

2013 (7)

B. Hopkins, A. N. Poddubny, A. E. Miroshnichenko, and Y. S. Kivshar, “Revisiting the physics of Fano resonances for nanoparticle oligomers,” Phys. Rev. A 88(5), 053819 (2013).
[Crossref]

J. Butet, B. Gallinet, K. Thyagarajan, and O. J. F. Martin, “Second harmonic generation from periodic arrays of arbitrary shape plasmonic nanostructures: A surface integral approach,” J. Opt. Soc. Am. B 30(11), 2970–2979 (2013).
[Crossref]

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

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]

G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
[Crossref] [PubMed]

M. Rahmani, B. Luk’yanchuck, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Phot. Rev. 7(3), 329–349 (2013).
[Crossref]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

2012 (11)

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

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic nanoclusters: Near-Field properties of the Fano resonance interrogated with Sers,” Nano Lett. 12(3), 1660–1667 (2012).
[Crossref] [PubMed]

M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (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]

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Y. H. Fu, J. B. Zhang, Y. F. Yu, and B. Luk’yanchuk, “Generating and manipulating higher order Fano resonances in dual-disk ring plasmonic nanostructures,” ACS Nano 6(6), 5130–5137 (2012).
[Crossref] [PubMed]

A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012).
[Crossref] [PubMed]

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]

M. Hentschel, T. Utikal, H. Giessen, and M. Lippitz, “Quantitative modeling of the third harmonic emission spectrum of plasmonic nanoantennas,” Nano Lett. 12(7), 3778–3782 (2012).
[Crossref] [PubMed]

M. Navarro-Cia and S. A. Maier, “Broad-band near-infrared plasmonic nanoantennas for higher harmonic generation,” ACS Nano 6(4), 3537–3544 (2012).
[Crossref] [PubMed]

V. K. Valev, “Characterization of nanostructured plasmonic surfaces with second harmonic generation,” Langmuir 28(44), 15454–15471 (2012).
[Crossref] [PubMed]

2011 (12)

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19(23), 23386–23399 (2011).
[Crossref] [PubMed]

H. Liu, G. X. Li, K. F. Li, S. M. Chen, S. N. Zhu, C. T. Chan, and K. W. Cheah, “Linear and nonlinear Fano resonance on two-dimensional magnetic metamaterials,” Phys. Rev. B 84(23), 235437 (2011).
[Crossref]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).
[Crossref] [PubMed]

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, K. C. Toussaint, and C. Toussaint, “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011).
[Crossref] [PubMed]

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]

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: The role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

B. Gallinet and O. J. F. Martin, “Ab-initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011).
[Crossref]

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano 5(11), 8999–9008 (2011).
[Crossref] [PubMed]

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: A parameter-free modeling approach,” Nano Lett. 11(7), 2835–2840 (2011).
[Crossref] [PubMed]

B. Gallinet and O. J. F. Martin, “Relation between near-field and far-field properties of plasmonic Fano resonances,” Opt. Express 19(22), 22167–22175 (2011).
[Crossref] [PubMed]

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett. 11(2), 391–397 (2011).
[Crossref] [PubMed]

2010 (9)

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [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]

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010).
[Crossref] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010).
[Crossref] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

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

2009 (6)

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

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulation of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26(4), 732–740 (2009).
[Crossref]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[Crossref] [PubMed]

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652 (2009).
[Crossref] [PubMed]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Background-free third harmonic imaging of gold nanorods,” Nano Lett. 9(12), 4093–4097 (2009).
[Crossref] [PubMed]

2008 (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

H. Fischer and O. J. F. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16(12), 9144–9154 (2008).
[Crossref] [PubMed]

2007 (1)

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98(2), 026104 (2007).
[Crossref] [PubMed]

2005 (2)

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036626 (2005).
[Crossref] [PubMed]

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005).
[Crossref] [PubMed]

2004 (1)

A. R. P. Rau, “Perspectives on the Fano resonance formula,” Phys. Scr. 69(1), C10–C13 (2004).
[Crossref]

1999 (2)

S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. C 103(16), 3073–3077 (1999).
[Crossref]

J. 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]

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,” App. Phys. A 47(4), 347–357 (1988).
[Crossref]

1980 (1)

J. E. Sipe, C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

1972 (1)

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

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

1935 (1)

U. Fano, “Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco,” Nuovo Cim. 12(3), 154–161 (1935).
[Crossref]

Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).
[Crossref] [PubMed]

Ahorinta, R.

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

Albers, W. M.

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

Alivisatos, A. P.

M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010).
[Crossref] [PubMed]

Altug, H.

A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012).
[Crossref] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).
[Crossref] [PubMed]

Ambekar, R.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, K. C. Toussaint, and C. Toussaint, “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011).
[Crossref] [PubMed]

Amrania, H.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: A parameter-free modeling approach,” Nano Lett. 11(7), 2835–2840 (2011).
[Crossref] [PubMed]

Arju, N.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).
[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.

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

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [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]

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[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]

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

J. Butet, 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]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Biagioni, P.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

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]

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

J. Butet, 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]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Brida, D.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Brinks, D.

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

Butet, J.

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

J. Butet, S. Dutta-Gupta, and O. J. F. Martin, “Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties,” Phys. Rev. B 89(24), 245449 (2014).
[Crossref]

J. Butet, B. Gallinet, K. Thyagarajan, and O. J. F. Martin, “Second harmonic generation from periodic arrays of arbitrary shape plasmonic nanostructures: A surface integral approach,” J. Opt. Soc. Am. B 30(11), 2970–2979 (2013).
[Crossref]

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

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]

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

J. Butet, 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]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

Castro-Lopez, M.

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

Cerullo, G.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Cetin, A. E.

A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012).
[Crossref] [PubMed]

Chan, C. T.

H. Liu, G. X. Li, K. F. Li, S. M. Chen, S. N. Zhu, C. T. Chan, and K. W. Cheah, “Linear and nonlinear Fano resonance on two-dimensional magnetic metamaterials,” Phys. Rev. B 84(23), 235437 (2011).
[Crossref]

Cheah, K. W.

H. Liu, G. X. Li, K. F. Li, S. M. Chen, S. N. Zhu, C. T. Chan, and K. W. Cheah, “Linear and nonlinear Fano resonance on two-dimensional magnetic metamaterials,” Phys. Rev. B 84(23), 235437 (2011).
[Crossref]

Chen, S. M.

H. Liu, G. X. Li, K. F. Li, S. M. Chen, S. N. Zhu, C. T. Chan, and K. W. Cheah, “Linear and nonlinear Fano resonance on two-dimensional magnetic metamaterials,” Phys. Rev. B 84(23), 235437 (2011).
[Crossref]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Christy, R. W.

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

Dadap, J. I.

J. 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]

Dal Negro, L.

G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic Fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013).
[Crossref] [PubMed]

Danckwerts, M.

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98(2), 026104 (2007).
[Crossref] [PubMed]

Day, J. K.

Y. Zhang, Y.-R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat Commun 5, 4424 (2014).
[PubMed]

Dregely, D.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: The role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

Duboisset, J.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Duò, L.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Dutta-Gupta, S.

J. Butet, S. Dutta-Gupta, and O. J. F. Martin, “Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties,” Phys. Rev. B 89(24), 245449 (2014).
[Crossref]

Eigenthaler, U.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010).
[Crossref] [PubMed]

Eisenthal, K. B.

J. 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]

El-Sayed, M. A.

S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. C 103(16), 3073–3077 (1999).
[Crossref]

Fan, J. A.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Fang, N. X.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, K. C. Toussaint, and C. Toussaint, “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011).
[Crossref] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

U. Fano, “Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco,” Nuovo Cim. 12(3), 154–161 (1935).
[Crossref]

Finazzi, M.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Fischer, H.

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036626 (2005).
[Crossref] [PubMed]

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,” App. Phys. A 47(4), 347–357 (1988).
[Crossref]

Francescato, Y.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: A parameter-free modeling approach,” Nano Lett. 11(7), 2835–2840 (2011).
[Crossref] [PubMed]

Fu, Y. H.

Y. H. Fu, J. B. Zhang, Y. F. Yu, and B. Luk’yanchuk, “Generating and manipulating higher order Fano resonances in dual-disk ring plasmonic nanostructures,” ACS Nano 6(6), 5130–5137 (2012).
[Crossref] [PubMed]

Fukui, M.

J. E. Sipe, C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

Fung, K. H.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, K. C. Toussaint, and C. Toussaint, “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011).
[Crossref] [PubMed]

Gallinet, B.

J. Butet, B. Gallinet, K. Thyagarajan, and O. J. F. Martin, “Second harmonic generation from periodic arrays of arbitrary shape plasmonic nanostructures: A surface integral approach,” J. Opt. Soc. Am. B 30(11), 2970–2979 (2013).
[Crossref]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano 5(11), 8999–9008 (2011).
[Crossref] [PubMed]

B. Gallinet and O. J. F. Martin, “Ab-initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011).
[Crossref]

B. Gallinet and O. J. F. Martin, “Relation between near-field and far-field properties of plasmonic Fano resonances,” Opt. Express 19(22), 22167–22175 (2011).
[Crossref] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Giannini, V.

M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012).
[Crossref] [PubMed]

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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).
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Figures (14)

Fig. 1
Fig. 1

Linear optical properties of the 4-nanorod gold nanostructure. (a) Backward scattered intensity as a function of the incident wavelength. First inset: amplitudes of the dipole moments associated with the nanoantenna (red curve) and with the long nanorods (black curve). See the main text for details of the model. Second inset: mesh used for the numerical computations. The length of top and bottom rods is L = 120 nm. The central nanoantenna is composed of two 70 nm nanorods separated by a gap g = 25 nm. The width and height of the nanorods are 40 nm. The nanostructure is driven by an incident planewave propagating perpendicularly to the structure and polarized along the nanorods long axis. Normalized near-field intensity close to the 4-nanorod structure for an incident wavelength (b) λ = 680 nm, (c) λ = 740 nm, (d) λ = 820 nm, and (e) λ = 900 nm.

Fig. 2
Fig. 2

(a) SH intensity for the 4-nanorod structure as a function of the fundamental wavelength. The SH intensity has been integrated over a sphere with a 50 μm radius. The excitation conditions are identical to that of Fig. 1. Normalized near-field SH intensity close to 4-nanorod structure for an incident wavelength (b) λ = 680 nm, (c) λ = 740 nm, (d) λ = 820 nm, and (e) λ = 900 nm.

Fig. 3
Fig. 3

Normalized SH intensity scattered in the vertical (O, x, y) plane as a function of the scattering angle considering the SH scattered wave polarized (a)-(d) into and (b)-(h) perpendicularly to the vertical plane. The fundamental wavelength is (b), (f) 680 nm, (c), (g) 740 nm, and (d), (h) 840 nm.

Fig. 4
Fig. 4

Normalized SH intensity scattered in the vertical (O, x, y) plane as a function of the scattering angle considering the SH scattered wave polarized perpendicularly to the vertical plane for (a)-(e) the nanoantenna and (f)-(j) the two parallel nanorods. The fundamental wavelength is (b),(g) 680 nm, (c),(h) 740 nm, (d),(i) 820 nm, and (e),(j) 900 nm.

Fig. 5
Fig. 5

Normalized SH intensity scattered in the vertical (O, x, y) plane as a function of the scattering angle considering the SH scattered wave polarized into the vertical plane for (a)-(e) the nanoantenna and (f)-(j) the two parallel nanorods. The fundamental wavelength is (b),(g) 680 nm, (c),(h) 740 nm, (d),(i) 820 nm, and (e),(j) 900 nm.

Fig. 6
Fig. 6

(a-c) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized into the vertical plane. This configuration is closely related to the intensity of the quadrupolar emission (see Fig. 3). (d-f) SH intensity scattered along the x-axis and polarized perpendicularly to the vertical plane (along the z-axis). (g-i) SH intensity scattered along the y-axis and polarized perpendicularly to the vertical plane (along the z-axis). (b),(e),(h) SH intensity as a function of the fundamental wavelength for different distances between the nanoantenna arms: g = 25 nm (red curves), g = 30 nm (black curves), and g = 35 nm (blue curves). (c),(f),(i) SH intensity as a function of the fundamental wavelength for different long rod lengths: L = 120 nm (red curves), L = 130 nm (black curves), and L = 140 nm (blue curves).

Fig. 7
Fig. 7

Backward scattered intensity as a function of the incident wavelength for (a) various gaps g and (b) lengths L.

Fig. 8
Fig. 8

Linear optical properties of the gold pentamer and of its two subgroups. (a) Mesh used for the numerical computations. The disk diameter is 140 nm and the height is 60 nm. The interparticle distance is 20 nm. The gold pentamer and the subgroup structures are driven by an incident planewave propagating perpendicularly to the structure and polarized along the x-axis. (b) Backward scattered intensity as a function of the incident wavelength for the complete pentamer (black curve), the subgroup I (blue curve), and the subgroup II (red curve). Normalized near-field intensity close to (c) the subgroup I, (d)-(f) the complete pentamer, and (e) the subgroup II. The incident wavelength is (c)-(d) λ = 620 nm and (e)-(f) λ = 930 nm.

Fig. 9
Fig. 9

SHG from the gold pentamer and from its two subgroups. (a) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized into the vertical plane: complete pentamer (black curve), the subgroup I (blue curve), and the subgroup II (red curve). (b) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized perpendicularly to the vertical plane (along the z-axis): complete pentamer (black curve), the subgroup I (blue curve), and the subgroup II (red curve).

Fig. 10
Fig. 10

Normalized near-field SH intensity close to (a) the complete pentamer, (b) subgroup I, and (c) the subgroup II. The incident wavelength is λ = 520 nm. The real part of the x-component of the second harmonic electric field Re(Ex) close to (d) the complete pentamer, (e) subgroup I, and (f) the subgroup II.

Fig. 11
Fig. 11

(a) Backward scattered intensity as a function of the incident wavelength for a single nanodot. The disk diameter is 140 nm and the height is 60 nm. (b) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized into the vertical plane (red curve), perpendicularly to the vertical plane (blue curve), and the total intensity (black curve). Normalized near-field intensity close to the nanodot: The incident wavelength is (c) λ = 520 nm and (d) λ = 700 nm. Normalized near-field SH intensity close to the nanodot: The incident wavelength is (e) λ = 520 nm and (f) λ = 700 nm.

Fig. 12
Fig. 12

Linear optical properties of the gold quadrumer and of its two subgroups. (a) Mesh used for the numerical computations. The disk diameter is 140 nm and the height is 60 nm. The interparticle distance is 20 nm. The gold quadrumer and the subgroups structures are driven by an incident planewave propagating perpendicularly to the structure and polarized along the x-axis. (b) Backward scattered intensity as a function of the incident wavelength for the complete quadrumer (black curve), the subgroup I (blue curve), and the subgroup II (red curve). Normalized near-field intensity close to (c) the subgroup I, (d)-(f) the complete quadrumer, and (e) the subgroup II. The incident wavelength is (c)-(d) λ = 660 nm and (e)-(f) λ = 1000 nm.

Fig. 13
Fig. 13

SHG from the gold quadrumer and from its two subgroups. (a) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized into the vertical plane: complete quadrumer (black curve), the subgroup I (blue curve), and the subgroup II (red curve). (b) SH intensity scattered in the vertical (O, x, y) plane with a scattering angle of 45° and polarized perpendicularly to the vertical plane (along the z-axis): complete quadrumer (black curve), the subgroup I (blue curve), and the subgroup II (red curve).

Fig. 14
Fig. 14

Normalized near-field SH intensity close to (a) the complete quadrumer, (b) subgroup I, and (c) the subgroup II. The incident wavelength is λ = 660 nm. The real part of the x-component of the second harmonic electric field Re(Ex) close to (d) the complete quadrumer, (e) subgroup I, and (f) the subgroup II.

Equations (1)

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{ x ¨ 1 + γ 1 x ˙ 1 + ω 1 2 x 1 +g x 2 =0.5 P tot + α 1 E ext x ¨ 2 + γ 2 x ˙ 2 + ω 2 2 x 2 +g x 1 =0.5 P tot + α 2 E ext

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