Abstract

We present a multipolar tensor analysis of second-harmonic radiation from arrays of noncentrosymmetric L-shaped gold nanoparticles. Our approach is based on the fundamental differences in the radiative properties of electric dipoles and higher multipoles, which give rise to differences in the nonlinear response tensors for the reflected and transmitted second-harmonic signals. The results are analyzed by dividing the tensors into symmetric (dipolar) and antisymmetric (higher multipolar) parts between the two directions. The nonlinear response is found to be dominated by a tensor component, not resolved earlier [Kujala et. al, Phys. Rev. Lett. 98, 167403, (2007)], which is associated with chiral symmetry breaking of the sample and which also contains a strong multipolar contribution. The results are explained by a phenomenological model where asymmetrically-distributed defects on opposite sides of the particles give rise to dipolar and quadrupolar second-harmonic emission.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  52. K. Li, M. I. Stockman, and D. J. Bergman, "Enhanced second harmonic generation in a self-similar chain of metal nanospheres," Phys. Rev. B 72, 153,401 (2005).
    [CrossRef]
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    [CrossRef]

2007 (8)

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, "Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

R. Bukasov and J. S. Shumaker-Parry, "Highly Tunable Infrared Extinction Properties of Gold Nanocrescents," Nano Lett. 7, 1113-1118 (2007).
[CrossRef] [PubMed]

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

L. Cao, N. C. Panoiu, and R. M. J. Osgood, "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205,401 (2007).
[CrossRef]

M.W. Klein, M. Wegener, N. Feth, and S. Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials," Opt. Express 15, 5238-5247 (2007).
[CrossRef] [PubMed]

B. Bai and J. Turunen, "Fourier modal method for the analysis of second-harmonic generation in twodimensionally periodic structures containing anisotropic materials," J. Opt. Soc. Am. B 24, 1105-1112 (2007).
[CrossRef]

F. X. Wang, M. Siltanen, and M. Kauranen, "Uniqueness of determination of second-order nonlinear optical expansion coefficients of thin films," Phys. Rev. B 76, 085428 (2007).
[CrossRef]

2006 (7)

B. K. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, and M. Kauranen, "Chirality arising from small defects in gold nanoparticle arrays," Opt. Express 14, 950 (2006).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, "A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures," J. Opt. A: Pure Appl. Opt 8, S278 (2006).
[CrossRef]

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
[CrossRef]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef] [PubMed]

J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, "Experimental study of optical second-harmonic scattering from spherical nanoparticles," Phys Rev. A 73, 023,819 (2006).
[CrossRef]

T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, "Magnetic-field enhancement in gold nanosandwiches," Opt. Express 14, 8240-8246 (2006).
[CrossRef] [PubMed]

M.W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-Harmonic Generation from Magnetic Metamaterials," Science 313, 502-504 (2006).
[CrossRef] [PubMed]

2005 (9)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

V. Shalaev,W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (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, 165,407 (2005).
[CrossRef]

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

J. E. Millstone, S. Park, K. L. Shuford, L. D. Qin, G. C. Schatz, and C. A. Mirkin, "Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms," J. Am. Chem. Soc. 127, 5312 (2005).
[CrossRef] [PubMed]

K. L. Shuford, M. A. Ratner, and G. C. Schatz, "Multipolar excitation in triangular nanoprisms," J. Chem. Phys. 123, 114713 (2005).
[CrossRef]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, "Enhanced second harmonic generation in a self-similar chain of metal nanospheres," Phys. Rev. B 72, 153,401 (2005).
[CrossRef]

2004 (6)

J. I. Dadap, J. Shan, and T. F. Heinz, "Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit," J. Opt. Soc. Am. B 21, 1328 (2004).
[CrossRef]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

M. I. Stockman, D. J. Bergman, and T. Kobayashi, "Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems," Phys. Rev. B 69, 054,202 (2004).
[CrossRef]

2003 (7)

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-Field Second-Harmonic Generation Induced by Local Field Enhancement," Phys. Rev. Lett. 90, 013,903 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem B 107, 668 (2003).
[CrossRef]

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157,404 (2003).
[CrossRef]

V. L. Brudny, W. L. Mochán, J. A. Maytorena, and B. S. Mendoza, "Second harmonic generation from a collection of nanoparticles," Phys. Status Solidi B 240, 518-526 (2003).
[CrossRef]

L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt 5, 345-355 (2003).
[CrossRef]

C. I. Valencia, E. R. M�??endez, and B. S. Mendoza, "Second-harmonic generation in the scattering of light by two-dimensional particles," J. Opt. Soc. Am. B 20, 2150-2161 (2003).
[CrossRef]

2002 (2)

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
[CrossRef]

2001 (1)

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

2000 (1)

J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
[CrossRef]

1999 (3)

F. Hache, H. Mesnil, and M. C. Schanne-Klein, "Nonlinear circular dichroism in a liquid of chiral molecules: A theoretical investigation," Phys. Rev. B 60, 6405-6411 (1999).
[CrossRef]

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, "Light scattering from dipole and quadrupole nanoshell antennas," Appl. Phys. Lett. 75, 1063 (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, 4045 (1999).
[CrossRef]

1997 (3)

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

M. Kauranen, J. J. Maki, T. Verbiest, S. V. Elshocht, and A. Persoons, "Quantitative determination of electric and magnetic second-order susceptibility tensors of chiral surfaces," Phys. Rev. B 55, R1985 (1997).
[CrossRef]

S. V. Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, "Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film," J. Chem. Phys. 107, 8201-8203 (1997).
[CrossRef]

1996 (1)

1994 (1)

M. Kauranen, T. Verbiest, J. J. Maki, and A. Persoons, "Second-harmonic generation from chiral surfaces," J. Chem. Phys. 101, 8193 (1994).
[CrossRef]

1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. Shen, "General considerations on optical second-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Abrishamian, M. S.

Anceau, C.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

Andraud, C.

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

Aubard, J.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
[CrossRef]

Aussenegg, A.

J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
[CrossRef]

Aussenegg, F. R.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
[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 Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

B. Bai and J. Turunen, "Fourier modal method for the analysis of second-harmonic generation in twodimensionally periodic structures containing anisotropic materials," J. Opt. Soc. Am. B 24, 1105-1112 (2007).
[CrossRef]

Benichou, E.

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
[CrossRef]

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (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, 165,407 (2005).
[CrossRef]

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, "Enhanced second harmonic generation in a self-similar chain of metal nanospheres," Phys. Rev. B 72, 153,401 (2005).
[CrossRef]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

M. I. Stockman, D. J. Bergman, and T. Kobayashi, "Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems," Phys. Rev. B 69, 054,202 (2004).
[CrossRef]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-Field Second-Harmonic Generation Induced by Local Field Enhancement," Phys. Rev. Lett. 90, 013,903 (2003).
[CrossRef]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-Field Second-Harmonic Generation Induced by Local Field Enhancement," Phys. Rev. Lett. 90, 013,903 (2003).
[CrossRef]

Brasselet, S.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

Brevet, P. F.

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
[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, 165,407 (2005).
[CrossRef]

Brevet, P.-F.

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (2005).
[CrossRef]

Brotin, T.

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

Brudny, V. L.

V. L. Brudny, W. L. Mochán, J. A. Maytorena, and B. S. Mendoza, "Second harmonic generation from a collection of nanoparticles," Phys. Status Solidi B 240, 518-526 (2003).
[CrossRef]

Bukasov, R.

R. Bukasov and J. S. Shumaker-Parry, "Highly Tunable Infrared Extinction Properties of Gold Nanocrescents," Nano Lett. 7, 1113-1118 (2007).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

Cai, W.

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 Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, and M. Kauranen, "Chirality arising from small defects in gold nanoparticle arrays," Opt. Express 14, 950 (2006).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, "A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures," J. Opt. A: Pure Appl. Opt 8, S278 (2006).
[CrossRef]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

Cao, L.

L. Cao, N. C. Panoiu, and R. M. J. Osgood, "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205,401 (2007).
[CrossRef]

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. Shen, "General considerations on optical second-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Chena, M.W.

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

Chettiar, U.

Christ, A.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Clark, A. W.

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

Collet, A.

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

Cooper, J. M.

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem B 107, 668 (2003).
[CrossRef]

Cumming, D. R. S.

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

Dadap, J. I.

J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, "Experimental study of optical second-harmonic scattering from spherical nanoparticles," Phys Rev. A 73, 023,819 (2006).
[CrossRef]

J. I. Dadap, J. Shan, and T. F. Heinz, "Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit," J. Opt. Soc. Am. B 21, 1328 (2004).
[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, 4045 (1999).
[CrossRef]

Dmitriev, A.

Drachev, V.

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, 4045 (1999).
[CrossRef]

Elshocht, S. V.

S. V. Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, "Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film," J. Chem. Phys. 107, 8201-8203 (1997).
[CrossRef]

M. Kauranen, J. J. Maki, T. Verbiest, S. V. Elshocht, and A. Persoons, "Quantitative determination of electric and magnetic second-order susceptibility tensors of chiral surfaces," Phys. Rev. B 55, R1985 (1997).
[CrossRef]

Enkrich, C.

M.W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-Harmonic Generation from Magnetic Metamaterials," Science 313, 502-504 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

Etrich, C.

Félidj, N.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
[CrossRef]

Feth, N.

Fluegel, B.

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157,404 (2003).
[CrossRef]

Fujita, T.

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

Giessen, H.

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Gippius, N. A.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Glidle, A.

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

Granpayeh, N.

Gunnarsson, L.

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. Shen, "General considerations on optical second-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Hache, F.

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

F. Hache, H. Mesnil, and M. C. Schanne-Klein, "Nonlinear circular dichroism in a liquid of chiral molecules: A theoretical investigation," Phys. Rev. B 60, 6405-6411 (1999).
[CrossRef]

Halas, N. J.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, "Light scattering from dipole and quadrupole nanoshell antennas," Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Hale, G. D.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, "Light scattering from dipole and quadrupole nanoshell antennas," Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-Field Second-Harmonic Generation Induced by Local Field Enhancement," Phys. Rev. Lett. 90, 013,903 (2003).
[CrossRef]

Heinz, T. F.

J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, "Experimental study of optical second-harmonic scattering from spherical nanoparticles," Phys Rev. A 73, 023,819 (2006).
[CrossRef]

J. I. Dadap, J. Shan, and T. F. Heinz, "Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit," J. Opt. Soc. Am. B 21, 1328 (2004).
[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, 4045 (1999).
[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 Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

Inoue, A.

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

Jackson, J. B.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, "Light scattering from dipole and quadrupole nanoshell antennas," Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

Jefimovs, K.

B. K. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, and M. Kauranen, "Chirality arising from small defects in gold nanoparticle arrays," Opt. Express 14, 950 (2006).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, "A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures," J. Opt. A: Pure Appl. Opt 8, S278 (2006).
[CrossRef]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

Jonin, C.

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
[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, 165,407 (2005).
[CrossRef]

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (2005).
[CrossRef]

Käll, M.

T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, "Magnetic-field enhancement in gold nanosandwiches," Opt. Express 14, 8240-8246 (2006).
[CrossRef] [PubMed]

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

Kasemo, B.

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

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 Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

F. X. Wang, M. Siltanen, and M. Kauranen, "Uniqueness of determination of second-order nonlinear optical expansion coefficients of thin films," Phys. Rev. B 76, 085428 (2007).
[CrossRef]

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, "A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures," J. Opt. A: Pure Appl. Opt 8, S278 (2006).
[CrossRef]

B. K. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, and M. Kauranen, "Chirality arising from small defects in gold nanoparticle arrays," Opt. Express 14, 950 (2006).
[CrossRef] [PubMed]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

M. Kauranen, J. J. Maki, T. Verbiest, S. V. Elshocht, and A. Persoons, "Quantitative determination of electric and magnetic second-order susceptibility tensors of chiral surfaces," Phys. Rev. B 55, R1985 (1997).
[CrossRef]

S. V. Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, "Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film," J. Chem. Phys. 107, 8201-8203 (1997).
[CrossRef]

M. Kauranen, T. Verbiest, J. J. Maki, and A. Persoons, "Second-harmonic generation from chiral surfaces," J. Chem. Phys. 101, 8193 (1994).
[CrossRef]

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem B 107, 668 (2003).
[CrossRef]

Kildishev, A.

Klein, M.W.

M.W. Klein, M. Wegener, N. Feth, and S. Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials," Opt. Express 15, 5238-5247 (2007).
[CrossRef] [PubMed]

M.W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-Harmonic Generation from Magnetic Metamaterials," Science 313, 502-504 (2006).
[CrossRef] [PubMed]

Kobayashi, T.

M. I. Stockman, D. J. Bergman, and T. Kobayashi, "Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems," Phys. Rev. B 69, 054,202 (2004).
[CrossRef]

Koschny, T.

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N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
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J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
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J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
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H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
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N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
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J. E. Millstone, S. Park, K. L. Shuford, L. D. Qin, G. C. Schatz, and C. A. Mirkin, "Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms," J. Am. Chem. Soc. 127, 5312 (2005).
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J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
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Russier-Antoine, I.

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
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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, 165,407 (2005).
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J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (2005).
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N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
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K. L. Shuford, M. A. Ratner, and G. C. Schatz, "Multipolar excitation in triangular nanoprisms," J. Chem. Phys. 123, 114713 (2005).
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J. E. Millstone, S. Park, K. L. Shuford, L. D. Qin, G. C. Schatz, and C. A. Mirkin, "Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms," J. Am. Chem. Soc. 127, 5312 (2005).
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L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
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N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
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J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
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J. E. Millstone, S. Park, K. L. Shuford, L. D. Qin, G. C. Schatz, and C. A. Mirkin, "Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms," J. Am. Chem. Soc. 127, 5312 (2005).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
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J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, "Experimental study of optical second-harmonic scattering from spherical nanoparticles," Phys Rev. A 73, 023,819 (2006).
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K. Li, M. I. Stockman, and D. J. Bergman, "Enhanced second harmonic generation in a self-similar chain of metal nanospheres," Phys. Rev. B 72, 153,401 (2005).
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B. K. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, and M. Kauranen, "Chirality arising from small defects in gold nanoparticle arrays," Opt. Express 14, 950 (2006).
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B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

Vahimaa, P.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

Valencia, C. I.

Vallius, T.

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

Verbiest, T.

M. Kauranen, J. J. Maki, T. Verbiest, S. V. Elshocht, and A. Persoons, "Quantitative determination of electric and magnetic second-order susceptibility tensors of chiral surfaces," Phys. Rev. B 55, R1985 (1997).
[CrossRef]

S. V. Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, "Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film," J. Chem. Phys. 107, 8201-8203 (1997).
[CrossRef]

M. Kauranen, T. Verbiest, J. J. Maki, and A. Persoons, "Second-harmonic generation from chiral surfaces," J. Chem. Phys. 101, 8193 (1994).
[CrossRef]

Wang, F. X.

F. X. Wang, M. Siltanen, and M. Kauranen, "Uniqueness of determination of second-order nonlinear optical expansion coefficients of thin films," Phys. Rev. B 76, 085428 (2007).
[CrossRef]

Weeber, J.

J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
[CrossRef]

Wegener, M.

M.W. Klein, M. Wegener, N. Feth, and S. Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials," Opt. Express 15, 5238-5247 (2007).
[CrossRef] [PubMed]

M.W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-Harmonic Generation from Magnetic Metamaterials," Science 313, 502-504 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Yan, X. Q.

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

Yuan, H.

Zentgraf, T.

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Zhang, Y.

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157,404 (2003).
[CrossRef]

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem B 107, 668 (2003).
[CrossRef]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

Zou, S.

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

Zyss, J.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (6)

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

L. H. Qian, X. Q. Yan, T. Fujita, A. Inoue, and M.W. Chena, "Surface enhanced Raman scattering of nanoporous gold: Smaller pore sizes stronger enhancements," Appl. Phys. Lett. 90, 153,120 (2007).
[CrossRef]

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, "Light scattering from dipole and quadrupole nanoshell antennas," Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

J. Krenn, G. Schider, W. Rechberger, B. Lamprecht, F. Leitner, A. Aussenegg, and J. Weeber, "Design of multipolar plasmon excitations in silver nanoparticles," Appl. Phys. Lett. 77, 3379 (2000).
[CrossRef]

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, "Multiple plasmon resonances from gold nanostructures," Appl. Phys. Lett. 90, 143105 (2007).
[CrossRef]

B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, "Remarkable Polarization Sensitivity of Gold Nanoparticle Arrays," Appl. Phys. Lett. 86, 183,109 (2005).
[CrossRef]

Chem. Phys. Lett. (2)

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, "Wavelength dependence of the retardation effects in silver nanoparticles followed by polarization resolved hyper Rayleigh scattering," Chem. Phys. Lett. 415, 246 (2005).
[CrossRef]

M. C. Schanne-Klein, F. Hache, T. Brotin, C. Andraud, and A. Collet, "Magnetic chiroptical effects in surface second harmonic reflection," Chem. Phys. Lett. 338, 159-166 (2001).
[CrossRef]

J. Am. Chem. Soc. (1)

J. E. Millstone, S. Park, K. L. Shuford, L. D. Qin, G. C. Schatz, and C. A. Mirkin, "Observation of a quadrupole plasmon mode for a colloidal solution of gold nanoprisms," J. Am. Chem. Soc. 127, 5312 (2005).
[CrossRef] [PubMed]

J. Chem. Phys. (5)

K. L. Shuford, M. A. Ratner, and G. C. Schatz, "Multipolar excitation in triangular nanoprisms," J. Chem. Phys. 123, 114713 (2005).
[CrossRef]

S. V. Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, "Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film," J. Chem. Phys. 107, 8201-8203 (1997).
[CrossRef]

M. Kauranen, T. Verbiest, J. J. Maki, and A. Persoons, "Second-harmonic generation from chiral surfaces," J. Chem. Phys. 101, 8193 (1994).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10,871-10,875 (2004).
[CrossRef]

J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, "Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response," J. Chem. Phys. 125, 184,712 (2006).
[CrossRef]

J. Nonlinear Opt. Phys. (1)

H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. 11, 421 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt (2)

B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, "A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures," J. Opt. A: Pure Appl. Opt 8, S278 (2006).
[CrossRef]

L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt 5, 345-355 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

J. Phys. Chem B (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem B 107, 668 (2003).
[CrossRef]

J. Phys. Chem. B (1)

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined Plasmons in Nanofabricated Single Silver Particle Pairs: Experimental Observations of Strong Interparticle Interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

Nano Lett. (2)

R. Bukasov and J. S. Shumaker-Parry, "Highly Tunable Infrared Extinction Properties of Gold Nanocrescents," Nano Lett. 7, 1113-1118 (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 Noncentrosymmetric Nanodimers," Nano Lett. 7, 1251-1255 (2007).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys Rev. A (1)

J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, "Experimental study of optical second-harmonic scattering from spherical nanoparticles," Phys Rev. A 73, 023,819 (2006).
[CrossRef]

Phys. Rev. B (10)

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, 165,407 (2005).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, "Enhanced second harmonic generation in a self-similar chain of metal nanospheres," Phys. Rev. B 72, 153,401 (2005).
[CrossRef]

F. X. Wang, M. Siltanen, and M. Kauranen, "Uniqueness of determination of second-order nonlinear optical expansion coefficients of thin films," Phys. Rev. B 76, 085428 (2007).
[CrossRef]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn,M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface-enhanced Raman scattering," Phys. Rev. B 65, 075,419 (2002).
[CrossRef]

M. I. Stockman, D. J. Bergman, and T. Kobayashi, "Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems," Phys. Rev. B 69, 054,202 (2004).
[CrossRef]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B 70, 125113 (2004).
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M. Kauranen, J. J. Maki, T. Verbiest, S. V. Elshocht, and A. Persoons, "Quantitative determination of electric and magnetic second-order susceptibility tensors of chiral surfaces," Phys. Rev. B 55, R1985 (1997).
[CrossRef]

F. Hache, H. Mesnil, and M. C. Schanne-Klein, "Nonlinear circular dichroism in a liquid of chiral molecules: A theoretical investigation," Phys. Rev. B 60, 6405-6411 (1999).
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L. Cao, N. C. Panoiu, and R. M. J. Osgood, "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205,401 (2007).
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Phys. Rev. Lett. (5)

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157,404 (2003).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203,901 (2005).
[CrossRef] [PubMed]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-Field Second-Harmonic Generation Induced by Local Field Enhancement," Phys. Rev. Lett. 90, 013,903 (2003).
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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, 4045 (1999).
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M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, "Enhanced Second-Harmonic Generation by Metal Surfaces with Nanoscale Roughness: Nanoscale Dephasing, Depolarization, and Correlations," Phys. Rev. Lett. 92, 057402 (2004).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

V. L. Brudny, W. L. Mochán, J. A. Maytorena, and B. S. Mendoza, "Second harmonic generation from a collection of nanoparticles," Phys. Status Solidi B 240, 518-526 (2003).
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Science (2)

M.W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-Harmonic Generation from Magnetic Metamaterials," Science 313, 502-504 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

An array of L-shaped particles and the associated coordinate system.

Fig. 2.
Fig. 2.

Illustration of the differences in radiative properties of (a) electric dipole p, (b) magnetic dipole m and (c) electric quadrupole Q. Vectors k, E, and B are the wavevector, electric field, and magnetic field, respectively.

Fig. 3.
Fig. 3.

Measured optical density of our sample. Note that x-polarization is in resonance with the fundamental wavelength of our laser, 1060 nm.

Fig. 4.
Fig. 4.

(a) Experimental setup. P=polarizer; H=half wave plate; Q=quarter wave plate; VISF=long-wavelength pass filter; S=the sample; IRF=short-wavelength pass filter; A=analyzer; and PMT=photo-multiplier tube. (b) The experimental geometry.

Fig. 5.
Fig. 5.

Measured lineshapes. Asterisks: transmission SH data; circles: reflection SH data. Solid and dashed lines are fits to Eq. (5) in transmission and reflection geometries, respectively. The starting linear polarization was p for (a), (c), and (e), and s for (b), (d), and (f). QWP values 135° and 225° correspond to left- and right-hand circular polarizations, respectively. Estimations of the relative uncertainties due to detector noise are indicated with the symbol size, except for those measured in reflection geometry (dashed line) in plots (e) and (f), where the uncertainties are indicated with the errorbars.

Fig. 6.
Fig. 6.

(a) Visualization of L-shaped particle where laterally opposite sides have nonequivalent defects. (b) Example of an effective quadrupole formed from two displaced opposite dipoles.

Tables (2)

Tables Icon

Table 1. In-plane NRT components for (ideal) L-shaped nanoparticles and experimental values extracted from Eq. (5)

Tables Icon

Table 2. Multipolar contributions of NRT components.

Equations (12)

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

E i ( 2 ω ) = jk A ijk E j ( ω ) E k ( ω ) ,
A ijk T , R = A ijk s ± A ijk as ,
A ijk s = 1 2 ( A ijk T + A ijk R ) , A ijk as = 1 2 ( A ijk T A ijk R ) .
E i ( 2 ω ) = A ixx E x 2 ( ω ) + A iyy E y 2 ( ω ) + 2 A ixy E x ( ω ) E y ( ω ) ; i = x , y ,
I δ ( 2 ω ) = ( A xxx sin δ + A yxx cos δ ) E x 2 ( ω ) + ( A xyy sin δ + A yyy cos δ ) E y 2 ( ω ) +
2 ( A xxy sin δ + A yxy cos δ ) E x ( ω ) E y ( ω ) 2 ,
γ ijk = A ijk as A ijk s .
Q ap + pa ,
E Q i ( k · Q ) = i ( k · a ) + i ( k · p ) a ,
E Q i ( k · a ) p = i k a z p y = i k Q zy y .
E p 1 exp ( i k a z 2 ) + p 2 exp ( i k a z 2 ) ,
E p 1 + p 2 + ( p 2 p 1 ) i k a z 2 ,

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