Abstract

We present a multipolar tensor analysis of second-harmonic generation from arrays of noncentrosymmetric gold nanoparticles. In contrast to earlier results, where higher multipoles and symmetry-forbidden signals arising from sample defects play a significant role, the present results are completely dominated by symmetry-allowed electric-dipole tensor components. The result arises from significant improvement in sample quality, which suppresses the higher-multipole effects and enhances the overall response by an order of magnitude. The results are a prerequisite for metamaterials with controllable nonlinear properties.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
  5. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
    [CrossRef] [PubMed]
  6. B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
    [CrossRef] [PubMed]
  12. M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
    [CrossRef] [PubMed]
  13. M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
    [CrossRef]
  14. S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
    [CrossRef] [PubMed]
  15. M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
    [CrossRef] [PubMed]
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  17. M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
    [CrossRef]
  18. J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71(16), 165407 (2005).
    [CrossRef]
  19. 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]
  20. 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]
  21. S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004).
    [CrossRef]
  22. A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B 28(6), 1374–1384 (2011).
    [CrossRef]
  23. H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010).
    [CrossRef] [PubMed]
  24. 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(4), S278–S284 (2006).
    [CrossRef]
  25. M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
    [CrossRef]
  26. S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
    [CrossRef] [PubMed]

2011 (4)

F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36(9), 1533–1535 (2011).
[CrossRef] [PubMed]

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[CrossRef]

A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B 28(6), 1374–1384 (2011).
[CrossRef]

2010 (4)

H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (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]

M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature 467(7315), 541–542 (2010).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

2008 (1)

2007 (5)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (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 non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[CrossRef] [PubMed]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

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

2006 (3)

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(4), S278–S284 (2006).
[CrossRef]

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

M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

2005 (2)

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

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

2004 (3)

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

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

2003 (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(3), 668–677 (2003).
[CrossRef]

1999 (1)

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]

1998 (1)

M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
[CrossRef]

Anceau, C.

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

Bachelier, G.

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]

Bai, B.

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

Benichou, E.

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

Bergman, D. 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(5), 057402 (2004).
[CrossRef] [PubMed]

Bonn, M.

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

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(5), 057402 (2004).
[CrossRef] [PubMed]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Brevet, P.-F.

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

Butet, J.

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]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Canfield, B. K.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
[CrossRef] [PubMed]

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

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

B. K. Canfield, S. Kujala, K. Jefimovs, 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(4), S278–S284 (2006).
[CrossRef]

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (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(3), 668–677 (2003).
[CrossRef]

Dadap, J. I.

A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B 28(6), 1374–1384 (2011).
[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]

de Beer, A. G. F.

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]

Enkrich, Ch.

M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Enoch, S.

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

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Feth, N.

Fiebig, M.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Gentile, M.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Giessen, H.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Guo, H.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Harmsen, R. H.

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

Heinz, T. F.

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]

Hentschel, M.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Husu, H.

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[CrossRef]

H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010).
[CrossRef] [PubMed]

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

Jefimovs, K.

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(4), S278–S284 (2006).
[CrossRef]

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

Jonin, C.

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

Kauranen, M.

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[CrossRef]

H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010).
[CrossRef] [PubMed]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
[CrossRef] [PubMed]

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

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

B. K. Canfield, S. Kujala, K. Jefimovs, 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(4), S278–S284 (2006).
[CrossRef]

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
[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(3), 668–677 (2003).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

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(8), 5238–5247 (2007).
[CrossRef] [PubMed]

M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Kuipers, L.

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

Kuittinen, M.

H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010).
[CrossRef] [PubMed]

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

Kujala, S.

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[CrossRef]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
[CrossRef] [PubMed]

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

B. K. Canfield, S. Kujala, K. Jefimovs, 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(4), S278–S284 (2006).
[CrossRef]

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

Laukkanen, J.

H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010).
[CrossRef] [PubMed]

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

Linden, S.

Mäkitalo, J.

Nappa, J.

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

Niesler, F. B. P.

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Persoons, A.

M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
[CrossRef]

Petukhov, A. V.

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

Prangsma, J. C.

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

Revillod, G.

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

Roke, S.

A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B 28(6), 1374–1384 (2011).
[CrossRef]

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

Russier-Antoine, I.

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

Sandtke, M.

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

Schatz, G. C.

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(3), 668–677 (2003).
[CrossRef]

Segerink, F. B.

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

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Shan, J.

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]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature 467(7315), 541–542 (2010).
[CrossRef] [PubMed]

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

Svirko, Y.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
[CrossRef] [PubMed]

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

B. K. Canfield, S. Kujala, K. Jefimovs, 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(4), S278–S284 (2006).
[CrossRef]

Taubert, R.

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

Turunen, J.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express 16(22), 17196–17208 (2008).
[CrossRef] [PubMed]

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

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

B. K. Canfield, S. Kujala, K. Jefimovs, 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(4), S278–S284 (2006).
[CrossRef]

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

B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[CrossRef] [PubMed]

Vallius, T.

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

van Nieuwstadt, J. A. H.

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

Verbiest, T.

M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
[CrossRef]

Wegener, M.

F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36(9), 1533–1535 (2011).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[CrossRef] [PubMed]

M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Zdanowicz, M.

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[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(3), 668–677 (2003).
[CrossRef]

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(5), 057402 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (1)

M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011).
[CrossRef]

J. Mod. Opt. (1)

M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998).
[CrossRef]

J. Opt. A Pure Appl Opt. (1)

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

J. Opt. A Pure Appl. Opt. (1)

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(4), S278–S284 (2006).
[CrossRef]

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

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(3), 668–677 (2003).
[CrossRef]

Nano Lett. (1)

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

Nat. Photonics (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Nature (1)

M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature 467(7315), 541–542 (2010).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (2)

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

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

Phys. Rev. Lett. (5)

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

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. 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]

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

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

Science (2)

M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Other (1)

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

SEM images and geometry of arrays of L-shaped nanoparticles for present, high-quality (a) and earlier, low-quality (b) samples. (c) x- and y-polarized extinction spectra of high- and low-quality samples.

Fig. 2
Fig. 2

Experimental setup. L – lens, P – polarizer, A1, A2 – analyzers, HWP – half-wave plate, QWP – quarter wave plate, VISF – visible blocking filter, IRF1, IRF2 – infrared blocking filters, PMT1, PMT2 – photomultiplier tubes.

Fig. 3
Fig. 3

Normalized transmitted (-T) and reflected (-R) SHG signals from an array of L-shaped gold nanoparticles for metal incidence (M-) and substrate incidence (S-), and from the present high-quality sample. Symbols represent the data from the measurements and solid lines are theoretical fits. The starting and detected linear polarization was x.

Tables (2)

Tables Icon

Table 1 The expansion coefficients expressed as function of NRT components for specific configurations. The signs depend on measurement geometry (M-: metal side incidence, S-: substrate side incidence, -T: transmission, -R: reflection). Note that f and g are allowed for the ideal symmetry of the L shape, whereas h is forbidden.

Tables Icon

Table 2 Determined values of NRT components

Equations (2)

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

E i (2ω)= jk A ijk E j (ω) E k (ω) ,
E i (2ω)=f E x 2 (ω)+g E y 2 (ω)+h E x (ω) E y (ω),

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