Abstract

Second-harmonic generation from noble metal nanoparticles with a noncentrosymmetrical shape is theoretically investigated by using finite element method simulations. The relative weight of the dipolar and quadrupolar responses is investigated in terms of both light polarization and size dependence of the harmonic scattered intensity. It is shown that, even for small deformations as compared with purely spherical particles, the dipolar response dominates and scales as the nanoparticle surface area squared. The difference between gold and silver metal nanoparticles is also addressed.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
  2. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  3. T. K. Sau and C. J. Murphy, “Room temperature, high-yield synthesis of multiple shapes of gold nanoparticles in aqueous solution,” J. Am. Chem. Soc. 126, 8648-8649 (2004).
    [CrossRef] [PubMed]
  4. R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
    [CrossRef] [PubMed]
  5. C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
    [CrossRef] [PubMed]
  7. M. Moscovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-826 (1985).
    [CrossRef]
  8. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
    [CrossRef] [PubMed]
  9. C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
    [CrossRef]
  10. 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]
  11. S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
    [CrossRef] [PubMed]
  12. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
    [CrossRef] [PubMed]
  13. K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (2005).
    [CrossRef]
  14. G. S. Agarwal and S. S. Jha, “Theory of 2nd harmonic-generation at a metal-surface with surface-plasmon excitation,” Solid State Commun. 41, 499-501 (1982).
    [CrossRef]
  15. X. M. Hua and J. I. Gersten, “Theory of 2nd-harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756-3764 (1986).
    [CrossRef]
  16. D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
    [CrossRef]
  17. V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
    [CrossRef]
  18. 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, 4045-4048 (1999).
    [CrossRef]
  19. 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, 1328-1347 (2004).
    [CrossRef]
  20. E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
    [CrossRef]
  21. 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, 165407 (2005).
    [CrossRef]
  22. I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
    [CrossRef]
  23. 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, 5418-5423 (2004).
    [CrossRef] [PubMed]
  24. 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, 167403 (2007).
    [CrossRef] [PubMed]
  25. J. Jin, The Finite Elements Method in Electrodynamics (Wiley Interscience, 2002).
  26. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  27. P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985-7989 (1988).
    [CrossRef]
  28. S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15, 257-288 (1998).
    [CrossRef]
  29. S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
    [CrossRef]
  30. R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
    [CrossRef]
  31. 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, 246-250 (2005).
    [CrossRef]

2007 (3)

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

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (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, 167403 (2007).
[CrossRef] [PubMed]

2006 (2)

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

2005 (4)

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (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, 165407 (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, 246-250 (2005).
[CrossRef]

2004 (4)

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, 5418-5423 (2004).
[CrossRef] [PubMed]

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, 1328-1347 (2004).
[CrossRef]

T. K. Sau and C. J. Murphy, “Room temperature, high-yield synthesis of multiple shapes of gold nanoparticles in aqueous solution,” J. Am. Chem. Soc. 126, 8648-8649 (2004).
[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, 057402 (2004).
[CrossRef] [PubMed]

2003 (2)

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[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, 013903 (2003).
[CrossRef] [PubMed]

2002 (1)

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[CrossRef]

2000 (1)

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
[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, 4045-4048 (1999).
[CrossRef]

1998 (1)

1993 (1)

D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
[CrossRef]

1988 (1)

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

1986 (1)

X. M. Hua and J. I. Gersten, “Theory of 2nd-harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756-3764 (1986).
[CrossRef]

1985 (1)

M. Moscovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-826 (1985).
[CrossRef]

1983 (1)

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

1982 (1)

G. S. Agarwal and S. S. Jha, “Theory of 2nd harmonic-generation at a metal-surface with surface-plasmon excitation,” Solid State Commun. 41, 499-501 (1982).
[CrossRef]

1972 (1)

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

1966 (1)

R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
[CrossRef]

1965 (1)

S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. S. Jha, “Theory of 2nd harmonic-generation at a metal-surface with surface-plasmon excitation,” Solid State Commun. 41, 499-501 (1982).
[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, 057402 (2004).
[CrossRef] [PubMed]

Bachelier, G.

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[CrossRef]

Beermann, J.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

Benichou, E.

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[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, 246-250 (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, 165407 (2005).
[CrossRef]

Bennemann, K. H.

D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
[CrossRef]

Bergman, D. J.

K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (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]

Bersohn, R.

R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
[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, 013903 (2003).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

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, 013903 (2003).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

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]

S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15, 257-288 (1998).
[CrossRef]

Brevet, P. F.

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[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, 246-250 (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, 165407 (2005).
[CrossRef]

Brudny, V. L.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
[CrossRef]

Canfield, B. K.

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, 167403 (2007).
[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, 5418-5423 (2004).
[CrossRef] [PubMed]

Chen, C. K.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

Christy, R. W.

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

Coello, V.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

Cyvin, S. J.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
[CrossRef]

Dadap, J. I.

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, 1328-1347 (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, 4045-4048 (1999).
[CrossRef]

Danckwerts, M.

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

Decius, J. C.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Eisenthal, K. B.

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

Frisch, H. L.

R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
[CrossRef]

Gersten, J. I.

X. M. Hua and J. I. Gersten, “Theory of 2nd-harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756-3764 (1986).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

Hafner, J. H.

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).

Hao, E. C.

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[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, 013903 (2003).
[CrossRef] [PubMed]

Heinz, T. F.

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, 1328-1347 (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, 4045-4048 (1999).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

Hua, X. M.

X. M. Hua and J. I. Gersten, “Theory of 2nd-harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756-3764 (1986).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Hupp, J. T.

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[CrossRef]

Jefimovs, K.

Jha, S. S.

G. S. Agarwal and S. S. Jha, “Theory of 2nd harmonic-generation at a metal-surface with surface-plasmon excitation,” Solid State Commun. 41, 499-501 (1982).
[CrossRef]

Jin, J.

J. Jin, The Finite Elements Method in Electrodynamics (Wiley Interscience, 2002).

Jin, R.

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

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

Johnson, R. C.

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[CrossRef]

Jonin, C.

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[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, 246-250 (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, 165407 (2005).
[CrossRef]

Jureller, J. E.

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

Kauranen, M.

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, 167403 (2007).
[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, 5418-5423 (2004).
[CrossRef] [PubMed]

Kim, H. Y.

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Kujala, S.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[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, 5418-5423 (2004).
[CrossRef] [PubMed]

Li, K. R.

K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (2005).
[CrossRef]

Liao, H.

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).

Mendoza, B. S.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
[CrossRef]

Mochan, W. L.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
[CrossRef]

Moscovits, M.

M. Moscovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-826 (1985).
[CrossRef]

Murphy, C. J.

T. K. Sau and C. J. Murphy, “Room temperature, high-yield synthesis of multiple shapes of gold nanoparticles in aqueous solution,” J. Am. Chem. Soc. 126, 8648-8649 (2004).
[CrossRef] [PubMed]

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, 165407 (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, 246-250 (2005).
[CrossRef]

Nehl, C. L.

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).

Novotny, L.

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
[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, 013903 (2003).
[CrossRef] [PubMed]

Oestling, D.

D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
[CrossRef]

Pao, Y.-H.

R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
[CrossRef]

Rauch, J. E.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
[CrossRef]

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, 165407 (2005).
[CrossRef]

Ricard, D.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

Russier-Antoine, I.

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[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, 165407 (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, 246-250 (2005).
[CrossRef]

Sau, T. K.

T. K. Sau and C. J. Murphy, “Room temperature, high-yield synthesis of multiple shapes of gold nanoparticles in aqueous solution,” J. Am. Chem. Soc. 126, 8648-8649 (2004).
[CrossRef] [PubMed]

Schatz, G. C.

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[CrossRef]

Scherer, N. F.

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

Shan, J.

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, 1328-1347 (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, 4045-4048 (1999).
[CrossRef]

Shen, Y. R.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

Stampfli, P.

D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
[CrossRef]

Stockman, M. I.

K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (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]

Svirko, Y.

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

Turunen, J.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[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, 5418-5423 (2004).
[CrossRef] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

-Y. Laluet, J.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[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]

S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15, 257-288 (1998).
[CrossRef]

Arch. Hist. Exact Sci. (1)

C. L. Nehl, H. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Arch. Hist. Exact Sci. 6, 683-688 (2006).

Chem. Phys. Lett. (1)

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, 246-250 (2005).
[CrossRef]

J. Am. Chem. Soc. (2)

T. K. Sau and C. J. Murphy, “Room temperature, high-yield synthesis of multiple shapes of gold nanoparticles in aqueous solution,” J. Am. Chem. Soc. 126, 8648-8649 (2004).
[CrossRef] [PubMed]

R. Jin, J. E. Jureller, H. Y. Kim, and N. F. Scherer, “Correlating second harmonic optical responses of single Ag nanoparticles with morphology,” J. Am. Chem. Soc. 127, 12482-12483 (2005).
[CrossRef] [PubMed]

J. Chem. Phys. (3)

S. J. Cyvin, J. E. Rauch, and J. C. Decius, “Theory of hyper-Raman effects (nonlinear inelastic light scattering): selection rules and depolarization ratios for the second-order polarizability,” J. Chem. Phys. 43, 4083-4095 (1965).
[CrossRef]

R. Bersohn, Y.-H. Pao, and H. L. Frisch, “Double-quantum light scattering by molecules,” J. Chem. Phys. 45, 3184-3198 (1966).
[CrossRef]

E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, “Hyper-Rayleigh scattering from silver nanoparticles,” J. Chem. Phys. 117, 5963-5966 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. C (1)

I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, and P. F. Brevet, “Multipolar contributions of the second harmonic generation from silver and gold nanoparticles,” J. Phys. Chem. C 111, 9044-9048 (2007).
[CrossRef]

Nature (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. -Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (7)

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, 165407 (2005).
[CrossRef]

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

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

K. R. Li, M. I. Stockman, and D. J. Bergman, “Enhanced second harmonic generation in a self-similar chain of metal nanospheres,” Phys. Rev. B 72, 153401 (2005).
[CrossRef]

X. M. Hua and J. I. Gersten, “Theory of 2nd-harmonic generation by small metal spheres,” Phys. Rev. B 33, 3756-3764 (1986).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152-11162 (2000).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced 2nd-harmonic generation and Raman-scattering,” Phys. Rev. B 27, 1965-1979 (1983).
[CrossRef]

Phys. Rev. Lett. (6)

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]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[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, 013903 (2003).
[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, 4045-4048 (1999).
[CrossRef]

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (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, 167403 (2007).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. Moscovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-826 (1985).
[CrossRef]

Solid State Commun. (1)

G. S. Agarwal and S. S. Jha, “Theory of 2nd harmonic-generation at a metal-surface with surface-plasmon excitation,” Solid State Commun. 41, 499-501 (1982).
[CrossRef]

Z. Phys. D: At., Mol. Clusters (1)

D. Oestling, P. Stampfli, and K. H. Bennemann, “Theory of nonlinear-optical properties of small metallic spheres,” Z. Phys. D: At., Mol. Clusters 28, 169-175 (1993).
[CrossRef]

Other (3)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

J. Jin, The Finite Elements Method in Electrodynamics (Wiley Interscience, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic of the geometrical configuration used for the simulations: γ is the angle of polarization of the linearly polarized incident beam E in ( r , ω ) propagating along the z axis (wave vector k in ). δ R corresponds to the deformation applied to the upper half-sphere part of the particle. The vertically polarized electric field E V ( r , 2 ω ) scattered at the harmonic frequency is collected at a right angle in the y axis direction.

Fig. 2
Fig. 2

Normalized polar plots of the vertically polarized SHG intensity as a function of the incident polarization angle γ for different orientation of the particle in the x O y plane determined by the angle ϕ: (a) ϕ = 0 , (b) ϕ = π 4 , (c) ϕ = π 2 , (d) averaged. γ = 0 coincides with the right-hand side of the horizontal axis, and γ increases anticlockwise. The radius of the gold particle is 5 nm , and the deformation is δ R R = 15 % .

Fig. 3
Fig. 3

Normalized polar plots of the vertically polarized SHG intensity as a function of the incident polarization angle γ for different deformations of a 5 nm radius gold particle. γ = 0 coincides with the right-hand side of the horizontal axis, and γ increases anticlockwise. The scattered intensity is averaged over the orientations of the particles in the x O y plane determined by the angle ϕ. (a) δ R R = 0 % , (b) δ R R = 10 % , (c) δ R R = 20 % , (d) δ R R = 40 % .

Fig. 4
Fig. 4

Plot of the ζ V parameter for a gold nanoparticle as a function of the relative deformation δ R R (circles) for a fixed particle size ( 5 nm radius) and as a function of the particle size (diamonds) for a fixed deformation ( δ R R = 30 % ) . The scattered intensity used for the computation of ζ V is averaged over the orientations of the particles in the x O y plane determined by the angle ϕ. The lines are guides for the eye.

Fig. 5
Fig. 5

Normalized polar plots of the vertically polarized SHG intensity as a function of the incident polarization angle γ for different a gold particle sizes with a fixed relative deformation of δ R R = 30 % . γ = 0 coincides with the right-hand side of the horizontal axis, and γ increases anticlockwise. The scattered intensity is averaged over the orientations of the particles in the x O y plane determined by the angle ϕ. (a) R = 2.5 nm , (b) R = 5 nm , (c) R = 10 nm , (d) R = 20 nm .

Fig. 6
Fig. 6

Size dependence of the vertically polarized SHG intensity for a gold particle with a relative deformation of δ R R = 30 % . The scattered intensity is averaged over the orientations of the particles in the x O y plane determined by the angle ϕ. The dotted and dashed curves correspond to a surface area squared ( R 4 ) and volume squared ( R 6 ) dependence, respectively (log–log plot).

Equations (5)

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

P surf ( r , 2 ω ) = χ surf : E ( r , ω ) E ( r , ω )
P bulk ( r , 2 ω ) = α [ E ( r , ω ) E ( r , ω ) ] + β [ E ( r , ω ) ] E ( r , ω ) ,
P surf , ( r , 2 ω ) = χ surf , E ex , 2 ( r , ω ) ,
I SHG V ( γ ) = a V cos 4 ( γ ) + b V cos 2 ( γ ) sin 2 ( γ ) + c V sin 4 ( γ ) + d V cos 3 ( γ ) sin ( γ ) + e V cos ( γ ) sin 3 ( γ ) ,
ζ V = b V ( a V + c V ) b V .

Metrics