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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 8 — Aug. 1, 2012
  • pp: 2213–2221

Nonlinear Mie theory for the second harmonic generation in metallic nanoshells

Jérémy Butet, Isabelle Russier-Antoine, Christian Jonin, Noëlle Lascoux, Emmanuel Benichou, and Pierre-François Brevet  »View Author Affiliations

JOSA B, Vol. 29, Issue 8, pp. 2213-2221 (2012)

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In this work, Mie theory extended to the specific case of the optical second harmonic generation (SHG) from metallic nanoshells is described. Our model results from a combination of the Mie theory developed for the linear optical response of concentric nanospheres and the Mie theory developed for the SHG from nanospheres. This approach leads to a multipolar expansion of the second harmonic scattered electric fields. The total scattered intensity and the relative contribution of each multipole to the scattered wave are directly calculated within this framework. Our model is then applied to the calculation of the second harmonic cross section for nanoshells made of the most common metals used in plasmonics, namely gold and silver. Finally, the effect of the aspect ratio, i.e., the ratio between the inner and the outer radii of the metallic nanoshell, a parameter that is known to greatly impact the surface plasmon resonance properties of the system, is discussed notably in terms of the tunability of the optical SHG from metallic nanoshells.

© 2012 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4350) Nonlinear optics : Nonlinear optics at surfaces
(240.4350) Optics at surfaces : Nonlinear optics at surfaces
(290.4020) Scattering : Mie theory

ToC Category:
Nonlinear Optics

Original Manuscript: April 20, 2012
Revised Manuscript: June 27, 2012
Manuscript Accepted: June 28, 2012
Published: August 1, 2012

Virtual Issues
Vol. 7, Iss. 10 Virtual Journal for Biomedical Optics

Jérémy Butet, Isabelle Russier-Antoine, Christian Jonin, Noëlle Lascoux, Emmanuel Benichou, and Pierre-François Brevet, "Nonlinear Mie theory for the second harmonic generation in metallic nanoshells," J. Opt. Soc. Am. B 29, 2213-2221 (2012)

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  1. R. D. Averitt, D. Sarkar, and N. J. Halas, “Plasmon resonance of Au-coated Au2S nanoshells: Insight into multicomponent nanoparticle growth,” Phys. Rev. Lett. 78, 4217–4220 (1997). [CrossRef]
  2. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef]
  3. E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004). [CrossRef]
  4. E. Prodan and P. Nordlander, “Structural tunability of the plasmon resonances in metallic nanoshells,” Nano Lett. 3, 543–547 (2003). [CrossRef]
  5. C. L. Nehl, N. K. Grady, G. P. Goodrich, F. Tam, N. J. Halas, and J. Hafner, “Scattering spectra of single gold nanoshells,” Nano Lett. 4, 2355–2359 (2004). [CrossRef]
  6. T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Radiative decay of plasmons in a metallic nanoshell,” Phys. Rev. B 69, 155402 (2004). [CrossRef]
  7. C. Loo, A. Lowery, N. J. Halas, J. West, and R. Drezek, “Immunotargeted nanoshells for integrated cancer imaging and therapy,” Nano Lett. 5, 709–711 (2005). [CrossRef]
  8. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209, 171–176 (2004). [CrossRef]
  9. G. Raschke, S. Brogl, A. S. Susha, A. L. Rogach, T. A. Klar, J. Feldmann, B. Fieres, N. Petkov, T. Bein, A. Nichtl, and K. Kürzinger, “Gold nanoshells improve single nanoparticle molecular sensors,” Nano Lett. 4, 1853–1857 (2004). [CrossRef]
  10. S. J. Oldenburg, S. L. Westcott, R. D. Averitt, and N. J. Halas, “Surface enhanced Raman scattering in the near infrared using metal nanoshell substrates,” J. Chem. Phys. 111, 4729–4735 (1999). [CrossRef]
  11. F. Le, D. W. Brandl, Y. A. Urzhumov, H. Wang, J. Kundu, N. J. Halas, J. Aizpurua, and P. Nordlander, “Metallic nanoparticle arrays: A common substrate for both surface-enhanced Raman scattering and surface-enhanced infrared absorption,” ACS Nano 2, 707–718 (2008). [CrossRef]
  12. Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104, 207402 (2010). [CrossRef]
  13. S. Zaiba, F. Lerouge, A.-M. Gabudean, M. Focsan, J. Lerme, T. Gallavardin, O. Maury, C. Andraud, S. Parola, and P. Baldeck, “Transparent plasmonic nanocontainers protect organic fluorophores against photobleaching,” Nano Lett. 11, 2043–2047 (2011). [CrossRef]
  14. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Toward the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011). [CrossRef]
  15. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007). [CrossRef]
  16. N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010). [CrossRef]
  17. J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10, 1717–1721 (2010). [CrossRef]
  18. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interferences between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105, 077401 (2010). [CrossRef]
  19. J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensionnal mapping of single gold nanaoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18, 22314–22323 (2010). [CrossRef]
  20. J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P.-F. Brevet, “Nonlinear fano-profiles in the optical second-harmonic generation from silver nanoparticles,” (in press).
  21. R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Dipole limit in second-harmonic generation from arrays of gold nanoparticles,” Opt. Express 19, 26866–26871 (2011). [CrossRef]
  22. Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11, 5519–5523 (2011). [CrossRef]
  23. B. K. Canfield, H. Husu, J. Laukkanen, B. F. 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]
  24. V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from Chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104, 127401 (2010). [CrossRef]
  25. V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: Switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9, 3945–3948 (2009). [CrossRef]
  26. A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J.-F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20, 220–227 (2012). [CrossRef]
  27. A. Bouhelier, M. Beversluis, A. Hartschuch, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003). [CrossRef]
  28. R. Kullock, A. Hille, A. Haußmann, S. Grafström, and L. M. Eng, “SHG simulations of plasmonic nanoparticles using curved elements,” Opt. Express 19, 14426–14436 (2011). [CrossRef]
  29. Y. Zeng, W. Hoyer, J. J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109 (2009). [CrossRef]
  30. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008). [CrossRef]
  31. A. Benedetti, M. Centini, M. Bertolotti, and C. Sibilia, “Second harmonic generation from 3D nanoantennas: on the surface and bulk contributions by far-field pattern analysis,” Opt. Express 19, 26752–26767 (2011). [CrossRef]
  32. 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]
  33. 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]
  34. Y. Pavlyukh, and W. Hübner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70, 245434 (2004). [CrossRef]
  35. D. Östling, P. Stampfli, and K. H. Benneman, “Theory of nonlinear optical properties of small metallic spheres,” Z. Phys. D 28, 169–175 (1993). [CrossRef]
  36. G. Gonella, and H.-L. Dai, “Determination of adsorption geometry on spherical particles from nonlinear Mie theory analysis of surface second harmonic generation,” Phys. Rev. B 84, 121402(R) (2011). [CrossRef]
  37. B. Schürer, S. Wunderlich, C. Sauerbeck, U. Peschel, and W. Peukert, “Probing colloidal interfaces by angle-resolved second harmonic light scattering,” Phys. Rev. B 82, 241404 (2010). [CrossRef]
  38. S. Wunderlich, B. Schürer, C. Sauerbeck, W. Peukert, and U. Peschel, “Molecular Mie model for second harmonic generation and sum frequency generation,” Phys. Rev. B 84, 235403 (2011). [CrossRef]
  39. A. G. F. de Beer, and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79, 155420 (2009). [CrossRef]
  40. J. Xu, and X. Zhang, “Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres,” Opt. Express 20, 1668–1684 (2012). [CrossRef]
  41. A. L. Aden, and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951). [CrossRef]
  42. C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  43. Z. J. Li, S. Y. Gao, and D. Han, “Tuning the mapping of second-harmonic generation in silver nanoshell,” Eur. Phys. J. Appl. Phys. 56, 10404 (2011). [CrossRef]
  44. G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, and P. F. Brevet, “Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions,” Phys. Rev. B 82, 235403 (2010). [CrossRef]
  45. F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80, 233402 (2009). [CrossRef]
  46. J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980). [CrossRef]
  47. T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena (Elsevier, 1991), pp. 353–415.
  48. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
  49. U. Kreibig and M. Vollmer, Optical Properties of Metal Cluster, Springer Series in Materials Science (Springer-Verlag, 1995.
  50. J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971). [CrossRef]
  51. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  52. C. Sönnischen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402(2002). [CrossRef]
  53. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticle,” Nano Lett. 12, 1697–1701 (2012). [CrossRef]

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