OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 10 — Nov. 8, 2013

Surface integral method for second harmonic generation in metal nanoparticles including both local-surface and nonlocal-bulk sources

Carlo Forestiere, Antonio Capretti, and Giovanni Miano  »View Author Affiliations


JOSA B, Vol. 30, Issue 9, pp. 2355-2364 (2013)
http://dx.doi.org/10.1364/JOSAB.30.002355


View Full Text Article

Enhanced HTML    Acrobat PDF (756 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a numerical method, based on surface integral equations (SIE), for evaluating the second harmonic (SH) scattering by metal nanoparticles (NPs) of arbitrary shape, considering both nonlocal-bulk and local-surface SH sources, induced by the electromagnetic field at the fundamental frequency. We demonstrate that the contribution of the nonlocal-bulk sources can be taken into account through equivalent surface electric and magnetic currents. We numerically solve the SIE problem by using the Galerkin method and the Rao–Wilton–Glisson basis functions in the framework of the distribution theory. The accuracy of the proposed method is verified by comparing with the SH-Mie analytical solution. As an example of a complex-shaped particle, we investigate the SH scattering by a triangular nanoprism. This method paves the way for a better understanding of the SH generation process in arbitrarily shaped NPs and can also have a high impact on the design of novel nanoplasmonic devices with enhanced SH emission.

© 2013 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4350) Nonlinear optics : Nonlinear optics at surfaces
(240.6680) Optics at surfaces : Surface plasmons
(290.5850) Scattering : Scattering, particles
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 7, 2013
Revised Manuscript: June 16, 2013
Manuscript Accepted: July 12, 2013
Published: August 7, 2013

Virtual Issues
Vol. 8, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Carlo Forestiere, Antonio Capretti, and Giovanni Miano, "Surface integral method for second harmonic generation in metal nanoparticles including both local-surface and nonlocal-bulk sources," J. Opt. Soc. Am. B 30, 2355-2364 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josab-30-9-2355


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012). [CrossRef]
  2. S. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).
  3. 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]
  4. T. F. Heinz, Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), Chap. 5, pp. 397–405.
  5. 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]
  6. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B 33, 8254–8263 (1986). [CrossRef]
  7. 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]
  8. Y. Pavlyukh and W. Hübner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70, 245434 (2004). [CrossRef]
  9. 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]
  10. 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]
  11. C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” J. Opt. Soc. Am. B 21, 36–44 (2004). [CrossRef]
  12. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Nonlinear Mie theory for the second harmonic generation in metallic nanoshells,” J. Opt. Soc. Am. B 29, 2213–2221 (2012). [CrossRef]
  13. B. Lambrecht, A. Leitner, and F. Aussenegg, “Femtosecond decay-time measurement of electron-plasma oscillation in nanolithographically designed silver particles,” Appl. Phys. B 64, 269–272 (1997). [CrossRef]
  14. B. 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]
  15. S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett. 109, 015502 (2012). [CrossRef]
  16. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006). [CrossRef]
  17. M. D. McMahon, R. Lopez, R. F. Haglund, E. A. Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]
  18. A. Capretti, G. F. Walsh, S. Minissale, J. Trevino, C. Forestiere, G. Miano, and L. D. Negro, “Multipolar second harmonic generation from planar arrays of au nanoparticles,” Opt. Express 20, 15797–15806 (2012). [CrossRef]
  19. 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]
  20. 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]
  21. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 7196, 757–760 (2008).
  22. W. L. Schaich, “Second harmonic generation by periodically structured metal surfaces,” Phys. Rev. B 78, 195416 (2008). [CrossRef]
  23. Y. Zeng, W. Hoyer, 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]
  24. 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]
  25. 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]
  26. C. Cirac, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012). [CrossRef]
  27. A. Benedetti, M. Centini, C. Sibilia, and M. Bertolotti, “Engineering the second harmonic generation pattern from coupled gold nanowires,” J. Opt. Soc. Am. B 27, 408–416 (2010). [CrossRef]
  28. 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]
  29. J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011). [CrossRef]
  30. 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]
  31. N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968). [CrossRef]
  32. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 1984).
  33. J. G. Van Bladel, Electromagnetic Fields (IEEE Press Series on Electromagnetic Wave Theory) (Wiley, 2007).
  34. J. Van Bladel, “Some remarks on Green’s dyadic for infinite space,” IRE Trans. Antennas Propag. 9, 563–566 (1961). [CrossRef]
  35. J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B 35, 9091–9094 (1987). [CrossRef]
  36. R. Harrington, Field Computation by Moment Methods (Macmillan, 1968).
  37. S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982). [CrossRef]
  38. J. Meixner, “The behavior of electromagnetic fields at edges,” IEEE Trans. Antennas Propag. 20, 442–446 (1972). [CrossRef]
  39. R. Graglia, G. Lombardi, D. Wilton, and W. Johnson, “Modeling edge singularities in the method of moments,” in Proceedings of IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 3A, pp. 56–59.
  40. R. Graglia, “On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle,” IEEE Trans. Antennas Propag. 41, 1448–1455 (1993). [CrossRef]
  41. A. Capretti, C. Forestiere, L. Dal Negro, and G. Miano, “Full-wave analytical solution of second-harmonic generation in metal nanospheres,” Plasmonics, arXiv:1301.1628 (to be published).
  42. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
  43. 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]
  44. 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]
  45. M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007). [CrossRef]
  46. 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, 184712 (2006). [CrossRef]
  47. 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, 077401 (2010). [CrossRef]
  48. G. Gonella, W. Gan, B. Xu, and H.-L. Dai, “The effect of composition, morphology, and susceptibility on nonlinear light scattering from metallic and dielectric nanoparticles,” J. Phys. Chem. Lett. 3, 2877–2881 (2012). [CrossRef]
  49. T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009). [CrossRef]
  50. M. Centini, A. Benedetti, M. Scalora, C. Sibilia, and M. Bertolotti, “Second harmonic generation from metallic 2D scatterers,” Proc. SPIE 7354, 73540F (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited