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Second-Order Nonlinear Optical Properties of Plasmonic Nanostructures

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Plasmonics: Theory and Applications

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 15))

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Abstract

We review our work on second-order nonlinear optical properties of plasmonic nanostructures. In order to achieve the required non-centrosymmetry of the structures, our samples consist of arrays of L-shaped nanoparticles and T-shaped nanodimers. The samples are investigated by polarization-dependent second-harmonic generation to address the tensorial nonlinear response. We show that the response can be strongly modified by symmetry-breaking defects and other deviations of the samples from ideal. Nonlinear sources localized to defects can also give rise to higher-multipolar emission. The defect problem is overcome with a recent and significant improvement in sample quality, allowing the dipole limit of the nonlinear response to be reached. This achievement opens the path towards plasmonic metamaterials with tailorable nonlinear properties. As a demonstration of this possibility, we modify the nonlinear response by the mutual arrangement of the L-shaped particles in the array. We will also summarize our numerical boundary-element method to describe the nonlinear response of nanoparticles.

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References

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

    Google Scholar 

  2. S. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007)

    Google Scholar 

  3. K. Kelly, E. Coronado, L. Zhao, G. Schatz, The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment. J. Phys. Chem. B 107, 668–677 (2003)

    CAS  Google Scholar 

  4. V.M. Shalaev, Optical negative-index metamaterials. Nat. Photon. 1, 41 (2007)

    CAS  Google Scholar 

  5. C.M. Soukoulis, M. Wegener, Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nat. Photon. 5, 523–530 (2011)

    CAS  Google Scholar 

  6. S. Linden, J. Kuhl, H. Giessen, Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction. Phys. Rev. Lett. 86, 4688–4691 (2001)

    CAS  Google Scholar 

  7. L. Zhao, K.L. Kelly, G.C. Schatz, The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width. J. Phys. Chem. B 107, 7343–7350 (2003)

    CAS  Google Scholar 

  8. A. Christ, S.G. Tikhodeev, N.A. Gippius, J. Kuhl, H. Giessen, Waveguide-plasmon polaritons: Strong coupling of photonic and electronic resonances in a metallic photonic crystal slab. Phys. Rev. Lett. 91, 183901 (2003)

    CAS  Google Scholar 

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

    Google Scholar 

  10. Y. Chu, E. Schonbrun, T. Yang, K.B. Crozier, Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays. Appl. Phys. Lett. 93, 181108 (2008)

    Google Scholar 

  11. B. Auguié, W.L. Barnes, Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 101, 143902 (2008)

    Google Scholar 

  12. K.D. Ko, A. Kumar, K.H. Fung, R. Ambekar, G.L. Liu, N.X. Fang, K.C. Toussaint, Nonlinear optical response from arrays of au bowtie nanoantennas. Nano Lett. 11, 61–65 (2011)

    CAS  Google Scholar 

  13. E. Prodan, C. Radloff, N.J. Halas, P. Nordlander, A hybridization model for the plasmon response of complex nanostructures. Science 302, 419–422 (2003)

    CAS  Google Scholar 

  14. T.D. Corrigan, P.W. Kolb, A.B. Sushkov, H.D. Drew, D.C. Schmadel, R.J. Phaneuf, Optical plasmonic resonances in split-ring resonator structures: An improved LC model. Opt. Express 16, 19850–19864 (2008)

    CAS  Google Scholar 

  15. K. Aydin, I. Pryce, H. Atwater, Symmetry breaking and strong coupling in planar optical metamaterials. Opt. Express 18, 13407–13417 (2010)

    CAS  Google Scholar 

  16. P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, M. Orenstein, Resonances on-demand for plasmonic nano-particles. Nano Lett. 11, 2329–2333 (2011)

    CAS  Google Scholar 

  17. K. Li, M.I. Stockman, D.J. Bergman, Self-similar chain of metal nanospheres as an efficient nanolens. Phys. Rev. Lett. 91, 227402 (2003)

    Google Scholar 

  18. M. Stockman, D. Bergman, C. Anceau, S. Brasselet, J. Zyss, Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: Nanoscale dephasing, depolarization, and correlations. Phys. Rev. Lett. 92, 057402 (2004)

    Google Scholar 

  19. K. Kneipp, Y. Wang, H. Kneipp, L.T. Perelman, I. Itzkan, R.R. Dasari, M.S. Feld, Single molecule detection using surface-enhanced Raman scattering (SERS). Phys. Rev. Lett. 78, 1667–1670 (1997)

    CAS  Google Scholar 

  20. S. Nie, S.R. Emory, Probing single molecules and single nanoparticles by surface-enhanced Raman scattering. Science 275, 1102–1106 (1997)

    CAS  Google Scholar 

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

    Google Scholar 

  22. T.F. Heinz, H.W.K. Tom, Y.R. Shen, Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation. Phys. Rev. A 28, 1883–1885 (1983)

    CAS  Google Scholar 

  23. T. Rasing, Y.R. Shen, M.W. Kim, P. Valint, J. Bock, Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation. Phys. Rev. A 31, 537–539 (1985)

    CAS  Google Scholar 

  24. T.F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, ed. by H.-E. Ponath, G.I. Stegeman. Second-Order Nonlinear Optical Effects at Surfaces and Interfaces (Elsevier, Amsterdam, 1991), pp. 353–416

    Google Scholar 

  25. B. Canfield, S. Kujala, K. Laiho, K. Jefimovs, J. Turunen, M. Kauranen, Chirality arising from small defects in gold nanoparticle arrays. Opt. Express 14, 950–955 (2006)

    Google Scholar 

  26. G. Mie, Beiträge zur optik trüber medien, speziell kolloidaler metallösungen. Annal. der Phys. 330, 377–445 (1908)

    Google Scholar 

  27. C.F. Bohren, D.R. Huffman, Absorption and Scattering by an Arbitrary Particle. Wiley-VCH Verlag GmbH, 2007)

    Google Scholar 

  28. B. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, M. Kauranen, A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures. J. Opt. A 8, S278–S284 (2006)

    Google Scholar 

  29. R.W. Boyd, Nonlinear Optics, 3rd edn. (Academic Press, San Diego, 2008)

    Google Scholar 

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

    Google Scholar 

  31. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, P.-F. Brevet, Multipolar second-harmonic generation in noble metal nanoparticles. J. Opt. Soc. Am. B 25, 955–960 (2008)

    CAS  Google Scholar 

  32. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, 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)

    CAS  Google Scholar 

  33. L. Novotny, B. Hecht, Principles of Nano-optics, 1st edn. (Cambridge University Press, Cambridge, 2007)

    Google Scholar 

  34. M. Kauranen, T. Verbiest, S. Elshocht, A. Persoons, Chirality in surface nonlinear optics. Opt. Mater. 9, 286–294 (1998)

    CAS  Google Scholar 

  35. M. Zdanowicz, S. Kujala, H. Husu, M. Kauranen, Effective medium multipolar tensor analysis of second-harmonic generation from metal nanoparticles. New J. Phys. 13, 023025 (2011)

    Google Scholar 

  36. B. Lamprecht, A. Leitner, F. Aussenegg, SHG studies of plasmon dephasing in nanoparticles. Appl. Phys. B 68, 419–423 (1999)

    CAS  Google Scholar 

  37. H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N.-V. Tkachenko, H. Lemmetyinen, Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles. J. Nonlinear Opt. Phys. Mater. 11, 421–432 (2002)

    CAS  Google Scholar 

  38. B. Canfield, K. Kujala, K. Jefimovs, J. Turunen, M. Kauranen, Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles. Opt. Express 12, 5418–5423 (2004)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  40. B. Canfield, H. Husu, J. Kontio, J. Viheriälä, T. Rytkönen, T. Niemi, E. Chandler, A. Hrin, J. Squier, M. Kauranen, Inhomogeneities in the nonlinear tensorial responses of arrays of gold nanodots. New J. Phys. 10, 013001 (2008)

    Google Scholar 

  41. S. Kujala, B. Canfield, M. Kauranen, Y. Svirko, J. Turunen, Multipolar analysis of second-harmonic radiation from gold nanoparticles. Opt. Express 16, 17196–17208 (2008)

    CAS  Google Scholar 

  42. S. Kujala, B. Canfield, M. Kauranen, Y. Svirko, T. Turunen, Multipole interference in the second-harmonic optical radiation from gold nanoparticles. Phys. Rev. Lett. 98, 167403 (2007)

    Google Scholar 

  43. C.K. Chen, A.R.B. de Castro, Y.R. Shen, Surface-enhanced second-harmonic generation. Phys. Rev. Lett. 46, 145–148 (1981)

    CAS  Google Scholar 

  44. I.I. Smolyaninov, A.V. Zayats, C.C. Davis, Near-field second harmonic generation from a rough metal surface. Phys. Rev. B 56, 9290–9293 (1997)

    CAS  Google Scholar 

  45. A.V. Zayats, T. Kalkbrenner, V. Sandoghdar, J. Mlynek, Second-harmonic generation from individual surface defects under local excitation. Phys. Rev. B 61, 4545–4548 (2000)

    CAS  Google Scholar 

  46. S.I. Bozhevolnyi, J. Beermann, V. Coello, Direct observation of localized second-harmonic enhancement in random metal nanostructures. Phys. Rev. Lett. 90, 197403 (2003)

    Google Scholar 

  47. C. Anceau, S. Brasselet, J. Zyss, P. Gadenne, Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy. Opt. Lett. 28, 713–715 (2003)

    CAS  Google Scholar 

  48. R. Jin, J.E. Jureller, H.Y. Kim, N.F. Scherer, Correlating second harmonic optical responses of single Ag nanoparticles with morphology. J. Am. Chem. Soc. 127, 12482–12483 (2005)

    CAS  Google Scholar 

  49. M. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, P.-M. Adam, Near-field second-harmonic generation in single gold nanoparticles. Appl. Phys. Lett. 92, 093119 (2008)

    Google Scholar 

  50. S. Takahashi, A.V. Zayats, Near-field second-harmonic generation at a metal tip apex. Appl. Phys. Lett. 80, 3479–3481 (2002)

    CAS  Google Scholar 

  51. A. Bouhelier, M. Beversluis, A. Hartschuh, L. Novotny, Near-field second-harmonic generation induced by local field enhancement. Phys. Rev. Lett. 90, 013903 (2003)

    CAS  Google Scholar 

  52. C.C. Neacsu, G.A. Reider, M.B. Raschke, Second-harmonic generation from nanoscopic metal tips: Symmetry selection rules for single asymmetric nanostructures. Phys. Rev. B 71, 201402 (2005)

    Google Scholar 

  53. J. Kontio, H. Husu, J. Simonen, M. Huttunen, J. Tommila, M. Pessa, M. Kauranen, Nanoimprint fabrication of gold nanocones with 10 nm tips for enhanced optical interactions. Opt. Lett. 34, 1979–1981 (2009)

    Google Scholar 

  54. A. Nahata, R.A. Linke, T. Ishi, K. Ohashi, Enhanced nonlinear optical conversion from a periodically nanostructured metal film. Opt. Lett. 28, 423–425 (2003)

    Google Scholar 

  55. Y. Zhang, N.K. Grady, C. Ayala-Orozco, N.J. Halas, Three-dimensional nanostructures as highly efficient generators of second harmonic light. Nano Lett. 11, 5519–5523 (2011)

    CAS  Google Scholar 

  56. M. Klein, C. Enkrich, M. Wegener, S. Linden, Second-harmonic generation from magnetic metamaterials. Science 313, 502–504 (2006)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  58. M.W. Klein, M. Wegener, N.-A. Feth, S. Linden, Experiments on second- and third-harmonic generation from magnetic metamaterials: Erratum. Opt. Express 16, 8055–8055 (2008)

    Google Scholar 

  59. N. Feth, S. Linden, M. Klein, M. Decker, F. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. Koch, J. Moloney, M. Wegener, Second-harmonic generation from complementary split-ring resonators. Opt. Lett. 33, 1975–1977 (2008)

    CAS  Google Scholar 

  60. Y. Zeng, W. Hoyer, J. Liu, S.W. Koch, J.V. Moloney, Classical theory for second-harmonic generation from metallic nanoparticles. Phys. Rev. B 79, 235109 (2009)

    Google Scholar 

  61. F.B.P. Niesler, N. Feth, S. Linden, M. Wegener, Second-harmonic optical spectroscopy on split-ring-resonator arrays. Opt. Lett. 36, 1533–1535 (2011)

    Google Scholar 

  62. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391, 667–669 (1998)

    CAS  Google Scholar 

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

    Google Scholar 

  64. T. Xu, X. Jiao, G.-P. Zhang, S. Blair, Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement. Opt. Express 15, 13894–13906 (2007)

    CAS  Google Scholar 

  65. F. Eftekhari, R. Gordon, Enhanced second harmonic generation from noncentrosymmetric nanohole arrays in a gold film. IEEE J. Sel. Top. Quant. Electron. 14, 1552–1558 (2008)

    CAS  Google Scholar 

  66. A. Lesuffleur, L.K. Swaroop Kumar, R. Gordon, Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film. Appl. Phys. Lett. 88, 261104 (2006)

    Google Scholar 

  67. M.D. McMahon, R. Lopez, R.F. Haglund, E.A. Ray, P.H. Bunton, Second-harmonic generation from arrays of symmetric gold nanoparticles. Phys. Rev. B 73, 041401 (2006)

    Google Scholar 

  68. M. McMahon, D. Ferrara, C. Bowie, R. Lopez, Second harmonic generation from resonantly excited arrays of gold nanoparticles. Appl. Phys. B 87, 256–265 (2007)

    Google Scholar 

  69. J. Nappa, I. Russier-Antoine, E. Benichou, C. Jonin, P. Brevet, Second harmonic generation from small gold metallic particles: From the dipolar to the quadrupolar response. J. Chem. Phys. 125, 184712 (2006)

    Google Scholar 

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

    CAS  Google Scholar 

  71. J. Duboisset, I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, P.F. Brevet, Single metallic nanoparticle sensitivity with hyper Rayleigh scattering. J. Phys. Chem. C 113, 13477–13481 (2009)

    CAS  Google Scholar 

  72. J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, P.-F. Brevet, Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium. Nano Lett. 10, 1717–1721 (2010)

    CAS  Google Scholar 

  73. J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, P.-F. Brevet, Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation. Opt. Express 18, 22314–22323 (2010)

    CAS  Google Scholar 

  74. G. Bachelier, J. Butet, I. Russier-Antoine, C. Jonin, E. Benichou, 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)

    Google Scholar 

  75. C. Awada, C. Jonin, F. Kessi, P. Adam, S. Kostcheev, R. Bachelot, P. Royer, M. Samah, I. Russier-Antoine, E. Benichou, G. Bachelier, P. Brevet, Polarized second harmonic response of square, hexagonal and random arrays of gold metallic nanocylinders. Opt. Mater. 33, 1440–1444 (2011)

    CAS  Google Scholar 

  76. C. Awada, F. Kessi, C. Jonin, P.M. Adam, S. Kostcheev, R. Bachelot, P. Royer, I. Russier-Antoine, E. Benichou, G. Bachelier, P.F. Brevet, On- and off-axis second harmonic generation from an array of gold metallic nanocylinders. J. Appl. Phys. 110, 023109 (2011)

    Google Scholar 

  77. T. Atay, J.-H. Song, A. Nurmikko, Strongly interacting plasmon nanoparticle pairs: From dipole-dipole interaction to conductively coupled regime. Nano Lett. 4, 1627–1631 (2004)

    CAS  Google Scholar 

  78. J. Aizpurua, G.W. Bryant, L.J. Richter, F.J.G. De Abajo, B.K. Kelley, T. Mallouk, Optical properties of coupled metallic nanorods for field-enhanced spectroscopy. Phys. Rev. B 71, 235420 (2005)

    Google Scholar 

  79. I. Romero, J. Aizpurua, G.W. Bryant, F.J.G. De Abajo, Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers. Opt. Express 14, 9988–9999 (2006)

    Google Scholar 

  80. A. Sundaramurthy, K.B. Crozier, G.S. Kino, D.P. Fromm, P.J. Schuck, W.E. Moerner, Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles. Phys. Rev. B 72, 165409 (2005)

    Google Scholar 

  81. M. Danckwerts, L. Novotny, Optical frequency mixing at coupled gold nanoparticles. Phys. Rev. Lett. 98, 026104 (2007)

    Google Scholar 

  82. K. Li, M.I. Stockman, D.J. Bergman, Enhanced second harmonic generation in a self-similar chain of metal nanospheres. Phys. Rev. B 72, 153401 (2005)

    Google Scholar 

  83. B. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, M. Kauranen, Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers. Nano Lett. 7, 1251–1255 (2007)

    CAS  Google Scholar 

  84. H. Husu, B. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, M. Kauranen, Chiral coupling in gold nanodimers. Appl. Phys. Lett. 93, 183115 (2008)

    Google Scholar 

  85. J. Maki, M. Kauranen, A. Persoons, Surface second-harmonic generation from chiral materials. Phys. Rev. B 51, 1425–1434 (1995)

    CAS  Google Scholar 

  86. P. Biagioni, J.-S. Huang, B. Hecht, Nanoantennas for visible and infrared radiation. Rep. Prog. Phys. 75, 024402 (2012)

    Google Scholar 

  87. H. Duan, A.I. Fernandez-Dominguez, M. Bosman, S.A. Maier, J.K.W. Yang, Nanoplasmonics: Classical down to the nanometer scale. Nano Lett. 12, 1683–1689 (2012)

    CAS  Google Scholar 

  88. R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, M. Kauranen, Dipole limit in second-harmonic generation from arrays of gold nanoparticles. Opt. Express 19, 26866–26871 (2011)

    CAS  Google Scholar 

  89. M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, M. Kuittinen, Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating. Appl. Phys. Lett. 91, 111109 (2007)

    Google Scholar 

  90. A. Saari, G. Genty, M. Siltanen, P. Karvinen, P. Vahimaa, M. Kuittinen, M. Kauranen, Giant enhancement of second-harmonic generation in multiple diffraction orders from sub-wavelength resonant waveguide grating. Opt. Express 18, 12298–12303 (2010)

    CAS  Google Scholar 

  91. H. Husu, J. Mäkitalo, R. Siikanen, G. Genty, H. Pietarinen, J. Lehtolahti, J. Laukkanen, M. Kuittinen, M. Kauranen, Spectral control in anisotropic resonance-domain metamaterials. Opt. Lett. 36, 2375–2377 (2011)

    Google Scholar 

  92. H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, M. Kauranen, Metamaterials with tailored nonlinear optical response. Nano Lett. 12, 673–677 (2012)

    CAS  Google Scholar 

  93. M. Karamehmedovic, R. Schuh, V. Schmidt, T. Wriedt, C. Matyssek, W. Hergert, A. Stalmashonak, G. Seifert, O. Stranik, Comparison of numerical methods in near-field computation for metallic nanoparticles. Opt. Express 19, 8939–8953 (2011)

    CAS  Google Scholar 

  94. M.G. Araújo, J.M. Taboada, D.M. Solís, J. Rivero, L. Landesa, F. Obelleiro, Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers. Opt. Express 20, 9161–9171 (2012)

    Google Scholar 

  95. R. Garg, Analytical and Computational Methods in Electromagnetics. Artech House Electromagnetic Analysis Series (Artech House, London, 2008)

    Google Scholar 

  96. Y.R. Shen, Surface properties probed by second-harmonic and sum-frequency generation. Nature 337, 519–525 (1989)

    CAS  Google Scholar 

  97. N. Bloembergen, R. Chang, S. Jha, C. Lee, Optical second-harmonic generation in reflection from media with inversion symmetry. Phys. Rev. 174, 813–822 (1968)

    CAS  Google Scholar 

  98. D. Colton, R. Kress, Integral Equation Methods in Scattering Theory. Pure and Applied Mathematics Series (Krieger Publishing Company, Malabar, 1991)

    Google Scholar 

  99. J.D. Jackson, Classical Electrodynamics, 2nd edn. (Wiley, New York, 1975)

    Google Scholar 

  100. W. Gibson, The Method of Moments in Electromagnetics. Electrical Engineering (Chapman and Hall/CRC, New York, 2008)

    Google Scholar 

  101. J. Sipe, New green-function formalism for surface optics. J. Opt. Soc. Am. B 4, 481–498 (1987)

    Google Scholar 

  102. L. Cao, N.C. Panoiu, R.M. Osgood, Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures. Phys. Rev. B 75, 205401 (2007)

    Google Scholar 

  103. L. Cao, N.C. Panoiu, R.D.R. Bhat, R.M. Osgood, Surface second-harmonic generation from scattering of surface plasmon polaritons from radially symmetric nanostructures. Phys. Rev. B 79, 235416 (2009)

    Google Scholar 

  104. J. Dewitz, W. Hübner, K. Bennemann, Theory for nonlinear Mie-scattering from spherical metal clusters. Zeits. Phys. D Atoms, Mol. Clusters 37, 75–84 (1996)

    Google Scholar 

  105. J. Dadap, J. Shan, T. 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)

    CAS  Google Scholar 

  106. Y. Pavlyukh, W. Hübner, Nonlinear Mie scattering from spherical particles. Phys. Rev. B 70, 245434 (2004)

    Google Scholar 

  107. A.G.F. de Beer, S. Roke, Nonlinear Mie theory for second-harmonic and sum-frequency scattering. Phys. Rev. B 79, 155420 (2009)

    Google Scholar 

  108. J. Xu, X. Zhang, Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres. Opt. Express 20, 1668–1684 (2012)

    Google Scholar 

  109. E. Centeno, D. Felbacq, Second-harmonic emission in two-dimensional photonic crystals. J. Opt. Soc. Am. B 23, 2257–2264 (2006)

    CAS  Google Scholar 

  110. C.G. Biris, N.C. Panoiu, Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires. Phys. Rev. B 81, 195102 (2010)

    Google Scholar 

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

    Google Scholar 

  112. W.L. Schaich, Second harmonic generation by periodically-structured metal surfaces. Phys. Rev. B 78, 195416 (2008)

    Google Scholar 

  113. W. Nakagawa, R.-C. Tyan, Y. Fainman, Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation. J. Opt. Soc. Am. A 19, 1919–1928 (2002)

    Google Scholar 

  114. B. Bai, J. Turunen, Fourier modal method for the analysis of second-harmonic generation in two-dimensionally periodic structures containing anisotropic materials. J. Opt. Soc. Am. B 24, 1105–1112 (2007)

    CAS  Google Scholar 

  115. S.I. Bozhevolnyi, V.Z. Lozovski, Self-consistent model for second-harmonic near-field microscopy. Phys. Rev. B 61, 11139–11150 (2000)

    CAS  Google Scholar 

  116. A. Benedetti, M. Centini, C. Sibilia, M. Bertolotti, Engineering the second harmonic generation pattern from coupled gold nanowires. J. Opt. Soc. Am. B 27, 408–416 (2010)

    CAS  Google Scholar 

  117. M. Centini, A. Benedetti, C. Sibilia, M. Bertolotti, Coupled 2D Ag nano-resonator chains for enhanced and spatially tailored second harmonic generation. Opt. Express 19, 8218–8232 (2011)

    CAS  Google Scholar 

  118. J. Mäkitalo, S. Suuriniemi, M. Kauranen, Boundary element method for surface nonlinear optics of nanoparticles. Opt. Express 19, 23386–23399 (2011)

    Google Scholar 

  119. J. Aizpurua, P. Hanarp, D.S. Sutherland, M. Käll, G.W. Bryant, F. Garcia de Abajo, Optical properties of gold nanorings. J. Phys. Rev. Lett. 90, 057401 (2003)

    Google Scholar 

  120. G.W. Bryant, F.J. Garcia de Abajo, J. Aizpurua, Mapping the plasmon resonances of metallic nanoantennas. Nano Lett. 8, 631–636 (2008)

    Google Scholar 

  121. A.M. Kern, O.J.F. Martin, Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures. J. Opt. Soc. Am. A 26, 732–740 (2009)

    Google Scholar 

  122. B. Gallinet, A.M. Kern, O.J.F. Martin, Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach. J. Opt. Soc. Am. A 27, 2261–2271 (2010)

    CAS  Google Scholar 

  123. J.A. Stratton, Electromagnetic Theory, 1st edn. (McGraw-Hill, New York, 1941)

    Google Scholar 

  124. S. Rao, D. Wilton, A. Glisson, Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Ant. Propag. 30, 409–418 (1982)

    Google Scholar 

  125. R.F. Harrington, Field Computation by Moment Methods (Wiley-IEEE Press, New York, 1993)

    Google Scholar 

  126. G. Valerio, P. Baccarelli, P. Burghignoli, A. Galli, Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions. IEEE Trans. Ant. Propag. 55, 1630–1643 (2007)

    Google Scholar 

  127. R. Coifman, V. Rokhlin, S. Wandzura, The fast multipole method for the wave equation: A pedestrian prescription. IEEE Ant. Propag. Mag. 35, 7–12 (1993)

    Google Scholar 

  128. M. Bebendorf, Approximation of boundary element matrices. Numerische Mathematik 86, 565–589 (2000)

    Google Scholar 

  129. N.J. Halas, S. Lal, W.-S. Chang, S. Link, P. Nordlander, Plasmons in strongly coupled metallic nanostructures. Chem. Rev. 111, 3913–3961 (2011)

    CAS  Google Scholar 

  130. F. Wang, F. Rodríguez, W. Albers, R. Ahorinta, J. Sipe, M. Kauranen, Surface and bulk contributions to the second-order nonlinear optical response of a gold film. Phys. Rev. B 80, 233402 (2009)

    Google Scholar 

  131. Y. Zeng, J. Moloney, Volume electric dipole origin of second-harmonic generation from metallic membrane with noncentrosymmetric patterns. Opt. Lett. 34, 2844–2846 (2009)

    Google Scholar 

  132. S. Tang, D.J. Cho, H. Xu, W. Wu, Y.R. Shen, L. Zhou, Nonlinear responses in optical metamaterials: theory and experiment. Opt. Express 19, 18283–18293 (2011)

    CAS  Google Scholar 

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Acknowledgments

We thank B. K. Canfield, G. Genty, K. Koskinen, S. Kujala, H. Pietarinen, R. Siikanen, S. Suuriniemi, Y. Svirko, and J. Turunen for fruitful discussions and/or help in measurements. This work was supported by the Academy of Finland (132438 and 134980), by the Graduate School of the Tampere University of Technology, by the Finnish Foundation for Technology Promotion, and by the Wihuri Foundation.

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Authors and Affiliations

  1. Department of Physics, Tampere University of Technology, P.O. Box 692, 33101, Tampere, Finland

    Martti Kauranen, Hannu Husu, Jouni Mäkitalo, Robert Czaplicki & Mariusz Zdanowicz

  2. Centre for Metrology and Accreditation (MIKES), P.O. Box 9, 02151, Espoo, Finland

    Hannu Husu

  3. National Institute of Telecommunications, Szachowa 1, 04894, Warsaw, Poland

    Mariusz Zdanowicz

  4. Department of Physics and Mathematics, University of Eastern Finland, 80101, Joensuu, Finland

    Joonas Lehtolahti, Janne Laukkanen & Markku Kuittinen

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  1. Martti Kauranen
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Correspondence to Martti Kauranen .

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  1. Department of Physics, Jackson State University, Jackson, USA

    Tigran V. Shahbazyan

  2. Georgia State University Dept. Physics & Astronomy, Atlanta, Georgia, USA

    Mark I. Stockman

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Kauranen, M. et al. (2013). Second-Order Nonlinear Optical Properties of Plasmonic Nanostructures. In: Shahbazyan, T., Stockman, M. (eds) Plasmonics: Theory and Applications. Challenges and Advances in Computational Chemistry and Physics, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7805-4_6

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