## Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres |

Optics Express, Vol. 20, Issue 2, pp. 1668-1684 (2012)

http://dx.doi.org/10.1364/OE.20.001668

Acrobat PDF (2264 KB)

### Abstract

The theory of second harmonic generation (SHG) in three-dimensional structures consisting of arbitrary distributions of metallic spheres made of centrosymmetric materials is developed by means of multiple scattering of electromagnetic multipole fields. The electromagnetic field at both the fundamental frequency and second harmonic, as well as the scattering cross section, are calculated in a series of particular cases such as a single metallic sphere, two metallic spheres, chains of metallic spheres, and other distributions of the metallic spheres. It is shown that the linear and nonlinear optical response of all ensembles of metallic spheres is strongly influenced by the excitation of localized surface plasmon-polariton resonances. The physical origin for such a phenomenon has also been analyzed.

© 2012 OSA

## 1. Introduction

6. 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**(12), 121402(R) (2011). [CrossRef]

7. K. B. Eisenthal, “Second harmonic spectroscopy of aqueous nano- and microparticle interfaces,” Chem. Rev. **106**(4), 1462–1477 (2006). [CrossRef] [PubMed]

12. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. **105**(7), 077401 (2010). [CrossRef] [PubMed]

12. J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. **105**(7), 077401 (2010). [CrossRef] [PubMed]

13. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science **305**(5685), 788–792 (2004). [CrossRef] [PubMed]

16. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature **455**(7211), 376–379 (2008). [CrossRef] [PubMed]

17. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. **90**(1), 013903 (2003). [CrossRef] [PubMed]

18. C. C. Neacsu, G. A. Reider, and M. B. Raschke, “Second-harmonic generation from nanoscopic metal tips: Symmetry selection rules for single asymmetric nanostructures,” Phys. Rev. B **71**(20), 201402 (2005). [CrossRef]

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

20. J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, “Experimental study of optical second-harmonic scattering from spherical nanoparticles,” Phys. Rev. A **73**(2), 023819 (2006). [CrossRef]

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

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

23. M. C. Larciprete, A. Belardini, M. G. Cappeddu, D. de Ceglia, M. Centini, E. Fazio, C. Sibilia, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A **77**(1), 013809 (2008). [CrossRef]

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

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

26. H. Husu, B. K. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Chiral coupling in gold nanodimers,” Appl. Phys. Lett. **93**(18), 183115 (2008). [CrossRef]

27. E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, “Nonlinear optical spectroscopy of photonic metamaterials,” Phys. Rev. B **78**(11), 113102 (2008). [CrossRef]

28. Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B **70**(24), 245434 (2004). [CrossRef]

37. 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**(12), 127401 (2010). [CrossRef] [PubMed]

38. C. G. Biris and N. C. Panoiu, “Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires,” Phys. Rev. B **81**(19), 195102 (2010). [CrossRef]

39. C. G. Biris and N. C. Panoiu, “Nonlinear pulsed excitation of high-Q optical modes of plasmonic nanocavities,” Opt. Express **18**(16), 17165–17179 (2010). [CrossRef] [PubMed]

## 2. Theory and method

### 2.1 Calculation of the fields at the fundamental frequency

40. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. **34**(21), 4573–4588 (1995). [CrossRef] [PubMed]

47. J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: Numerical simulations,” Phys. Rev. B **72**(8), 085130 (2005). [CrossRef]

40. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. **34**(21), 4573–4588 (1995). [CrossRef] [PubMed]

40. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. **34**(21), 4573–4588 (1995). [CrossRef] [PubMed]

47. J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: Numerical simulations,” Phys. Rev. B **72**(8), 085130 (2005). [CrossRef]

### 2.2 Calculation of the fields at the second harmonic

51. F. X. Wang, F. J. Rodríguez, 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**(23), 233402 (2009). [CrossRef]

3. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. **83**(20), 4045–4048 (1999). [CrossRef]

52. J. Xu and X. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express **19**(23), 22999–23007 (2011). [CrossRef] [PubMed]

52. J. Xu and X. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express **19**(23), 22999–23007 (2011). [CrossRef] [PubMed]

5. 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**(7), 1328–1347 (2004). [CrossRef]

52. J. Xu and X. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express **19**(23), 22999–23007 (2011). [CrossRef] [PubMed]

**19**(23), 22999–23007 (2011). [CrossRef] [PubMed]

### 2.3 Calculation of scattering cross sections

## 3. Numerical results and discussion

### 3.1 A single metallic sphere

53. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. **24**(24), 4493–4499 (1985). [CrossRef] [PubMed]

54. D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. **96**(7), 3626–3634 (2004). [CrossRef]

3. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. **83**(20), 4045–4048 (1999). [CrossRef]

5. 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**(7), 1328–1347 (2004). [CrossRef]

6. 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**(12), 121402(R) (2011). [CrossRef]

3. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. **83**(20), 4045–4048 (1999). [CrossRef]

5. 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**(7), 1328–1347 (2004). [CrossRef]

### 3.2 A spherical metallic dimer

### 3.3 A chain of metallic spheres

56. J. Du, S. Liu, Z. Lin, J. Zi, and S. T. Chui, “Guiding electromagnetic energy below the diffraction limit with dielectric particle arrays,” Phys. Rev. A **79**(5), 051801 (2009). [CrossRef]

38. C. G. Biris and N. C. Panoiu, “Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires,” Phys. Rev. B **81**(19), 195102 (2010). [CrossRef]

### 3.4 A cluster of metallic spheres

## 4. Summary

## Acknowledgments

## References and links

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2. | T. F. Heinz, |

3. | 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. |

4. | H. Wang, E. Yan, E. Borguet, and K. B. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett. |

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6. | 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 |

7. | K. B. Eisenthal, “Second harmonic spectroscopy of aqueous nano- and microparticle interfaces,” Chem. Rev. |

8. | M. D. McMahon, R. Lopez, R. F. Haglund Jr, E. A. Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B |

9. | 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. |

10. | 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. |

11. | J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. |

12. | 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. |

13. | D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science |

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16. | J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature |

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19. | 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 |

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22. | M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express |

23. | M. C. Larciprete, A. Belardini, M. G. Cappeddu, D. de Ceglia, M. Centini, E. Fazio, C. Sibilia, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A |

24. | S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express |

25. | B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. |

26. | H. Husu, B. K. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Chiral coupling in gold nanodimers,” Appl. Phys. Lett. |

27. | E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, “Nonlinear optical spectroscopy of photonic metamaterials,” Phys. Rev. B |

28. | Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B |

29. | C. I. Valencia, E. R. Mendez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” J. Opt. Soc. Am. B |

30. | A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B |

31. | J. Petschulat, A. Chipouline, A. Tünnermann, and T. Pertsch, “Multipole nonlinearity of metamaterials,” Phys. Rev. A |

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38. | C. G. Biris and N. C. Panoiu, “Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires,” Phys. Rev. B |

39. | C. G. Biris and N. C. Panoiu, “Nonlinear pulsed excitation of high-Q optical modes of plasmonic nanocavities,” Opt. Express |

40. | Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. |

41. | N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. |

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48. | J. D. Jackson, |

49. | M. Abramowitz and I. A. Stegun, |

50. | V. Yannopapas and N. V. Vitanov, “Electromagnetic Green’s tensor and local density of states calculations for collections of sphererical scatters,” Phys. Rev. B |

51. | F. X. Wang, F. J. Rodríguez, 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 |

52. | J. Xu and X. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express |

53. | M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. |

54. | D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. |

55. | S. A. Maier, |

56. | J. Du, S. Liu, Z. Lin, J. Zi, and S. T. Chui, “Guiding electromagnetic energy below the diffraction limit with dielectric particle arrays,” Phys. Rev. A |

**OCIS Codes**

(160.4330) Materials : Nonlinear optical materials

(190.2620) Nonlinear optics : Harmonic generation and mixing

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 25, 2011

Revised Manuscript: December 3, 2011

Manuscript Accepted: December 7, 2011

Published: January 11, 2012

**Citation**

Jinying Xu and Xiangdong Zhang, "Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres," Opt. Express **20**, 1668-1684 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1668

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### References

- U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, Berlin, 1995).
- T. F. Heinz, Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991) Chap. 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(20), 4045–4048 (1999). [CrossRef]
- H. Wang, E. Yan, E. Borguet, and K. B. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.259(1-2), 15–20 (1996). [CrossRef]
- 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. B21(7), 1328–1347 (2004). [CrossRef]
- 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. B84(12), 121402(R) (2011). [CrossRef]
- K. B. Eisenthal, “Second harmonic spectroscopy of aqueous nano- and microparticle interfaces,” Chem. Rev.106(4), 1462–1477 (2006). [CrossRef] [PubMed]
- 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. B73(4), 041401(R) (2006). [CrossRef]
- S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett.98(16), 167403 (2007). [CrossRef] [PubMed]
- 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(20), 207402 (2010). [CrossRef] [PubMed]
- J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010). [CrossRef] [PubMed]
- J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett.105(7), 077401 (2010). [CrossRef] [PubMed]
- D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007). [CrossRef] [PubMed]
- V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]
- J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008). [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(1), 013903 (2003). [CrossRef] [PubMed]
- C. C. Neacsu, G. A. Reider, and M. B. Raschke, “Second-harmonic generation from nanoscopic metal tips: Symmetry selection rules for single asymmetric nanostructures,” Phys. Rev. B71(20), 201402 (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. B71(16), 165407 (2005). [CrossRef]
- J. Shan, J. I. Dadap, I. Stiopkin, G. A. Reider, and T. F. Heinz, “Experimental study of optical second-harmonic scattering from spherical nanoparticles,” Phys. Rev. A73(2), 023819 (2006). [CrossRef]
- M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006). [CrossRef] [PubMed]
- M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express15(8), 5238–5247 (2007). [CrossRef] [PubMed]
- M. C. Larciprete, A. Belardini, M. G. Cappeddu, D. de Ceglia, M. Centini, E. Fazio, C. Sibilia, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A77(1), 013809 (2008). [CrossRef]
- S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipolar analysis of second-harmonic radiation from gold nanoparticles,” Opt. Express16(22), 17196–17208 (2008). [CrossRef] [PubMed]
- B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett.7(5), 1251–1255 (2007). [CrossRef] [PubMed]
- H. Husu, B. K. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Chiral coupling in gold nanodimers,” Appl. Phys. Lett.93(18), 183115 (2008). [CrossRef]
- E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, “Nonlinear optical spectroscopy of photonic metamaterials,” Phys. Rev. B78(11), 113102 (2008). [CrossRef]
- Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B70(24), 245434 (2004). [CrossRef]
- C. I. Valencia, E. R. Mendez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” J. Opt. Soc. Am. B21(1), 36–44 (2004). [CrossRef]
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