## Dipole limit in second-harmonic generation from arrays of gold nanoparticles |

Optics Express, Vol. 19, Issue 27, pp. 26866-26871 (2011)

http://dx.doi.org/10.1364/OE.19.026866

Acrobat PDF (845 KB)

### Abstract

We present a multipolar tensor analysis of second-harmonic generation from arrays of noncentrosymmetric gold nanoparticles. In contrast to earlier results, where higher multipoles and symmetry-forbidden signals arising from sample defects play a significant role, the present results are completely dominated by symmetry-allowed electric-dipole tensor components. The result arises from significant improvement in sample quality, which suppresses the higher-multipole effects and enhances the overall response by an order of magnitude. The results are a prerequisite for metamaterials with controllable nonlinear properties.

© 2011 OSA

1. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics **1**(1), 41–48 (2007). [CrossRef]

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

1. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics **1**(1), 41–48 (2007). [CrossRef]

4. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics **1**(4), 224–227 (2007). [CrossRef]

5. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science **328**(5976), 337–339 (2010). [CrossRef] [PubMed]

6. 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]

7. 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]

8. F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. **36**(9), 1533–1535 (2011). [CrossRef] [PubMed]

9. B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A Pure Appl Opt. **7**(2), S110–S117 (2005). [CrossRef]

10. 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**(22), 5418–5423 (2004). [CrossRef] [PubMed]

13. M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B **105**(1), 149–162 (2011). [CrossRef]

14. 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]

15. 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**(5), 057402 (2004). [CrossRef] [PubMed]

16. M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature **467**(7315), 541–542 (2010). [CrossRef] [PubMed]

14. 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]

17. M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. **13**(2), 023025 (2011). [CrossRef]

18. 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]

19. 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]

20. 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]

21. S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B **70**(11), 115106 (2004). [CrossRef]

22. A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B **28**(6), 1374–1384 (2011). [CrossRef]

^{2}.

17. M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. **13**(2), 023025 (2011). [CrossRef]

*A*[24

_{ijk}24. B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A Pure Appl. Opt. **8**(4), S278–S284 (2006). [CrossRef]

*ijk*refer to the polarization components of the respective fields. NRT is strictly specific to a given experiment rather than the sample itself. Its benefit is that it includes all multipole effects implicitly and it allows the signals to be analyzed using electric-dipole symmetry rules. Within the effective medium approach, NRT is proportional to the effective susceptibility of the nanostructure. Furthermore, the NRT approach can be extended to account for effective electric-dipole and higher-multipole effects. Due to difficulties in separating magnetic and quadrupole effects from each other in coherent signals [25

25. M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. **45**(2), 403–423 (1998). [CrossRef]

17. M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. **13**(2), 023025 (2011). [CrossRef]

**13**(2), 023025 (2011). [CrossRef]

*z*direction, any SHG signal can always be expressed in the general formwhere the expansion coefficients

*f*,

*g*, and

*h*depend on the components of the three tensors and are different for the various experimental geometries. For our present sample, which exhibits a resonance for

*x*-polarized fundamental field, the SHG signal is expected to be dominated by its

*x*-polarized component. The expansion coefficients for

*x*-polarized detection and the various experimental geometries are shown in Table 1 . It is evident that if only symmetry-allowed (

*f*and

*g*) and dipolar effects play a role, all four signals should behave in the same way. On the other hand, symmetry-forbidden and higher-multipole effects contribute with varying signs to different signals, making possible the determination of all tensor components.

*x*or y direction and then continuously modulated with a quarter-wave plate (QWP). Any possible SHG light from the optical components preceding the sample was filtered with a visible-blocking filter. The SHG signals were detected by photomultiplier tubes and photon counting by first filtering away the fundamental beam with infrared-blocking filters and using analyzers to pass only

*x*-polarized SHG light.

*θ*less than 2°) to allow detection of reflected SH radiation. The angle is sufficiently small that the fields do not couple significantly to the normal direction (

*z*) of the sample [14

14. 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. 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*-axis (

*h*coefficient in Table 1) when the sample is flipped. All four signals should then show the same dependence on the polarization if only electric dipoles play role, whereas higher multipoles would lead to differences in the measured signals. All four measured lineshapes in Fig. 3 are seen to overlap almost perfectly. This result suggests that the SHG response of the present sample is strongly dominated by the electric-dipole interaction.

*f*,

*g*and

*h*for the measured signals were compared to their expressions in terms of the components of the tensors (Table 1). This results in a group of linear equations, whose solution yields the relative complex values of the components (Table 2 ). The values are normalized to the dominant component

**13**(2), 023025 (2011). [CrossRef]

*y*-polarized SHG signals. They were always found to be weaker than the

*x*-polarized signals by an order of magnitude and also dominated by electric-dipole effects. These results will thus not change the general conclusion presented above. Improvements in the sample quality have thus allowed us to reach essentially the dipole limit in the SHG response.

## Acknowledgments

## References and links

1. | V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics |

2. | U. Kreibig and M. Vollmer, |

3. | K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B |

4. | W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics |

5. | T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science |

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

8. | F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. |

9. | B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A Pure Appl Opt. |

10. | 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 |

11. | J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. |

12. | M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science |

13. | M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B |

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

15. | 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. |

16. | M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature |

17. | M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. |

18. | 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 |

19. | 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. |

20. | 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. |

21. | S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B |

22. | A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B |

23. | H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express |

24. | B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A Pure Appl. Opt. |

25. | M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. |

26. | 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. |

**OCIS Codes**

(160.3900) Materials : Metals

(190.0190) Nonlinear optics : Nonlinear optics

(160.4236) Materials : Nanomaterials

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 2, 2011

Revised Manuscript: December 7, 2011

Manuscript Accepted: December 7, 2011

Published: December 15, 2011

**Citation**

Robert Czaplicki, Mariusz Zdanowicz, Kalle Koskinen, Janne Laukkanen, Markku Kuittinen, and Martti Kauranen, "Dipole limit in second-harmonic generation from arrays of gold nanoparticles," Opt. Express **19**, 26866-26871 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26866

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### References

- V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
- U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer, New York, 1995).
- K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]
- W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]
- T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [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]
- 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]
- F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36(9), 1533–1535 (2011). [CrossRef] [PubMed]
- B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, “Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,” J. Opt. A Pure Appl Opt. 7(2), S110–S117 (2005). [CrossRef]
- 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(22), 5418–5423 (2004). [CrossRef] [PubMed]
- J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006). [CrossRef] [PubMed]
- M. W. Klein, Ch. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]
- M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, and M. Fiebig, “Investigation of the nonlinear optical properties of metamaterials by second harmonic generation,” Appl. Phys. B 105(1), 149–162 (2011). [CrossRef]
- 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]
- 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(5), 057402 (2004). [CrossRef] [PubMed]
- M. I. Stockman, “Nanoscience: Dark-hot resonances,” Nature 467(7315), 541–542 (2010). [CrossRef] [PubMed]
- M. Zdanowicz, S. Kujala, H. Husu, and M. Kauranen, “Effective medium multipolar tensor analysis of second harmonic generation from metal nanoparticles,” New J. Phys. 13(2), 023025 (2011). [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(16), 165407 (2005). [CrossRef]
- 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]
- 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]
- S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: The concept of effective susceptibility,” Phys. Rev. B 70(11), 115106 (2004). [CrossRef]
- A. G. F. de Beer, S. Roke, and J. I. Dadap, “Theory of optical second-harmonic and sum-frequency scattering from arbitrarily shaped particles,” J. Opt. Soc. Am. B 28(6), 1374–1384 (2011). [CrossRef]
- H. Husu, J. Mäkitalo, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Particle plasmon resonances in L-shaped gold nanoparticles,” Opt. Express 18(16), 16601–16606 (2010). [CrossRef] [PubMed]
- B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, “A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,” J. Opt. A Pure Appl. Opt. 8(4), S278–S284 (2006). [CrossRef]
- M. Kauranen, T. Verbiest, and A. Persoons, “Second-order nonlinear optical signatures of surface chirality,” J. Mod. Opt. 45(2), 403–423 (1998). [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]

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