## Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles

Optics Express, Vol. 12, Issue 22, pp. 5418-5423 (2004)

http://dx.doi.org/10.1364/OPEX.12.005418

Acrobat PDF (435 KB)

### Abstract

An array of low-symmetry, L-shaped gold nanoparticles is shown to exhibit high sensitivity to the state of incident polarization. Small imperfections in the shape of the actual particles, including asymmetric arm lengths and edge distortions, break the symmetry attributed to an ideal particle. This broken symmetry leads to a large angular displacement of the extinction axes from their expected locations. More significantly, second-harmonic generation experiments reveal significant second-order susceptibility tensor components forbidden to the ideal symmetry.

© 2004 Optical Society of America

## 1. Introduction

1. W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Optical dichroism of lithographically designed silver nanoparticles,” Opt. Lett. **21**, 1099–1101 (1996). [CrossRef] [PubMed]

3. S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett. **86**, 4688–4691 (2001). [CrossRef] [PubMed]

4. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. **220**, 137–141 (2003). [CrossRef]

5. K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles,” Nano Lett. **3**, 1087–1090 (2003). [CrossRef]

6. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. d. Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. **90**, 057401 (2003). [CrossRef] [PubMed]

7. C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. V. Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays,” J. Phys. Chem. B **107**, 7337–7342 (2003). [CrossRef]

8. G. Schider, J. R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F. R. Aussenegg, W. L. Schaich, I. Puscasu, B. Monacelli, and G. Boreman, “Plasmon dispersion relation of Au and Ag nanowires,” Phys. Rev. B **68**, 155427 (2003). [CrossRef]

9. T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, “Optical activity in subwavelength-period arrays of chiral metallic particles,” Appl. Phys. Lett. **83**, 234–236 (2003). [CrossRef]

10. A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical Manifestations of Planar Chirality,” Phys. Rev. Lett. **90**, 107404 (2003). [CrossRef] [PubMed]

11. B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B **68**, 419–423 (1999). [CrossRef]

12. H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, and J. Turunen, “Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles,” J. Nonlinear Opt. Phys. **11**, 421–432 (2002). [CrossRef]

13. V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B **57**, 13,265–13,288 (1998). [CrossRef]

14. 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**, 057402 (2004). [CrossRef] [PubMed]

15. A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, “Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites,” Phys. Rev. B **60**, 16,389–16,408 (1999). [CrossRef]

16. K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. **91**, 227402 (2003). [CrossRef] [PubMed]

## 2. Sample and experimental apparatus

12. H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, and J. Turunen, “Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles,” J. Nonlinear Opt. Phys. **11**, 421–432 (2002). [CrossRef]

*µ*m)

^{2}.

*θ*, were conducted using the general setup shown in Fig. 1. The laser beam (Time-Bandwidth GLX-200, central wavelength 1060 nm, pulse length 200 fs, repetition rate 82 MHz, average power 350 mW) was chopped (not shown) and moderately focused at normal incidence on the sample with a lens (focal length 20 cm). Precise incident polarization was controlled by a polarizer and a zero-order half-wave plate. The visible (VIS) and infrared (IR) blocking filters were used only for SHG measurements. For the transmission measurement, the analyzer was not used. In the linear measurements, the detector consisted of a scatter plate and a photodiode connected to a lock-in amplifier (also not shown), referenced to the chopper frequency. In the SHG measurements, the detector was a photomultiplier tube, again connected to the lock-in. Note that the Y-polarization plasmon peak is nearly resonant with the laser wavelength.

## 3. Results and discussion

*α*, of the primary extinction axes from the expected axes X (45°) and Y (135°). We determined the location of these new axes, A and B, by fitting the transmission data to [17]

*T*

_{A}and

*T*

_{B}are the transmittances along axes A and B, respectively. (The factor of 45° relates the sample to the EBL writing frame for experimentally expedient alignment.) The fitted angular shift is

*α*=-7.6°±0.1°. This shift is much larger than expected based only on the difference in arm lengths.

*ρ*longer than its horizontal arm (length

*L*, Fig. 3). The axis angle,

*ϕ*, is determined from

*ϕ*=arctan(

*ρ*). For equal arm lengths,

*ρ*=1 and

*ϕ*=45°, matching the X-Y axes. For larger values of

*ρ*, the axes will be shifted from X and Y by

*α*=45°-

*ϕ*. Of course, this model of the nanoparticles is naïve, but it does yield the correct shifts for the limiting cases of the symmetric L (

*α*=0° for

*ρ*=1) and a vertical rod (

*α*⇒45° for

*ρ*≫1). (The model also holds for the converse situation, where the horizontal arm is longer than the vertical arm so that

*ρ*<1.) We therefore expect that for

*ρ*⋍1, it should yield a reasonable approximation if the arm length difference is the dominant source of the axis shift. For

*ρ*=1.05, as in our particles,

*α*≈-1.5°, much smaller than the observed shift. The large discrepancy between the model and experimentally observed shift points towards a different source: other structural imperfections that strongly influence the optical response of the nanoparticles, which may include rounded corners, perimeter deviations, a possible height profile bias, and small-scale deformities that lead to local-field hot spots. Indeed, a measurement performed at 820 nm yields an even larger angular shift of -11.5° [17]. Higher multipole interactions likely may also be involved, but due to the complexity of incorporating them into this simple model, they have not yet been addressed in detail. A proper theoretical treatment of the optical responses would, of course, require full multipolar calculations.

9. T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, “Optical activity in subwavelength-period arrays of chiral metallic particles,” Appl. Phys. Lett. **83**, 234–236 (2003). [CrossRef]

*ω; ω, ω*), where

*i, j, k*, can be X, Y, or Z. According to the electric-dipole approximation, the mirror symmetry of the ideal array determines whether a particular input/output polarization combination allows a nonlinear response or is forbidden [19]. Because higher multipole contributions (electric-quadrupole or magnetic-dipole) obey the same selection rules, a non-zero forbidden signal then clearly reveals broken symmetry [20

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

*C*

_{1h}symmetry group, due to the substrate-air interfacial asymmetry. A regular array of ideal particles then exhibits the same symmetry properties, where reflection through the X-axis (Y→-Y) is the sole non-trivial symmetry operation. Since our measurements are made at normal incidence, we will consider only the in-plane (XY) components. Accordingly, there are just four allowed components, of which only three are independent: XXX, XYY, and YXY=YYX. However, YXY and YYX are not individually accessible in our single-beam experiment due to the mixed nature of the input polarizations. There are two other directly accessible components that are forbidden: YXX and YYY (as are the inaccessible XXY=XYX). We therefore measured the responses for the four pure input/output polarization combinations XXX, XYY, YXX, and YYY. Because one may argue that A and B are the actual primary axes, we also measured the identical combinations with A replacing X and B replacing Y.

## 4. Conclusion

## Acknowledgments

## References and links

1. | W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Optical dichroism of lithographically designed silver nanoparticles,” Opt. Lett. |

2. | W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,” Appl. Phys. B |

3. | S. Linden, J. Kuhl, and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Phys. Rev. Lett. |

4. | W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. |

5. | K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles,” Nano Lett. |

6. | J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. d. Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. |

7. | C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. V. Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays,” J. Phys. Chem. B |

8. | G. Schider, J. R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F. R. Aussenegg, W. L. Schaich, I. Puscasu, B. Monacelli, and G. Boreman, “Plasmon dispersion relation of Au and Ag nanowires,” Phys. Rev. B |

9. | T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, “Optical activity in subwavelength-period arrays of chiral metallic particles,” Appl. Phys. Lett. |

10. | A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical Manifestations of Planar Chirality,” Phys. Rev. Lett. |

11. | B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B |

12. | H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, and J. Turunen, “Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles,” J. Nonlinear Opt. Phys. |

13. | V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B |

14. | 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. |

15. | A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, “Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites,” Phys. Rev. B |

16. | K. Li, M. I. Stockman, and D. J. Bergman, “Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,” Phys. Rev. Lett. |

17. | B. K. Canfield, S. Kujala, M. Kauranen, K. Jefimovs, T. Vallius, and J. Turunen, “Remarkable polarization sensitivity of gold nanoparticle arrays,” submitted Sept. 2004 to Appl. Phys. Lett. |

18. | Y. R. Shen, |

19. | R. W. Boyd, |

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

**OCIS Codes**

(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter

(260.3910) Physical optics : Metal optics

(260.5430) Physical optics : Polarization

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 1, 2004

Revised Manuscript: October 19, 2004

Published: November 1, 2004

**Citation**

Brian Canfield, Sami Kujala, Konstantins Jefimovs, Jari Turunen, and Martti Kauranen, "Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles," Opt. Express **12**, 5418-5423 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-22-5418

Sort: Journal | Reset

### References

- W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, �??Optical dichroism of lithographically designed silver nanoparticles,�?? Opt. Lett. 21, 1099�??1101 (1996). [CrossRef] [PubMed]
- W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, �??Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nanodesign,�?? Appl. Phys. B 63, 381�??384 (1996).
- S. Linden, J. Kuhl, and H. Giessen, �??Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,�?? Phys. Rev. Lett. 86, 4688�??4691 (2001). [CrossRef] [PubMed]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, �??Optical properties of two interacting gold nanoparticles,�?? Opt. Commun. 220, 137�??141 (2003). [CrossRef]
- K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, �??Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles,�?? Nano Lett. 3, 1087�??1090 (2003). [CrossRef]
- J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. d. Abajo, �??Optical properties of gold nanorings,�?? Phys. Rev. Lett. 90, 057401 (2003). [CrossRef] [PubMed]
- C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. V. Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, �??Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays,�?? J. Phys. Chem. B 107, 7337�??7342 (2003). [CrossRef]
- G. Schider, J. R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F. R. Aussenegg, W. L. Schaich, I. Puscasu, B. Monacelli, and G. Boreman, �??Plasmon dispersion relation of Au and Ag nanowires,�?? Phys. Rev. B 68, 155427 (2003). [CrossRef]
- T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, �??Optical activity in subwavelength-period arrays of chiral metallic particles,�?? Appl. Phys. Lett. 83, 234�??236 (2003). [CrossRef]
- A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, �??Optical Manifestations of Planar Chirality,�?? Phys. Rev. Lett. 90, 107404 (2003). [CrossRef] [PubMed]
- B. Lamprecht, A. Leitner, and F. R. Aussenegg, �??SHG studies of plasmon dephasing in nanoparticles,�?? Appl. Phys. B 68, 419�??423 (1999). [CrossRef]
- H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, and J. Turunen, �??Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles,�?? J. Nonlinear Opt. Phys. 11, 421�??432 (2002). [CrossRef]
- V. M. Shalaev and A. K. Sarychev, �??Nonlinear optics of random metal-dielectric films,�?? Phys. Rev. B 57, 13,265�??13,288 (1998). [CrossRef]
- 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, 057402 (2004). [CrossRef] [PubMed]
- A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, �??Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites,�?? Phys. Rev. B 60, 16,389�??16,408 (1999). [CrossRef]
- K. Li, M. I. Stockman, and D. J. Bergman, �??Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens,�?? Phys. Rev. Lett. 91, 227402 (2003). [CrossRef] [PubMed]
- B. K. Canfield, S. Kujala, M. Kauranen, K. Jefimovs, T. Vallius, and J. Turunen, �??Remarkable polarization sensitivity of gold nanoparticle arrays,�?? submitted Sept. 2004 to Appl. Phys. Lett.
- Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York, 1984).
- R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 1992).
- M. Kauranen, T. Verbiest, and A. Persoons, �??Second-order nonlinear optical signatures of surface chirality,�?? J. Mod. Opt. 45, 403�??423 (1998). [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.