## The dual annihilation of a surface plasmon and a photon by virtue of a three-wave mixing interaction |

Optics Express, Vol. 21, Issue 23, pp. 28856-28861 (2013)

http://dx.doi.org/10.1364/OE.21.028856

Acrobat PDF (1375 KB)

### Abstract

The enhanced nonlinear interactions that are driven by surface-plasmon resonances have readily been exploited for the purpose of optical frequency conversion in metallic structures. As of yet, however, little attention has been payed to the exact particulate nature of the conversion process. We show evidence that a surface plasmon and photon can annihilate simultaneously to generate a photon having the sum frequency. The signature for this nonlinear interaction is revealed by probing the condition for momentum conservation using a two-beam k-space spectroscopic method that is applied to a gold film in the Kretschmann geometry. The inverse of the observed nonlinear interaction—an exotic form of parametric down-conversion—would act as a source of surface plasmons in the near-field that are quantum correlated with photons in the far-field.

© 2013 OSA

## 1. Introduction

2. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B **54**, 3–15 (1999). [CrossRef]

3. G. I. Stegeman, J. J. Burke, and D. G. Hall, “Nonlinear optics of long range surface plasmons,” Appl. Phys. Lett. **41**, 906–908 (1982). [CrossRef]

4. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics **6**, 737–748 (2012). [CrossRef]

5. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. **33**, 1531–1534 (1974). [CrossRef]

6. F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. **36**, 216–219 (1976). [CrossRef]

10. R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. **248**, 249–256 (2005). [CrossRef]

*χ*

^{(3)}-interaction for 4WM on a structured surface [11

11. S. Palomba, S. Zhuang, Y. Park, G. Bartal, X. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. **11**, 34–38 (2012). [CrossRef]

*χ*

^{(2)}-interaction that drives SHG on a smooth metal film [12

12. N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear plasmon-photon interaction resolved by k-space spectroscopy,” Phys. Rev. Lett. **108**, 136802 (2012). [CrossRef] [PubMed]

## 2. Conceptual approach to plasmon-photon wave mixing in k-space spectroscopy

13. J. Renger, R. Quidant, N. van Hulst, S. Palomba, and L. Novotny, “Free-space excitation of propagating surface plasmon polaritons by nonlinear four-wave mixing,” Phys. Rev. Lett. **103**, 266802 (2009). [CrossRef]

14. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. **21**, 1530–1533 (1968). [CrossRef]

*ε*

_{prism}) reaches the interface between metal (

*ε*

_{m}) and dielectric (

*ε*

_{d}) as an evanescent wave. As described by Eq. (1), the wavevector’s component parallel to the surface can thus be matched to that of the SP by varying the angle of incidence

*θ*

_{in}. When this condition is met, the surface plasmon resonance (SPR) leads to a strong local enhancement of the fundamental field.

## 3. Experimental setup

*λ*= 880 nm provided pulses of 150 fs duration at a repetition rate of 76 MHz with a waist radius of 110

*μ*m at the sample. A Mach-Zehnder interferometer split the light into an auxiliary beam

*f′*of 20 mW and a scan beam

*f*of 60 mW. The delay

*τ*was adjustable. The relative phase in the Mach-Zehnder interferometer was dithered over a range of several fringes. The angle of incidence

*θ*

_{in}, under which the beams impinged on the sample, was varied by two independent travelling mirrors and the beams were focused onto the sample by a 60 mm achromatic lens.

## 4. Results

*τ*= 1 ps, ensuring that the beams do not interact. The scan beam

*f*is scanned from 40° to 50°. The strictly photonic conversion process

*ff*−

*f*

_{2}

*, where two incident photons of frequency*

_{ω}*ω*become a 2

*ω*photon, occurs over the whole angle range, thereby forming the diagonal line. When the scan beam approaches the angle for the surface plasmon resonance (

*θ*

_{in}= 42.6°), the harmonic intensity initially decreases and for larger angles

*θ*

_{in}increases two orders of magnitude due to the plasmonic field enhancement. Because of the angular width of the incident beam, plasmons

*p*are generated over a slightly extended range of incident angles and can then participate in nonlinear conversion processes. This leads to the observed horizontal elongation, which is spread over 0.5° of incident angles. It is identified as the

*pp*−

*f*

_{2}

*conversion of two fundamental plasmons*

_{ω}*p*into a harmonic photon [12

12. N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear plasmon-photon interaction resolved by k-space spectroscopy,” Phys. Rev. Lett. **108**, 136802 (2012). [CrossRef] [PubMed]

*θ*

_{out}= 42.2°. At angles very near to the diagonal, the

*pf*−

*f*

_{2}

*interaction is also thought to occur (Eq. (3)) and can hence not be discriminated from the*

_{ω}*pp*−

*f*

_{2}

*interaction.*

_{ω}*pp*−

*f*

_{2}

*wavevector-matching conditions.*

_{ω}*f′*is fixed at

*θ*

_{in}= 43.7°, which is off-resonant to the SPR and separates both beams sufficiently to avoid overlapping in k-space. The SHG from the auxiliary beam

*f′f′*−

*f*

_{2}

*exits at a constant angle of*

_{ω}*θ*

_{out}= 43.2°. There is half a degree offset of the exit angles

*θ*

_{out}for both beams compared with their respective

*θ*

_{in}due to the dispersion in gold and glass.

*f′*and scan beam

*f*overlapping in time (

*τ*= 0). The photonic SFG of the two beams

*ff′*−

*f*

_{2}

*is visible as an additional diagonal component. This wave-mixing signal shows, as seen in Fig. 2(a) for the scan beam, a horizontal elongation at the scan beam’s SP excitation angle of incidence. This feature is evaluated in Fig. 2(c).*

_{ω}*et al*[18

18. S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. **101**, 056802 (2008). [CrossRef] [PubMed]

19. 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]

20. Y. R. Shen, “Surfaces probed by nonlinear optics,” Surf. Sci. **299**, 551–562 (1994). [CrossRef]

21. P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B **38**, 7985–7989 (1988). [CrossRef]

22. P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett. **35**, 1551–1553 (2010). [CrossRef] [PubMed]

*θ*

_{in}and

*θ′*

_{in}. The dielectric function for gold

*ε*

_{m}was taken from [23

23. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. **125**, 164705 (2006). [CrossRef] [PubMed]

*θ*

_{out}for the generated harmonic light, matching conditions Eqs. (2)–(7) were applied.

*θ*

_{in}=42.3°. Also present is the drop in the SHG-intensity from the scan beam for angles

*θ*

_{in}just below the surface plasmon resonance. A slight horizontal broadening away from the diagonal in terms of incident angle is visible for scan and SFG beam, whose characteristic strongly depends on the beam waist and therefore the precision of the exciting beam’s wavevector.

## 5. Conclusion

*ω*SP and

*ω*photon was clearly isolated by comparing an effective one beam measurement, where both beams were not overlapping in time with a two-beam measurement, that enabled interaction. While the common photonic SHG was measurable over the entire angular range, plasmon-driven SFG was limited to the regime where SP’s are excited and could therefore be clearly distinguished. In particular the

*pf′*−

*f*

_{2}

*interaction has been observed. This process could be clearly identified by its unique signature in k-space due to the fact, that only a well-defined combination of wavevectors can take an active part in SFG. The results are in good agreement with our theoretical calculations. Accordingly, we have demonstrated a useful tool that can be applied to investigate particle-quasiparticle nonlinear interactions.*

_{ω}## References and links

1. | H. Raether, |

2. | J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B |

3. | G. I. Stegeman, J. J. Burke, and D. G. Hall, “Nonlinear optics of long range surface plasmons,” Appl. Phys. Lett. |

4. | M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics |

5. | H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. |

6. | F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. |

7. | C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett. |

8. | K. Liu, L. Zhan, Z. Y. Fan, M. Y. Quan, S. Y. Luo, and Y. X. Xia, “Enhancement of second-harmonic generation with phase-matching on periodic sub-wavelength structured metal film,” Opt. Commun. |

9. | Y. E. Lozovik, S. P. Merkulova, M. M. Nazarov, and A. P. Shkurinov, “From two-beam surface plasmon interaction to femtosecond surface optics and spectroscopy,” Phys. Lett. A |

10. | R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. |

11. | S. Palomba, S. Zhuang, Y. Park, G. Bartal, X. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater. |

12. | N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear plasmon-photon interaction resolved by k-space spectroscopy,” Phys. Rev. Lett. |

13. | J. Renger, R. Quidant, N. van Hulst, S. Palomba, and L. Novotny, “Free-space excitation of propagating surface plasmon polaritons by nonlinear four-wave mixing,” Phys. Rev. Lett. |

14. | R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. |

15. | E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A |

16. | Y. R. Shen, |

17. | R. W. Boyd, |

18. | S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. |

19. | J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B |

20. | Y. R. Shen, “Surfaces probed by nonlinear optics,” Surf. Sci. |

21. | P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B |

22. | P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett. |

23. | P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. |

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 17, 2013

Revised Manuscript: October 18, 2013

Manuscript Accepted: October 18, 2013

Published: November 15, 2013

**Virtual Issues**

Nonlinear Optics (2013) *Optics Express*

**Citation**

Jan Heckmann, Marie-Elena Kleemann, Nicolai B. Grosse, and Ulrike Woggon, "The dual annihilation of a surface plasmon and a photon by virtue of a three-wave mixing interaction," Opt. Express **21**, 28856-28861 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28856

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### References

- H. Raether, Surface Plasmons on Smooth Surfaces (Springer, 1988).
- J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999). [CrossRef]
- G. I. Stegeman, J. J. Burke, and D. G. Hall, “Nonlinear optics of long range surface plasmons,” Appl. Phys. Lett.41, 906–908 (1982). [CrossRef]
- M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748 (2012). [CrossRef]
- H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett.33, 1531–1534 (1974). [CrossRef]
- F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett.36, 216–219 (1976). [CrossRef]
- C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett.46, 145–148 (1981). [CrossRef]
- K. Liu, L. Zhan, Z. Y. Fan, M. Y. Quan, S. Y. Luo, and Y. X. Xia, “Enhancement of second-harmonic generation with phase-matching on periodic sub-wavelength structured metal film,” Opt. Commun.276, 8–13 (2007). [CrossRef]
- Y. E. Lozovik, S. P. Merkulova, M. M. Nazarov, and A. P. Shkurinov, “From two-beam surface plasmon interaction to femtosecond surface optics and spectroscopy,” Phys. Lett. A276, 127–132 (2000). [CrossRef]
- R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun.248, 249–256 (2005). [CrossRef]
- S. Palomba, S. Zhuang, Y. Park, G. Bartal, X. Yin, and X. Zhang, “Optical negative refraction by four-wave mixing in thin metallic nanostructures,” Nat. Mater.11, 34–38 (2012). [CrossRef]
- N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear plasmon-photon interaction resolved by k-space spectroscopy,” Phys. Rev. Lett.108, 136802 (2012). [CrossRef] [PubMed]
- J. Renger, R. Quidant, N. van Hulst, S. Palomba, and L. Novotny, “Free-space excitation of propagating surface plasmon polaritons by nonlinear four-wave mixing,” Phys. Rev. Lett.103, 266802 (2009). [CrossRef]
- R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett.21, 1530–1533 (1968). [CrossRef]
- E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A23, 2135–2136 (1968).
- Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
- R. W. Boyd, Nonlinear Optics (Academic, 1992).
- S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett.101, 056802 (2008). [CrossRef] [PubMed]
- J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B21, 4389–4402 (1980). [CrossRef]
- Y. R. Shen, “Surfaces probed by nonlinear optics,” Surf. Sci.299, 551–562 (1994). [CrossRef]
- P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B38, 7985–7989 (1988). [CrossRef]
- P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett.35, 1551–1553 (2010). [CrossRef] [PubMed]
- P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125, 164705 (2006). [CrossRef] [PubMed]

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