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.

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  1. H. Raether, Surface Plasmons on Smooth Surfaces (Springer, 1988).
  2. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 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. Photonics6, 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]
  7. 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]
  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.276, 8–13 (2007).
    [CrossRef]
  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. A276, 127–132 (2000).
    [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]
  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]
  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]
  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]
  15. E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A23, 2135–2136 (1968).
  16. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  17. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  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. B21, 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. B38, 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]
  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]

2012 (3)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748 (2012).
[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]

2010 (1)

2009 (1)

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]

2008 (1)

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

2007 (1)

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]

2006 (1)

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]

2005 (1)

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]

2000 (1)

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]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999).
[CrossRef]

1994 (1)

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

1988 (1)

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B38, 7985–7989 (1988).
[CrossRef]

1982 (1)

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]

1981 (1)

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]

1980 (1)

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]

1976 (1)

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

1974 (1)

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]

1968 (2)

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).

Arakawa, E. T.

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]

Bartal, G.

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]

Berkovitch, N.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Burke, J. J.

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]

Chen, C. K.

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]

Cowan, J. J.

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]

de Castro, A. R. B.

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]

De Martini, F.

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

Etchegoin, P. G.

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]

Fan, Z. Y.

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]

Fukui, M.

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]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999).
[CrossRef]

Ginzburg, P.

Grosse, N. B.

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]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B38, 7985–7989 (1988).
[CrossRef]

Hall, D. G.

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]

Hamm, R. N.

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]

Hashimoto, K.

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]

Hayat, A.

Heckmann, J.

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]

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999).
[CrossRef]

Kajikawa, K.

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]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748 (2012).
[CrossRef]

Kretschmann, E.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A23, 2135–2136 (1968).

Le Ru, E. C.

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]

Liu, K.

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]

Lozovik, Y. E.

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]

Luo, S. Y.

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]

Merkulova, S. P.

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]

Meyer, M.

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]

Mitchell, D. E.

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]

Naraoka, R.

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]

Nazarov, M. M.

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]

Novotny, L.

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]

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

Okawa, H.

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]

Orenstein, M.

Palomba, S.

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]

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]

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

Park, Y.

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]

Quan, M. Y.

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]

Quidant, R.

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]

Raether, H.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A23, 2135–2136 (1968).

H. Raether, Surface Plasmons on Smooth Surfaces (Springer, 1988).

Renger, J.

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]

Ritchie, R. H.

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]

Shen, Y. R.

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]

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]

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

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Shkurinov, A. P.

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]

Simon, H. J.

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]

Sipe, J. E.

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]

So, V. C. Y.

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]

Stegeman, G. I.

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]

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]

van Hulst, N.

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]

Watson, J. G.

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]

Woggon, U.

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]

Xia, Y. X.

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]

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999).
[CrossRef]

Yin, X.

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]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748 (2012).
[CrossRef]

Zhan, L.

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]

Zhang, X.

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]

Zhuang, S.

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]

Appl. Phys. Lett. (1)

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]

J. Chem. Phys. (1)

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]

Nat. Mater. (1)

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]

Nat. Photonics (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748 (2012).
[CrossRef]

Opt. Commun. (2)

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]

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]

Opt. Lett. (1)

Phys. Lett. A (1)

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]

Phys. Rev. B (2)

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]

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B38, 7985–7989 (1988).
[CrossRef]

Phys. Rev. Lett. (7)

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

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]

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]

Sensors Actuators B (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sensors Actuators B54, 3–15 (1999).
[CrossRef]

Surf. Sci. (1)

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

Z. Phys. A (1)

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Phys. A23, 2135–2136 (1968).

Other (3)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

H. Raether, Surface Plasmons on Smooth Surfaces (Springer, 1988).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for investigation of degenerate SFG in the Kretschmann geometry. The scan beam and an auxiliary beam are prepared from a fs-laser (λ = 880nm, pulselentgh 150fs). The angles of incidence under which the beams impinge on the sample and their relative time delay can be varied by two traveling mirrors TM1 and TM2 together with lens L2. The second-harmonic light, emitted by the sample, a gold-coated BK7-prism, is separated from the fundamental with a Pellin-Broca-prism and detected on a cooled CCD. The inset shows the participating beams and their respective incident and exit angles. F1,F2: color filters, GT: Glan-Taylor-polarizer, L1–L5: achromatic lenses, BS: non-polarizing beam-splitter, M1,M2: silver mirrors.

Fig. 2
Fig. 2

Resulting SHG-radiation as a function of incident and exit angle. (a) shows the SHG of two beams, that are not overlapping in time. The increased intensity when the scan-beam is adjusted to the SP-resonance is visible. In (b) the beams have a zero delay and the wave-mixing process and enhanced SFG are clearly visible. The mixing signal of the two incident beams is extracted in (c) by subtracting (a) from (b) and the pf′f2ω interaction is identified. The theoretical calculation is shown in (d). (a), (b) and (d) are in logarithmic scale while in (c) the intensity is scaled linear.

Equations (7)

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k ω sin ( θ in ) = k sp : = ω c ε m ε d ε m + ε d , where k ω = ω c ε prism ( ω )
f f f 2 ω : k ω sin ( θ in ) + k ω sin ( θ in ) = k 2 ω sin ( θ out )
p f f 2 ω : k sp ω + k ω sin ( θ in ) = k 2 ω sin ( θ out )
p p f 2 ω : k sp ω + k sp ω = k 2 ω sin ( θ out )
f f f 2 ω : k ω sin ( θ in ) + k ω sin ( θ in ) = k 2 ω sin ( θ out )
f f f 2 ω : k ω sin ( θ in ) + k ω sin ( θ in ) = k 2 ω sin ( θ out )
p f f 2 ω : k sp ω + k ω sin ( θ in ) = k 2 ω sin ( θ out )

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