Abstract

While metals benefit from a strong nonlinearity at optical frequencies, its practical exploitation is limited by the weak penetration of the electric field within the metal and the screening by the surface charges. It is shown here that this limitation can be bypassed by depositing a thin dielectric layer on the metal surface or, alternatively, using a thin metal film. This strategy enables us to enhance four-wave mixing in metals by up to four orders of magnitude.

© 2011 Optical Society of America

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References

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  1. R. Boyd, Nonlinear Optics (Academic Press, San Diego, 2008), 3rd ed.
  2. Y. R. Shen, The Principles of Nonlinear Optics (J. Wiley & Sons, New York, 1984).
  3. T. Heinz, Nonlinear Surface Electromagnetic Phenomena (Elsevier, Amsterdam, 1991).
  4. F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
    [Crossref]
  5. H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
    [Crossref]
  6. A. Leitner, “Second-harmonic generation in metal island films consisting of oriented silver particles of low symmetry,” Mol. Phys. 70, 197 (1990).
    [Crossref]
  7. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
    [Crossref] [PubMed]
  8. N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
    [Crossref]
  9. B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
    [Crossref]
  10. H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388–390 (1998).
    [Crossref]
  11. M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
    [Crossref] [PubMed]
  12. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
    [Crossref] [PubMed]
  13. N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
    [Crossref] [PubMed]
  14. H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
    [Crossref]
  15. Y. Wang, C.-Y. Lin, A. Nikolaenko, V. Raghunathan, and E. O. Potma, “Four-wave mixing microscopy of nanostructures,” Adv. Opt. Photon. 3, 1–52 (2011).
    [Crossref]
  16. C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.
  17. J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
    [Crossref] [PubMed]
  18. P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
    [Crossref]
  19. 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]
  20. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [Crossref]
  21. M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
    [Crossref]
  22. P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett. 35, 1551–1553 (2010).
    [Crossref] [PubMed]

2011 (1)

2010 (5)

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

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[Crossref]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[Crossref] [PubMed]

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

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]

2007 (1)

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
[Crossref] [PubMed]

2005 (1)

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
[Crossref] [PubMed]

2003 (2)

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[Crossref]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref] [PubMed]

1999 (2)

N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
[Crossref]

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
[Crossref]

1998 (1)

1991 (1)

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

1990 (1)

A. Leitner, “Second-harmonic generation in metal island films consisting of oriented silver particles of low symmetry,” Mol. Phys. 70, 197 (1990).
[Crossref]

1965 (1)

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[Crossref]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[Crossref]

Aussenegg, F. R.

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
[Crossref]

Bardhan, R.

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

Berkovitch, N.

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref] [PubMed]

Beversluis, M. R.

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[Crossref]

Blanchard, R.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[Crossref]

Bouhelier, A.

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[Crossref]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref] [PubMed]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic Press, San Diego, 2008), 3rd ed.

Brown, F.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[Crossref]

Capasso, F.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Chen, Z.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Danckwerts, M.

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
[Crossref] [PubMed]

Flytzanis, C.

C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.

Fu, J. S.

Gatzogiannis, E.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Genevet, P.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Ginzburg, P.

Grady, N. K.

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

Hache, F.

C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.

Halas, N. J.

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref] [PubMed]

Harutyunyan, H.

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[Crossref]

Hayat, A.

Heinz, T.

T. Heinz, Nonlinear Surface Electromagnetic Phenomena (Elsevier, Amsterdam, 1991).

Jiang, H. B.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Kats, M.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Klein, M.

C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.

Knight, M. W.

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

Krenn, J. R.

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
[Crossref]

Lamprecht, B.

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
[Crossref]

Leitner, A.

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83, 4421–4424 (1999).
[Crossref]

A. Leitner, “Second-harmonic generation in metal island films consisting of oriented silver particles of low symmetry,” Mol. Phys. 70, 197 (1990).
[Crossref]

Li, L.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Liao, H. B.

Lin, C.-Y.

Lippitz, M.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
[Crossref] [PubMed]

Loukakos, P. A.

N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
[Crossref]

Moustaizis, S. D.

N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
[Crossref]

Nikolaenko, A.

Novotny, L.

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[Crossref]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[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]

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).
[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, 013903 (2003).
[Crossref] [PubMed]

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[Crossref]

Orenstein, M.

Orrit, M.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
[Crossref] [PubMed]

Palomba, S.

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[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]

Papadogiannis, N. A.

N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
[Crossref]

Parks, R. E.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[Crossref]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[Crossref]

Potma, E. O.

Quidant, R.

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[Crossref]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[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]

Raghunathan, V.

Renger, J.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[Crossref] [PubMed]

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[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]

Ricard, D.

C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.

Roussignol, P.

C. Flytzanis, F. Hache, M. Klein, D. Ricard, and P. Roussignol, “1. Semiconductor and metal crystallites in dielectrics:,” in “Nonlinear Optics in Composite Materials:,” vol. 29 of Progress in Optics, E. Wolf, ed. (Elsevier, 1991), pp. 321–411.

Scully, M.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (J. Wiley & Sons, New York, 1984).

Sleeper, A. M.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[Crossref]

Tetienne, J.-P.

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

van Dijk, M. A.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
[Crossref] [PubMed]

van Hulst, N.

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010).
[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]

Wang, H.

Wang, W. C.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Wang, Y.

Wong, G. K. L.

Wong, K. S.

Xiao, R. F.

Zhang, Z. M.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Zheng, J. B.

H. B. Jiang, L. Li, W. C. Wang, J. B. Zheng, Z. M. Zhang, and Z. Chen, “Reflected second-harmonic generation at a silver surface,” Phys. Rev. B 44, 1220–1224 (1991).
[Crossref]

Adv. Opt. Photon. (1)

Mol. Phys. (1)

A. Leitner, “Second-harmonic generation in metal island films consisting of oriented silver particles of low symmetry,” Mol. Phys. 70, 197 (1990).
[Crossref]

Nano Lett. (4)

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5, 799–802 (2005).
[Crossref] [PubMed]

N. K. Grady, M. W. Knight, R. Bardhan, and N. J. Halas, “Optically-driven collapse of a plasmonic nanogap self-monitored by optical frequency mixing,” Nano Lett. 10, 1522–1528 (2010).
[Crossref] [PubMed]

H. Harutyunyan, S. Palomba, J. Renger, R. Quidant, and L. Novotny, “Nonlinear dark-field microscopy,” Nano Lett. 10, 5076–5079 (2010).
[Crossref]

P. Genevet, J.-P. Tetienne, E. Gatzogiannis, R. Blanchard, M. Kats, M. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).
[Crossref]

Opt. Commun. (1)

N. A. Papadogiannis, P. A. Loukakos, and S. D. Moustaizis, “Observation of the inversion of second and third harmonic generation efficiencies on a gold surface in the femtosecond regime,” Opt. Commun. 166, 133–139 (1999).
[Crossref]

Opt. Lett. (2)

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[Crossref]

Phys. Rev. B (2)

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Two incident laser beams with frequencies ω1 and ω2 give rise to frequency converted beams with frequencies ω4wm1 = 2ω1 – ω2 and ω4wm2 = 2ω2 – ω1, respectively. Three sample geometries are studied: (a) bulk metal, (b) thin metal layer on dielectric substrate, and (c) thin dielectric layer on bulk metal.

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Fig. 2
Fig. 2 Calculated four-wave mixing enhancement for a silver film overcoated with a dielectric layer of thickness d and index of refraction n. The enhancement maxima are the result of Fabry-Perot resonances that affect the in- and out-coupling of the waves at ω1, ω2 and ω4wm. The plot illustrates the behavior for TM incidence and angles as used in the experiments for λ4wm = 633 nm.

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Fig. 3
Fig. 3 Enhancement of four-wave mixing by a SiO2 surface layer. The thickness d of the layer is varied and the 4WM intensity enhancement is measured relative to a bare silver surface (d → 0). The oscillations are a result of Fabry-Perot resonances that affect the in- and out-coupling of the waves at ω1, ω2, ω4wm. Solid lines are theoretical curves and dots are experimental data.

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Fig. 4
Fig. 4 Enhancement of four-wave mixing by a TiO2 surface layer. The thickness d of the layer is varied and the 4WM intensity enhancement is measured relative to a bare silver surface (d → 0). The oscillations are a result of Fabry-Perot resonances that affect the in- and out-coupling of the waves at ω1, ω2, ω4wm. At the resonances the field inside the dielectric is strong and gives rise to an additional 4WM contribution. Solid lines are theoretical curves and dots are experimental data.

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Fig. 5
Fig. 5 Enhancement of four-wave mixing signal for thin gold films. The solid curve shows the theoretically predicted 4WM intensity for a gold film of thickness d deposited on a glass substrate. The 4WM intensity is normalized with the value calculated for d → ∞. Experimental measurements are represented by data points.

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Equations (7)

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ω 4 wm 1 = 2 ω 1 − ω 2 ω 4 wm 2 = 2 ω 2 − ω 1 ,
ω 4 wm 1 sin θ 4 wm 1 = ω 2 sin θ 2 − 2 ω 1 sin θ 1 ω 4 wm 2 sin θ 4 wm 2 = ω 1 sin θ 1 − 2 ω 2 sin θ 2 .
P = ɛ o χ ( 3 ) ( − ω 4 wm ; ω 1 , ω 1 , − ω 2 ) E 1 E 1 E 2 *
P = [ P x P y P z ] e i [ k 4 wm ⋅ r − ω 4 wm t ]
E i = E i o [ − cos θ i sin ϕ i t p ( θ i ) cos ϕ i t s ( θ i ) sin θ i sin ϕ i t p ( θ i ) ] e i [ k i ⋅ r − ω i t ]
E 4 wm = 1 2 ɛ o 1 ɛ 1 ɛ 2 [ k 4 wm , z − k ↓ , z k ↓ 2 − k 4 wm 2 ] e i [ k ↑ ⋅ r − ω 4 wm t ] [ t p ( θ 4 wm ) ( k ↓ , z P x + k ↓ , x P z ) ɛ 1 / ɛ 2 ( k ↓ 2 / k ↑ , z ) t s ( θ 4 wm ) P y − ( k ↑ , x / k ↓ , z ) t p ( θ 4 wm ) ( k ↓ , z P x − k ↓ , x P z ) ] .
t p , s ( λ , θ , d ) = [ t p , s ( 1 ) ( λ , θ ) t p , s ( 2 ) ( λ , θ ) e i k d , z 2 d 1 + r p , s ( 1 ) ( λ , θ ) r p , s ( 2 ) ( λ , θ ) e i k d , z 2 d ] .

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