Abstract

A theory is presented for surface plasmon-polariton (SPP) excitation by four-wave mixing on a noble metal surface with two incident laser beams. Calculations are presented for the dependence of the generated plasmonic power on the angles of incidence of the two beams. The predicted maximum power at the optimum angles for SPP excitation at 633 and 921nm is 2 and 4 orders of magnitude, respectively, larger than the value reported in a recent experiment on a gold surface.

© 2011 Optical Society of America

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  1. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
    [CrossRef]
  2. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
    [CrossRef]
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  4. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
    [CrossRef] [PubMed]
  5. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef] [PubMed]
  6. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
    [CrossRef]
  7. M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
    [CrossRef] [PubMed]
  8. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
    [CrossRef]
  9. P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
    [CrossRef]
  10. Z. Shi, G. Piredda, A. C. Liapis, M. A. Nelson, L. Novotny, and R. B. Boyd, “Surface-plasmon polaritons on metal–dielectric nanocomposite films,” Opt. Lett. 34, 3535–3537 (2009).
    [CrossRef] [PubMed]
  11. N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
    [CrossRef] [PubMed]
  12. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
    [CrossRef]
  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. N. E. Karatzas and A. T. Georges, “Model for ultrafast harmonic generation from a gold surface: extraction of dephasing times for continuum–continuum transitions,” J. Opt. Soc. Am. B 26, 2218–2227 (2009).
    [CrossRef]
  15. W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
    [CrossRef]
  16. G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
    [CrossRef]
  17. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  18. T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E.Ponath and G.I.Stegeman, eds. (Elsevier, 1991), Chap. 5, p. 353–416.
  19. A. T. Georges, “Coherent and incoherent multiple-harmonic generation from metal surfaces,” Phys. Rev. A 54, 2412–2418 (1996).
    [CrossRef] [PubMed]
  20. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  21. Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
    [CrossRef]

2010 (2)

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

2009 (5)

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]

N. E. Karatzas and A. T. Georges, “Model for ultrafast harmonic generation from a gold surface: extraction of dephasing times for continuum–continuum transitions,” J. Opt. Soc. Am. B 26, 2218–2227 (2009).
[CrossRef]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[CrossRef]

Z. Shi, G. Piredda, A. C. Liapis, M. A. Nelson, L. Novotny, and R. B. Boyd, “Surface-plasmon polaritons on metal–dielectric nanocomposite films,” Opt. Lett. 34, 3535–3537 (2009).
[CrossRef] [PubMed]

2008 (2)

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

2007 (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

2005 (2)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
[CrossRef]

Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
[CrossRef]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

1996 (1)

A. T. Georges, “Coherent and incoherent multiple-harmonic generation from metal surfaces,” Phys. Rev. A 54, 2412–2418 (1996).
[CrossRef] [PubMed]

1994 (1)

W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
[CrossRef]

1993 (1)

G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Andrews, S. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

Bennemann, K. H.

W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
[CrossRef]

Betz, M.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
[CrossRef] [PubMed]

Bohmer, K.

W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
[CrossRef]

Boyd, R. B.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Dai, Jianming

Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
[CrossRef]

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Fernandez-Dominguez, A. I.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

Francini, R.

G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
[CrossRef]

Garcia-Vidal, F. J.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

Georges, A. T.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

Guo, Chunlei

Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
[CrossRef]

Heinz, T. F.

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E.Ponath and G.I.Stegeman, eds. (Elsevier, 1991), Chap. 5, p. 353–416.

Hubner, W.

W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Karatzas, N. E.

Liapis, A. C.

Lienau, C.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[CrossRef]

MacDonald, K. F.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

Maier, S. A.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
[CrossRef]

Martellucci, S.

G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
[CrossRef]

Martin-Moreno, L.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

Nelson, M. A.

Noginov, M. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Novotny, L.

Z. Shi, G. Piredda, A. C. Liapis, M. A. Nelson, L. Novotny, and R. B. Boyd, “Surface-plasmon polaritons on metal–dielectric nanocomposite films,” Opt. Lett. 34, 3535–3537 (2009).
[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]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Palomba, S.

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]

Petrocelli, G.

G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
[CrossRef]

Piredda, G.

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Podolskiy, V. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Pomraenke, R.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[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]

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]

Ritzo, B. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Ropers, C.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[CrossRef]

Rotenberg, N.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
[CrossRef] [PubMed]

Samson, Z. L.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

Shen, Y. R.

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

Shi, Z.

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
[CrossRef]

Stockman, M. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

Teng, H.

Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
[CrossRef]

van Driel, H. M.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
[CrossRef] [PubMed]

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]

Vasa, P.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[CrossRef]

Williams, C. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
[CrossRef]

Zheludev, N. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

Zhu, G.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Appl. Phys. A (1)

G. Petrocelli, S. Martellucci, and R. Francini, “Wavelength dependence of second-harmonic generation at the copper surface,” Appl. Phys. A 56, 263–266 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photon. Rev. 3, 483–507 (2009).
[CrossRef]

Nat. Photon. (3)

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surface,” Nat. Photon. 2, 175–179 (2008).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58(2009).
[CrossRef]

Opt. Commun. (1)

Jianming Dai, H. Teng, and Chunlei Guo, “Second- and third-order interferometric autocorrelations based on harmonic generations from metal surfaces,” Opt. Commun. 252, 173–178(2005).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314(2005).
[CrossRef]

Phys. Rev. A (1)

A. T. Georges, “Coherent and incoherent multiple-harmonic generation from metal surfaces,” Phys. Rev. A 54, 2412–2418 (1996).
[CrossRef] [PubMed]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

W. Hubner, K. H. Bennemann, and K. Bohmer, “Theory for the nonlinear optical response of transition metals: polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B 50, 17597–17605 (1994).
[CrossRef]

Phys. Rev. Lett. (4)

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]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004).
[CrossRef] [PubMed]

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105, 017402 (2010).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Other (3)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E.Ponath and G.I.Stegeman, eds. (Elsevier, 1991), Chap. 5, p. 353–416.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of SPP excitation on a gold surface by FWM. The wave vectors, k 1 and k 2 , of the two incident laser beams have been drawn with angles of incidence corresponding to the optimum angles for SPPs at 633 nm . At this wavelength, the decay length of the plasmon field component | E 4 x ( z ) | shown in the drawing is 333 nm in the air and 28 nm in gold.

Fig. 2
Fig. 2

Plot of the sets of angles of incidence, ( θ 1 , θ 2 ) , for achieving phase matching of the FWM processes, ω 4 = 2 ω 1 ω 2 (top curve), and ω 4 = 2 ω 2 ω 1 (bottom curve). The open circles on the curves correspond to the optimum sets of angles.

Fig. 3
Fig. 3

Plot of the normalized SPP power in the case of λ 4 = 633 nm versus the angle θ 1 (the jointly varying value of the angle θ 2 can be read off from the top curve in Fig. 2). The inset shows the SPP power versus the angle θ 2 , with θ 1 = 68.50 ° .

Fig. 4
Fig. 4

Plot of the normalized SPP power in the case of λ 4 = 921 nm versus the angle θ 2 (the jointly varying value of the angle θ 1 can be read off from the bottom curve in Fig. 2). The inset shows the SPP power versus the angle θ 1 , with θ 2 = 67.50 ° .

Equations (12)

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P 4 z , s ( 3 ) ( x , t ) = P 4 z , s ( 3 ) e i ( ω 4 t k 4 x ) + c.c. ,
E 4 ( z ) = { [ E 4 x , d x ^ + E 4 z , d z ^ ] e α d z , z > 0 [ E 4 x , m x ^ + E 4 z , m z ^ ] e α m z , z < 0 .
E 4 x , d E 4 x , m = 1 ϵ m P 4 z , s ( 3 ) x ,
ϵ d E 4 z , d ϵ m E 4 z , m = 0 ,
E 4 x , d E 4 x , m = i k 4 ϵ m P 4 z , s ( 3 ) ,
ϵ d α m E 4 x , d + ϵ m α d E 4 x , m = 0.
E 4 x , d = i k 4 α d D P 4 z , s ( 3 ) ,
E 4 x , m = i k 4 α m ϵ d D ϵ m P 4 z , s ( 3 ) ,
k spp = k spp i k spp = ω 4 c ϵ d ϵ m ϵ d + ϵ m .
k 4 = 2 ω 1 c sin θ 1 ω 2 c sin θ 2 = k spp .
I 4 = k 4 ω 4 μ 0 | P 4 z , s | 2 { [ k 4 2 α d 2 1 ] k 4 2 α d | D | 2 + [ k 4 2 | α m | 2 cos 2 ϕ α m ] | k 4 α m ϵ d D ϵ m | 2 1 α m } ,
I 4 = ϵ 0 ϵ d ω 4 k 4 3 α d 1 | P 4 z , s / D | 2 .

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