Abstract

We consider the process of four-wave mixing in an array of gold nanowires strongly coupled to a gold film. Using full-wave simulations, we perform a quantitative comparison of the four-wave mixing efficiency associated with a bare film and films with nanowire arrays. We find that the strongly localized surface plasmon resonances of the coupled nanowires provide an additional local field enhancement that, along with the delocalized surface plasmon of the film, produces an overall four-wave mixing efficiency enhancement of up to six orders of magnitude over that of the bare film. The enhancement occurs over a wide range of excitation angles. The film-coupled nanowire array is easily amenable to nanofabrication, and could find application as an ultra-compact component for integrated photonic and quantum optic systems.

© 2012 OSA

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  38. Note that Eqs. (2) have been corrected from those published in [17].
  39. Comsol Multiphysics ( www.comsol.com ).
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    [CrossRef]
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    [CrossRef]
  43. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
    [CrossRef] [PubMed]

2011 (4)

2010 (7)

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

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (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]

D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “Real-time coherence holography,” Opt. Express 18, 13782–13787 (2010).
[CrossRef] [PubMed]

Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A 82, 043826 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

2009 (3)

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (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]

2008 (4)

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

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

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

2007 (1)

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75, 235426 (2007).
[CrossRef]

2006 (4)

2004 (1)

P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4, 2209–2213 (2004).
[CrossRef]

2003 (1)

2001 (3)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

2000 (1)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
[CrossRef]

1997 (1)

1988 (1)

F. Hacke, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
[CrossRef]

1986 (1)

1985 (1)

1983 (1)

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

1978 (1)

T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant rayleigh-type optical mixing,” Phys. Rev. A 17, 309–323 (1978).
[CrossRef]

1972 (1)

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

1962 (1)

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

1935 (1)

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, San Diego, 2007).

Akozbek, N.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Altepeter, J. B.

Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A 82, 043826 (2010).
[CrossRef]

Bauer, R.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Bloembergen, N.

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

Bloemer, M. J.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Boyd, R. W.

Centini, M.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Chemla, D. S.

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

Chen, H.

Chen, S.-Y.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

Chilkoti, A.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

Christ, A.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[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]

Claveau, R.

de Ceglia, D.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Degiron, A.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

Ebbesen, T. W.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Ezawa, T.

Fatome, J.

Finot, C.

Fischer, G.

Flytzanis, C.

Fogel, Y.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Foster, M. A.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006).
[CrossRef] [PubMed]

Gaeta, A. L.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Georges, A. T.

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Giessen, H.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

Gippius, N. A.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

Goodhue, W.

Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

Gregory, D. A.

Hache, F.

Hacke, F.

F. Hacke, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
[CrossRef]

Haji-Saeed, B.

Harutyunyan, H.

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

Heritage, J. P.

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

Hill, R. T.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

Holtom, G. R.

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Huang, Y.-P.

Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A 82, 043826 (2010).
[CrossRef]

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
[CrossRef]

Isaacs, E. D.

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

Jiang, H.

Johnson, P. B.

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

Khoury, J.

Kierstead, J.

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

Kreibig, U.

F. Hacke, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
[CrossRef]

Kreiter, M.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Kuhl, J.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

Kumar, P.

Lazarides, A. A.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

Lee, K. F.

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Liao, P. F.

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

Lipson, M.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006).
[CrossRef] [PubMed]

Liu, X.

X. Liu, Y. Wang, and E. O. Potma, “Surface-mediated four-wave mixing of nanostructures with counterpropagating surface plasmon polaritons,” Opt. Lett. 36, 2348–2350 (2011).
[CrossRef] [PubMed]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

Llen, K. M.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Lu, S.

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Lvque, G.

Martin, O. J. F.

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

McKinstrie, C. J.

Millot, G.

Min, W.

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Miyamoto, Y.

Mock, J. J.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

Morin, P.

Naik, D. N.

Nordlander, P.

P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4, 2209–2213 (2004).
[CrossRef]

Novotny, L.

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]

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

Okawachi, Y.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

Oldenburg, S. J.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

Osgood, R. M.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

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]

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

Papanikolaou, N.

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75, 235426 (2007).
[CrossRef]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Pershan, P. S.

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

Pitois, S.

Potma, E. O.

Prodan, E.

P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4, 2209–2213 (2004).
[CrossRef]

Quidant, R.

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]

Radic, S.

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.

Roppo, V.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Roussignol, P.

Rueckel, M.

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Rueda, A.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Salem, R.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Schmidt, B. S.

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

Sebba, D. S.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

Sengupta, S. K.

Shalaev, V.

V. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films (Springer Tracts in Modern Physics, v.158, Springer, Berlin Heidelberg, 2000).

Sharping, J. E.

Smith, D. D.

Smith, D. R.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

Souma, H.

T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant rayleigh-type optical mixing,” Phys. Rev. A 17, 309–323 (1978).
[CrossRef]

Stemmler, M.

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
[CrossRef]

Takeda, M.

Testorf, M.

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

Tikhodeev, S. G.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

Turner, A. C.

Turner-Foster, A. C.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Urzhumov, Y.

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (2010).
[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]

Vincenti, M. A.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Vlasov, Y. A.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

Wang, Y.

Wood, R. W.

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Woods, C. L

Xie, C.

Xie, X. S.

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Xue, C.

Yajima, T.

T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant rayleigh-type optical mixing,” Phys. Rev. A 17, 309–323 (1978).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
[CrossRef]

Zauscher, S.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

Zentgraf, T.

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

F. Hacke, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
[CrossRef]

Chem. Phys. Lett. (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

Electron. Lett. (1)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. C (1)

A. Rueda, M. Stemmler, R. Bauer, Y. Fogel, K. M. Llen, and M. Kreiter, “Localized plasmons seen by propagating surface plasmons: unique determination of their dielectric response,” J. Phys. Chem. C 112, 14801–14811 (2008).
[CrossRef]

Nano Lett. (5)

P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4, 2209–2213 (2004).
[CrossRef]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[CrossRef] [PubMed]

R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150–4154 (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]

W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

Nat. Photonics (2)

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4, 557–560 (2010).
[CrossRef]

Nature (1)

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. (2)

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

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

Phys. Rev. A (3)

Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A 82, 043826 (2010).
[CrossRef]

T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant rayleigh-type optical mixing,” Phys. Rev. A 17, 309–323 (1978).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828 (2010).
[CrossRef]

Phys. Rev. B (4)

A. Christ, T. Zentgraf, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Controlling the interaction between localized and delocalized surface plasmon modes: experiment and numerical calculations,” Phys. Rev. B 74, 155435 (2006).
[CrossRef]

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75, 235426 (2007).
[CrossRef]

D. S. Chemla, J. P. Heritage, P. F. Liao, and E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
[CrossRef]

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

Phys. Rev. Lett (1)

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

Phys. Rev. Lett. (3)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[CrossRef] [PubMed]

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

Other (5)

V. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films (Springer Tracts in Modern Physics, v.158, Springer, Berlin Heidelberg, 2000).

Note that Eqs. (2) have been corrected from those published in [17].

Comsol Multiphysics ( www.comsol.com ).

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, San Diego, 2007).

R. W. Boyd, Nonlinear Optics, 2nd Ed. (Academic Press, San Diego, 2005).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the gold film geometry with array of nanowires. Two waves with frequencies ω1 and ω2 are incident on the film, producing two mixing components with frequencies ω3 and ω4. The inset shows the dimensions of a single nanowire element over the metal film.

Fig. 2
Fig. 2

Norm of the generated FWM field from a plain gold film as a function of excitation angles. (a) Analytical calculation with λ1 = 628 nm, λ2 = 780 nm. (b) solid black: analytical and numerical results along the white line in (a); dash-dot black: similar calculation for the pump arrangement used in [27] (λ1 = 707 nm, λ2 = 800 nm, θ2 = θ1 + 60°). The excitation amplitude is 40 MV/m in all cases. The parameters of [41] are used for the dielectric function of gold.

Fig. 3
Fig. 3

(a) Linear spectral response of the NW-film system with a 880 nm period spaced 0.6 nm from the film; (b) same as (a) for a 70 nm period NW spacing. The insets show the norm of the electric field for the first Wood’s anomaly peak (a) and for the off-resonant excitation with a small period (b).

Fig. 4
Fig. 4

(a) FWM peak intensity for the 880 nm (solid green) and the 70 nm (dashed blue) systems, versus the plain film configurations shown in Fig. 2(b) (dash-dot and dotted black) (b) Power flow for the same cases as in (a).

Equations (2)

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P N L ( ω 3 ) = ɛ 0 χ ( 3 ) ( ω 3 ; ω 1 , ω 1 , ω 2 ) E 1 E 1 E 2 * , P N L ( ω 4 ) = ɛ 0 χ ( 3 ) ( ω 4 ; ω 2 , ω 2 , ω 1 ) E 2 E 2 E 1 * .
E x R = k y R ɛ 0 ( k T 2 k S 2 ) ( k x T ɛ r k x R ) [ k T 2 P y N L k y S ( k x S P x N L + k y S P y N L ) k x T ( k x S P y N L k y S P x N L ) ] ; E y R = k x R ɛ 0 ( k T 2 k S 2 ) ( k x T ɛ r k x R ) [ k T 2 P y N L k y S ( k x S P x N L + k y S P y N L ) k x T ( k x S P y N L k y S P x N L ) ] ,

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