Abstract

We develop a concept of surface plasmon polaritons (SPPs) based four-wave mixing (4WM), in which a laser-launched evanescent SPP field is utilized as a coherent pumping source to involve directly in a nonlinear 4WM process at the dielectric/metal interface. Conversion efficiency of the resulting 4WM radiation is expected to be dramatically increased due to the local-field enhancement effect. Feasibility of implementing this concept at the air/gold film and graphene flake/gold film interfaces is further examined by numerical simulations. The concept shows intriguing promise for applications in newly emerging nanophotonics, optoelectronics, and active plasmonics.

© 2011 OSA

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2011 (3)

2010 (5)

A. V. Krasavin and A. V. Zayats, “Numerical analysis of long-range surface plasmon polariton modes in nanoscale plasmonic waveguides,” Opt. Lett. 35(13), 2118–2120 (2010).
[CrossRef] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[CrossRef] [PubMed]

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(9), 091904 (2010).
[CrossRef]

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(1), 017402 (2010).
[CrossRef] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010).
[CrossRef] [PubMed]

2009 (3)

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(26), 266802 (2009).
[CrossRef]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

2008 (1)

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

2007 (3)

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. 2(7), 426–429 (2007).
[CrossRef]

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

2005 (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

2004 (3)

J. R. Krenn and J.-C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. Lond. A 362(1817), 739–756 (2004).
[CrossRef]

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

2003 (3)

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (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(1), 013903 (2003).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[CrossRef] [PubMed]

1984 (1)

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

1982 (1)

1979 (1)

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[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(26), 1531–1534 (1974).
[CrossRef]

1968 (1)

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Aloukos, P.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

Beermann, J.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[CrossRef] [PubMed]

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(1), 017402 (2010).
[CrossRef] [PubMed]

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(1), 013903 (2003).
[CrossRef] [PubMed]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

Boyd, G. T.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[CrossRef] [PubMed]

Brongersma, M. L.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. 2(7), 426–429 (2007).
[CrossRef]

Calado, V. E.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(9), 091904 (2010).
[CrossRef]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Chen, C. K.

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[CrossRef]

Coello, V.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[CrossRef] [PubMed]

Couris, S.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

de Castro, A. R. B.

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[CrossRef]

DeMartini, F.

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[CrossRef]

Dragnea, B.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Dynowska, E.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

Feldmann, J.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Ganeev, R. A.

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

Geim, A. K.

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Gryczynski, I.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

Gryczynski, Z.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Hale, P. J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (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(1), 013903 (2003).
[CrossRef] [PubMed]

Hendry, E.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[CrossRef] [PubMed]

Kaminska, E.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

Kowarik, S.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Krasavin, A. V.

Krenn, J. R.

J. R. Krenn and J.-C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. Lond. A 362(1817), 739–756 (2004).
[CrossRef]

Kretschmann, E.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Kulagin, I. A.

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

Lakhtakia, A.

J. A. Polo and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

Lakowicz, J. R.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

Leite, J. R. R.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

Leone, S. R.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Lin, C.-Y.

Malicka, J.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Mikhailov, S. A.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[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(26), 1531–1534 (1974).
[CrossRef]

Moger, J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[CrossRef] [PubMed]

Nassau, K.

Nikolaenko, A.

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Novotny, L.

J. Renger, R. Quidant, and L. Novotny, “Enhanced nonlinear response from metal surfaces,” Opt. Express 19(3), 1777–1785 (2011).
[CrossRef] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 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(26), 266802 (2009).
[CrossRef]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[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(1), 013903 (2003).
[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(26), 266802 (2009).
[CrossRef]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Piotrowska, A.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

Polo, J. A.

J. A. Polo and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

Potma, E. O.

Quidant, R.

J. Renger, R. Quidant, and L. Novotny, “Enhanced nonlinear response from metal surfaces,” Opt. Express 19(3), 1777–1785 (2011).
[CrossRef] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 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(26), 266802 (2009).
[CrossRef]

Raether, H.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Raghunathan, V.

Rasing, Th.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

Renger, J.

J. Renger, R. Quidant, and L. Novotny, “Enhanced nonlinear response from metal surfaces,” Opt. Express 19(3), 1777–1785 (2011).
[CrossRef] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 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(26), 266802 (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(1), 017402 (2010).
[CrossRef] [PubMed]

Ryasnyansky, A. I.

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[CrossRef] [PubMed]

Shen, Y. R.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[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(26), 1531–1534 (1974).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Szarko, J. M.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Tugushev, R. I.

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

Usmanov, T.

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

van de Sanden, M. C. M.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(9), 091904 (2010).
[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(1), 017402 (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(4), 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(26), 266802 (2009).
[CrossRef]

Wang, Y.

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(26), 1531–1534 (1974).
[CrossRef]

Weber, J. W.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(9), 091904 (2010).
[CrossRef]

Weeber, J.-C.

J. R. Krenn and J.-C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. Lond. A 362(1817), 739–756 (2004).
[CrossRef]

Weimann, T.

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Wood, D. L.

Xenogiannopoulou, E.

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

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A. V. Krasavin and A. V. Zayats, “Numerical analysis of long-range surface plasmon polariton modes in nanoscale plasmonic waveguides,” Opt. Lett. 35(13), 2118–2120 (2010).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Zia, R.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. 2(7), 426–429 (2007).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(9), 091904 (2010).
[CrossRef]

J. Phys. Chem. B (1)

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[CrossRef] [PubMed]

Laser Photonics Rev. (1)

J. A. Polo and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

Nano Lett. (1)

B. Dragnea, J. M. Szarko, S. Kowarik, T. Weimann, J. Feldmann, and S. R. Leone, “Near-field surface plasmon excitation on structured gold films,” Nano Lett. 3(1), 3–7 (2003).
[CrossRef]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. 2(7), 426–429 (2007).
[CrossRef]

Opt. Commun. (2)

R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyansky, R. I. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229(1–6), 403–412 (2004).
[CrossRef]

E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, and E. Dynowska, “Third-order nonlinear optical properties of thin sputtered gold films,” Opt. Commun. 275(1), 217–222 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Philos. Trans. R. Soc. Lond. A (1)

J. R. Krenn and J.-C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. Lond. A 362(1817), 739–756 (2004).
[CrossRef]

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Phys. Rev. B (1)

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30(2), 519–526 (1984).
[CrossRef]

Phys. Rev. Lett. (9)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
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S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[CrossRef] [PubMed]

C. K. Chen, A. R. B. de Castro, Y. R. Shen, and F. DeMartini, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43(13), 946–949 (1979).
[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(26), 1531–1534 (1974).
[CrossRef]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 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(26), 266802 (2009).
[CrossRef]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010).
[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(1), 017402 (2010).
[CrossRef] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[CrossRef] [PubMed]

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A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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Science (1)

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D. W. Lynch, and W. R. Hunter, in Handbook of Optical Constants of Solids, E. Palik, ed. (Academic Press, 1985), pp. 286–295.

H. Raether, in Physics of Thin Films, G. Hass, M. H. Francombe, and R. W. Hoffman, eds. (Academic Press, 1977), Vol. 9, Chap. 3, pp. 145–262.

M. L. Brongersma and P. G. Kik, eds., Surface Plasmon Nanophotonics (Springer, 2007).

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

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North-Holland, 1982).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, 1988).

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

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Figures (5)

Fig. 1
Fig. 1

Diagram of the two SPPs-based 4WM schemes and sketches of the corresponding configurations for the case of air/gold film interface (see text for details).

Fig. 3
Fig. 3

The 4WM wavelength distributions [(c), (f), and (i), see also Fig. 2] and their corresponding 4WM conversion efficiencies for two particular cases at the air/gold film interface: (1) the λ opt beam is p-polarized [(c1), (f1), and (i1)]; (2) the λ opt beam is s-polarized [(c2), (f2), and (i2)]. As in Fig. 2, the top, middle, and bottom rows correspond, respectively, to the configurations (a1), (a2), and (b1) as sketched in Fig. 1. The scalar bar in each panel of the middle and right columns shows the relative 4WM intensities in arbitrary units.

Fig. 2
Fig. 2

2D-WAD spectra of θ opt(λ exc, λ opt) (left column) and θ 4wm(λ exc, λ opt) (middle column), and the corresponding 4WM wavelength distributions (right column) for the case of air/gold film interface. The top, middle, and bottom rows correspond, respectively, to the configurations (a1), (a2), and (b1) shown in Fig. 1.

Fig. 4
Fig. 4

Upper panel: Schematic of graphene’s band structure with the three resonant-field energies (double arrows) involved in the two schemes of SPPs-based 4WM. Lower panels: Sketches of the two working configurations for scheme (a) (left) and scheme (b) (right) when applied to the graphene flake/thin gold film system.

Fig. 5
Fig. 5

2D-WAD spectra of θ opt(λ exc, λ opt) (left column) and θ 4wm(λ exc, λ opt) (middle column), and the corresponding 4WM wavelength distributions (right column) for the case of graphene flake/gold film interface. The upper and lower rows correspond, respectively, to schemes (a) and (b) shown in Fig. 4.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

ω 4wm(a) = 2 ω spp ω opt    [scheme (a)],
ω 4wm(b) = 2 ω opt ω spp    [scheme (b)] .
P ( a ) ( ω 4wm(a) = 2 ω spp ω opt ) = ε 0 χ Au (3) ( ω 4wm(a) ; ω spp , ω spp , ω opt ) ×                                                E spp ( ω spp ) E spp ( ω spp ) E opt * ( ω opt ) ,
P ( b ) ( ω 4wm(b) = 2 ω opt ω spp ) = ε 0 χ Au (3) ( ω 4wm(b) ; ω opt , ω opt , ω spp ) ×                                                E opt ( ω opt ) E opt ( ω opt ) E spp * ( ω spp ) ,
P ( a'  ) ( ω 4wm(a') = 2 ω exc ω opt ) = ε 0 χ Au (3) ( ω 4wm(a' ) ; ω exc , ω exc , ω opt ) ×                                                E exc ( ω exc ) E exc ( ω exc ) E opt * ( ω opt ) ,
G = | E spp ( ω spp ) E exc ( ω spp ) | 4 ,
k 4wm(a) / / = k 4wm(a) sin θ 4wm(a) = 2 Re ( k spp ) + k opt sin θ opt ,
k 4wm(a) = k 4wm(a) cos θ 4wm(a) = k opt cos θ opt ,
k 4wm(a) = ω 4wm(a) c ,    k opt = ω opt c ,   and   k spp = ω spp c ε d ε m ( ω spp ) ε d + ε m ( ω spp ) ,
θ opt = arcsin ( 1 η 2 η λ opt λ exc 1 η ) ,
θ 4wm(a) = arcsin ( 1 + η 2 η λ 4wm(a) λ exc 1 η λ 4wm(a) λ opt ) ,
λ exc = 2 π c ω spp ,    λ opt = 2 π c ω opt ,    λ 4wm(a) = 2 π c ω 4wm(a) ,
η = Re ( ε d ε m ( ω spp ) ε d + ε m ( ω spp ) ) .
sin θ spp ( λ exc ) = η ( λ exc ) n s ,

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