Abstract

We present a theoretical study on the possibilities to achieve nonlinear frequency conversion in plasmonic slot waveguides having a χ(2) nonlinear medium as its core. Second-harmonic generation is used as a referential process to discuss the possibilities in achieving strong nonlinear interactions. We show that geometrical dispersion allows for the possibility of modal phase matching without resorting to other mechanisms like birefringence phase matching or periodic poling of the nonlinear medium. We disclose that in strongly dissipative systems two effects, the damping of individual modes and the phase-matching condition, have to be carefully balanced to assure an efficient energy conversion. Besides second-harmonic generation, emphasis is put on exploring the application of potentially more importance: the parametric amplification in the waveguide with the purpose to enhance its propagation length.

© 2012 Optical Society of America

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  1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
    [CrossRef]
  2. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
    [CrossRef]
  3. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
    [CrossRef]
  4. N. Talebi, M. Shahabadi, W. Khunsin, and R. Vogelgesang, “Plasmonic grating as a nonlinear converter-coupler,” Opt. Express 20, 1392–1405 (2012).
    [CrossRef]
  5. W. Fan, S. Zhang, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second-harmonic generation from patterned gaas inside a subwavelength metallic hole array,” Opt. Express 14, 9570–9575 (2006).
    [CrossRef]
  6. H. Y. Lin and Y. F. Chen, “Giant enhancement of luminescence induced by second-harmonic surface plasmon resonance,” Appl. Phys. Lett. 88, 101914 (2006).
    [CrossRef]
  7. K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
    [CrossRef]
  8. N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80, 161407 (2009).
    [CrossRef]
  9. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
    [CrossRef]
  10. T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
    [CrossRef]
  11. J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011).
    [CrossRef]
  12. F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36, 1533–1535 (2011).
    [CrossRef]
  13. E. Feigenbaum and M. Orenstein, “Plasmon-soliton,” Opt. Lett. 32, 674–676 (2007).
    [CrossRef]
  14. A. Marini, D. V. Skryabin, and B. Malomed, “Stable spatial plasmon solitons in a dielectric-metal-dielectric geometry with gain and loss,” Opt. Express 19, 6616–6622 (2011).
    [CrossRef]
  15. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Self-focusing and spatial plasmon-polariton solitons,” Opt. Express 17, 21732–21737 (2009).
    [CrossRef]
  16. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).
  17. Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
    [CrossRef]
  18. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
    [CrossRef]
  19. A. D. Falco, C. Conti, and G. Assanto, “Quadratic phase matching in slot waveguides,” Opt. Lett. 31, 3146–3148 (2006).
    [CrossRef]
  20. J.-l. Kou, Q. Wang, Z.-y. Yu, F. Xu, and Y.-q. Lu, “Broadband and highly efficient quadratic interactions in double-slot lithium niobate waveguides through phase matching,” Opt. Lett. 36, 2533–2535 (2011).
    [CrossRef]
  21. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
    [CrossRef]
  22. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17, 20063–20068 (2009).
    [CrossRef]
  23. F. F. Lu, T. Li, J. Xu, Z. D. Xie, L. Li, S. N. Zhu, and Y. Y. Zhu, “Surface plasmon polariton enhanced by optical parametric amplification in nonlinear hybrid waveguide,” Opt. Express 19, 2858–2865 (2011).
    [CrossRef]
  24. Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-thz conversion efficiency by metallic slot waveguides,” Opt. Express 17, 13502–13515 (2009).
    [CrossRef]
  25. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
    [CrossRef]
  26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  27. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).

2012

2011

F. F. Lu, T. Li, J. Xu, Z. D. Xie, L. Li, S. N. Zhu, and Y. Y. Zhu, “Surface plasmon polariton enhanced by optical parametric amplification in nonlinear hybrid waveguide,” Opt. Express 19, 2858–2865 (2011).
[CrossRef]

A. Marini, D. V. Skryabin, and B. Malomed, “Stable spatial plasmon solitons in a dielectric-metal-dielectric geometry with gain and loss,” Opt. Express 19, 6616–6622 (2011).
[CrossRef]

F. B. P. Niesler, N. Feth, S. Linden, and M. Wegener, “Second-harmonic optical spectroscopy on split-ring-resonator arrays,” Opt. Lett. 36, 1533–1535 (2011).
[CrossRef]

J.-l. Kou, Q. Wang, Z.-y. Yu, F. Xu, and Y.-q. Lu, “Broadband and highly efficient quadratic interactions in double-slot lithium niobate waveguides through phase matching,” Opt. Lett. 36, 2533–2535 (2011).
[CrossRef]

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011).
[CrossRef]

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

2010

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

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

2009

2008

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

2007

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

E. Feigenbaum and M. Orenstein, “Plasmon-soliton,” Opt. Lett. 32, 674–676 (2007).
[CrossRef]

2006

2005

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef]

1998

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

1972

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

Assanto, G.

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Borys, N. J.

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80, 161407 (2009).
[CrossRef]

Boyd, R. W.

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

Bozhevolnyi, S. I.

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

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Brueck, S. R. J.

Chen, K.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

Chen, Y. F.

H. Y. Lin and Y. F. Chen, “Giant enhancement of luminescence induced by second-harmonic surface plasmon resonance,” Appl. Phys. Lett. 88, 101914 (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]

Conti, C.

Davoyan, A. R.

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).

Durak, C.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Falco, A. D.

Fan, S.

Fan, W.

Feigenbaum, E.

Fejer, M. M.

Feth, N.

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Geiss, R.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Giessen, H.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Gramotnev, D. K.

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

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).

Han, Z.

He, S.

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Heflin, J. R.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

Hentschel, M.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Hu, W.

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Hu, X.-k.

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Iliew, R.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Jin, J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[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]

Kauranen, M.

Khunsin, W.

Kim, S.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Kim, S.-W.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Kim, Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Kim, Y.-J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Kivshar, Y. S.

Kou, J.-l.

Kratzer, K.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Lederer, F.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Li, L.

Li, T.

Lin, H. Y.

H. Y. Lin and Y. F. Chen, “Giant enhancement of luminescence induced by second-harmonic surface plasmon resonance,” Appl. Phys. Lett. 88, 101914 (2006).
[CrossRef]

Linden, S.

Lippitz, M.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Liu, L.

Lu, F. F.

Lu, Y.-q.

J.-l. Kou, Q. Wang, Z.-y. Yu, F. Xu, and Y.-q. Lu, “Broadband and highly efficient quadratic interactions in double-slot lithium niobate waveguides through phase matching,” Opt. Lett. 36, 2533–2535 (2011).
[CrossRef]

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Lupton, J. M.

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80, 161407 (2009).
[CrossRef]

Mäkitalo, J.

Malloy, K. J.

Malomed, B.

Marini, A.

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Molnar, D.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Neshev, D. N.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Niesler, F. B. P.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).

Orenstein, M.

Osgood, R. M.

Panoiu, N. C.

Park, I.-Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Paul, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Pertsch, T.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Robinson, H. D.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

Rockstuhl, C.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Rosencher, E.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Ruan, Z.

Schumacher, T.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Shadrivov, I. V.

Shahabadi, M.

Skryabin, D. V.

Solntsev, A. S.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Sukhorukov, A. A.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Suuriniemi, S.

Talebi, N.

Utikal, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Veronis, G.

Vodopyanov, K. L.

Vogelgesang, R.

Walter, M. J.

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80, 161407 (2009).
[CrossRef]

Wang, Q.

Wegener, M.

Wu, Z.-j.

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Xie, Z. D.

Xu, F.

J.-l. Kou, Q. Wang, Z.-y. Yu, F. Xu, and Y.-q. Lu, “Broadband and highly efficient quadratic interactions in double-slot lithium niobate waveguides through phase matching,” Opt. Lett. 36, 2533–2535 (2011).
[CrossRef]

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Xu, J.

Yu, Z.-y.

J.-l. Kou, Q. Wang, Z.-y. Yu, F. Xu, and Y.-q. Lu, “Broadband and highly efficient quadratic interactions in double-slot lithium niobate waveguides through phase matching,” Opt. Lett. 36, 2533–2535 (2011).
[CrossRef]

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

Zentgraf, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Zhang, S.

Zhu, S. N.

Zhu, Y. Y.

Appl. Phys. Lett.

H. Y. Lin and Y. F. Chen, “Giant enhancement of luminescence induced by second-harmonic surface plasmon resonance,” Appl. Phys. Lett. 88, 101914 (2006).
[CrossRef]

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98, 231110 (2011).
[CrossRef]

Nano Lett.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef]

Nat. Commun

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun 2, 333 (2011).
[CrossRef]

Nat. Photon.

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

Nature

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Opt. Express

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011).
[CrossRef]

N. Talebi, M. Shahabadi, W. Khunsin, and R. Vogelgesang, “Plasmonic grating as a nonlinear converter-coupler,” Opt. Express 20, 1392–1405 (2012).
[CrossRef]

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-thz conversion efficiency by metallic slot waveguides,” Opt. Express 17, 13502–13515 (2009).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17, 20063–20068 (2009).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Self-focusing and spatial plasmon-polariton solitons,” Opt. Express 17, 21732–21737 (2009).
[CrossRef]

F. F. Lu, T. Li, J. Xu, Z. D. Xie, L. Li, S. N. Zhu, and Y. Y. Zhu, “Surface plasmon polariton enhanced by optical parametric amplification in nonlinear hybrid waveguide,” Opt. Express 19, 2858–2865 (2011).
[CrossRef]

A. Marini, D. V. Skryabin, and B. Malomed, “Stable spatial plasmon solitons in a dielectric-metal-dielectric geometry with gain and loss,” Opt. Express 19, 6616–6622 (2011).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef]

W. Fan, S. Zhang, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second-harmonic generation from patterned gaas inside a subwavelength metallic hole array,” Opt. Express 14, 9570–9575 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. B

Z.-j. Wu, X.-k. Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.-q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82, 155107 (2010).
[CrossRef]

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

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80, 161407 (2009).
[CrossRef]

Phys. Rev. Lett.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106, 133901 (2011).
[CrossRef]

Science

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Other

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

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic illustration of the metallic slot waveguides. Thickness and width are denoted by t and w , respectively. (b)–(d) Modal distribution of the electric field’s x component according to the coordinate frame shown in (a) for mode order M = 0 , 1, 2, respectively. Dielectric core (shaded) is made up of LiNbO 3 , while the dielectric substrate has permittivity ϵ r = 1.96 .

Fig. 2.
Fig. 2.

Linear dispersion of the modes. Horizontal axis defines the frequency of FH while the subscript of SH in the legend stands for the mode order. Width of the core is set to w = 20 nm . Thickness is defined as t = 170 nm for (a),(b) and t = 360 nm for (c),(d). M = 2 mode at SH shown in (a),(b) undergoes cutoff near 210 THz.

Fig. 3.
Fig. 3.

Phase mismatch Δ n L M between L = 0 mode at FH and SH mode (a) M = 0 , (b) M = 1 , and (c) M = 2 . Dashed blue curve indicates the line where phase matching takes place. Black area denotes regions in the parameter space where the SH plasmonic mode is cut off.

Fig. 4.
Fig. 4.

Mode overlap coefficient | b L M | as defined in Eq. (2) between L = 0 mode at FH and SH modes of order (a) M = 0 , (b) M = 1 , and (c) M = 2 . Linear modes have been normalized to unit power. Black area denotes regions in the parameter space where the SH plasmonic mode is cut off.

Fig. 5.
Fig. 5.

(a) Phase-matching configuration [ n eff , L ( ω 0 ) = n eff , M ( 2 ω 0 ) ] of the slot waveguide extracted from Fig. 3. (b) Value of nonlinear coupling coefficient | b 0 M | at phase-matched points extracted from Fig. 4.

Fig. 6.
Fig. 6.

Nonlinear conversion efficiency η M of the SH mode order (a) M = 0 , (b) M = 1 , and (c) M = 2 . Input pump power of FH is equal to 1 W. Black area denotes regions in the parameter space where the plasmonic mode is cut off.

Fig. 7.
Fig. 7.

Evolution of SH power with propagation distance. (a)  w = 20 nm , t = 170 nm , (b)  w = 172 nm , t = 415 nm ; (c)  w = 20 nm , t = 360 nm ; (d)  w = 200 nm , t = 929 nm .

Fig. 8.
Fig. 8.

Linear propagation length κ q ( ω p ) of the modes when (a), (b) Δ n 0 , 1 = 0 , and (c), (d) Δ n 0 , 2 = 0 . q stands for the mode order, while p = { 0 , 2 } denote FH and SH, respectively.

Fig. 9.
Fig. 9.

Ratio of the seed signal’s propagation length obtained with a nonlinear pump ( κ NL ) to the linear propagation ( κ LIN ) when pumped from the mode of order (a) M = 1 and (b) M = 2 at SH.

Equations (6)

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d A d z = β L ( ω 0 ) A + i M a L M A * B M exp ( i Δ β L M z ) ,
d B M d z = β M ( ω 2 ) B M + i b L M A 2 exp ( i Δ β L M z ) .
a L M = ω 0 d r [ χ ¯ ¯ ( 2 ) ( r ) : e L * ( r , ω 0 ) e M ( r , ω 2 ) ] · [ e L , ( r , ω 0 ) e L , z ( r , ω 0 ) ] 2 d r [ e L , ( r , ω 0 ) × h L , ( r , ω 0 ) ] z ,
b L M = ω 2 d r [ χ ¯ ¯ ( 2 ) ( r ) : e L ( r , ω 0 ) 2 ] · [ e M , ( r , ω 2 ) e M , z ( r , ω 2 ) ] 2 d r [ e M , ( r , ω 2 ) × h M , ( r , ω 2 ) ] z .
a L M 2 ω 0 ϵ 0 d r d 33 ( r ) | e L , x ( r , ω 0 ) | 2 e M , x ( r , ω 2 ) d r [ e L , ( r , ω 0 ) × h L , ( r , ω 0 ) ] z ,
b L M ω 2 ϵ 0 d r d 33 ( r ) e L , x ( r , ω 0 ) 2 e M , x ( r , ω 2 ) d r [ e M , ( r , ω 2 ) × h M , ( r , ω 2 ) ] z .

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