Abstract

The lifetime and propagation length of gap surface plasmon polaritons in nanoscopically thin metal-cladded planar dielectric slots are investigated theoretically. It is shown that both can, in principle, be accurately estimated from the width of peaks in angle-resolved spectroscopic data, such as that obtained by the attenuated total reflection experiment. The propagation length is shown to be given by the product of lifetime and group velocity. Their dependence on geometric parameters is investigated and simple long-wavelength limit expressions are derived. Based on these, it is possible to make quick estimates of the lifetime and propagation length for a given structure.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  2. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
    [CrossRef]
  3. H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
    [CrossRef]
  4. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
    [CrossRef]
  5. R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
    [CrossRef]
  6. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997).
    [CrossRef]
  7. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
    [CrossRef]
  8. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442–2446 (2004).
    [CrossRef]
  9. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [CrossRef]
  10. W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93 (2006).
    [CrossRef]
  11. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
    [CrossRef]
  12. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
    [CrossRef]
  13. R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
    [CrossRef]
  14. P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
    [CrossRef]
  15. Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B 75, 035411 (2007).
    [CrossRef]
  16. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
    [CrossRef]
  17. G. J. Kovacs and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
    [CrossRef]
  18. C.-I. Lin and T. K. Gaylord, “Loss measurement of plasmonic modes in planar metal–insulator–metal waveguides by an attenuated total reflection method,” Opt. Lett. 35, 3814–3816 (2010).
    [CrossRef]
  19. E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
    [CrossRef]
  20. C.-I. Lin and T. K. Gaylord, “Attenuation and mode profile determination of leaky/lossy modes in multilayer planar waveguides by a coupling simulation method,” Appl. Opt. 48, 3603–3613 (2009).
    [CrossRef]
  21. C.-I. Lin and T. K. Gaylord, “Characterization of the loss of plasmonic modes in planar metal-insulator-metal waveguides by a coupling-simulation approach,” Appl. Opt. 49, 936–944 (2010).
    [CrossRef]
  22. C.-I. Lin and T. K. Gaylord, “Multimode metal-insulator-metal waveguides: analysis and experimental characterization,” Phys. Rev. B 85, 085405 (2012).
    [CrossRef]
  23. M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
    [CrossRef]
  24. R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
    [CrossRef]
  25. P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
    [CrossRef]
  26. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  27. F. Garcia de Abajo, “Plasmons go quantum,” Nature 483, 417–418 (2012).
    [CrossRef]
  28. V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, “The ag dielectric function in plasmonic metamaterials,” Opt. Express 16, 1186–1195 (2008).
    [CrossRef]
  29. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  30. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  31. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  32. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
    [CrossRef]

2013

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

2012

C.-I. Lin and T. K. Gaylord, “Multimode metal-insulator-metal waveguides: analysis and experimental characterization,” Phys. Rev. B 85, 085405 (2012).
[CrossRef]

F. Garcia de Abajo, “Plasmons go quantum,” Nature 483, 417–418 (2012).
[CrossRef]

2010

C.-I. Lin and T. K. Gaylord, “Characterization of the loss of plasmonic modes in planar metal-insulator-metal waveguides by a coupling-simulation approach,” Appl. Opt. 49, 936–944 (2010).
[CrossRef]

C.-I. Lin and T. K. Gaylord, “Loss measurement of plasmonic modes in planar metal–insulator–metal waveguides by an attenuated total reflection method,” Opt. Lett. 35, 3814–3816 (2010).
[CrossRef]

M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[CrossRef]

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

2009

2008

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, “The ag dielectric function in plasmonic metamaterials,” Opt. Express 16, 1186–1195 (2008).
[CrossRef]

2007

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B 75, 035411 (2007).
[CrossRef]

2006

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93 (2006).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

2004

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1999

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

1997

1985

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

1977

G. J. Kovacs and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[CrossRef]

1972

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

1969

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

1965

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Aizpurua, J.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Alaee, R.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93 (2006).
[CrossRef]

Bin Hasan, S.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Boltasseva, A.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Borghs, G.

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Brongersma, M. L.

Brunets, I.

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Cai, W.

Catrysse, P. B.

Chen, L.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Chettiar, U. K.

Christy, R. W.

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

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

Dionne, J. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Dong, Z.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Drachev, V. P.

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Emani, N.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Garcia de Abajo, F.

F. Garcia de Abajo, “Plasmons go quantum,” Nature 483, 417–418 (2012).
[CrossRef]

Garcìa de Abajo, F. J.

M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[CrossRef]

Gaylord, T. K.

Geluk, E. J.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Hill, M. T.

Hou, J.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Huebner, U.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Ishii, S.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Jiang, S.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[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]

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Karouta, F.

Kildishev, A. V.

Kobayashi, T.

Kovacs, G. J.

G. J. Kovacs and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Kuipers, L. K.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

Kurokawa, Y.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B 75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef]

Kuttge, M.

M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[CrossRef]

Lagae, L.

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

Lederer, F.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Leong, E. S. P.

Lezec, H. J.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

Liao, Y.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Lin, C.-I.

Luo, Y.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Marell, M.

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Menzel, C.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B 75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef]

Morimoto, A.

Moskovits, M.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

Naik, G.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Neutens, P.

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

Ning, C.-Z.

Nötzel, R.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Oei, Y.-S.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Pertsch, T.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Polman, A.

M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[CrossRef]

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Pshenay-Severin, E.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Rockstuhl, C.

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Schmitz, J.

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Scott, G. D.

G. J. Kovacs and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[CrossRef]

Selker, M. D.

Shalaev, V.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Shalaev, V. M.

Smalbrugge, B.

Smit, M. K.

Sun, M.

Sweatlock, L. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Takahara, J.

Taki, H.

Van Dorpe, P.

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

van Loon, R.

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

van Veldhoven, P. J.

Verhagen, E.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Walters, R.

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

West, P.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Xu, H.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Yamagishi, S.

Yang, J.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Yuan, H.-K.

Zhang, C.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Zhang, L.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Zhang, R.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Zhang, Y.

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

Zhu, Y.

Zia, R.

Appl. Opt.

Comput. J.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

J. Opt. A

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Laser Photon. Rev.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Nano Lett.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Electrical excitation of confined surface plasmon polaritons in metallic slot waveguides,” Nano Lett. 10, 1429–1432 (2010).
[CrossRef]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

M. Kuttge, F. J. Garcìa de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[CrossRef]

R. Alaee, C. Menzel, U. Huebner, E. Pshenay-Severin, S. Bin Hasan, T. Pertsch, C. Rockstuhl, and F. Lederer, “Deep-subwavelength plasmonic nanoresonators exploiting extreme coupling,” Nano Lett. 13, 3482–3486 (2013).
[CrossRef]

Nat. Mater.

R. Walters, R. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Nature

R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. Yang, and J. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[CrossRef]

F. Garcia de Abajo, “Plasmons go quantum,” Nature 483, 417–418 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Phys. Rev. B

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B 75, 035411 (2007).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[CrossRef]

G. J. Kovacs and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[CrossRef]

C.-I. Lin and T. K. Gaylord, “Multimode metal-insulator-metal waveguides: analysis and experimental characterization,” Phys. Rev. B 85, 085405 (2012).
[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.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef]

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Rev. Mod. Phys.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

Other

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) Schematics of the three-phase metal–insulator–metal geometry with the explanation of field components. The dielectric slot thickness is d, while the optical properties of constituents are described by dielectric permittivities εm(ω) and εd. (b) Excitation of the gap SPP in the ATR setup.

Fig. 2.
Fig. 2.

Map of |G(k,ω)|2 overlaid by the gap SPP dispersion (red diamonds), dielectric lightline (blue circles), and the ωspr line (black squares). For better contrast, the plotted quantity is log10(1+|G(k,ω)|2). The insets show the value of |G(k,ω)|2 along cross sections indicated by the red cross around ω=2eV.

Fig. 3.
Fig. 3.

Explanation of the physical meaning of (a) Lsp and (b) τsp, being directly observed in space- and time-resolved experiments, respectively. The exact (red dots) and fitted (black diamonds) values of (c) Lsp and (d) ωsp plotted as a function of photon energy for three different values of dielectric thickness d. The dashed lines are the long-wavelength approximate values τspapp and Lspapp explained in the next section.

Fig. 4.
Fig. 4.

Parametric analysis of τsp and the approximate expressions. (a) The gap SPP dispersion for εd=2.25 and d=50nm. (b) Dependence of τsp on the electron intraband scattering rate τel. (c) Decrease of τsp with increasing εd. (d) Gap SPP Q-factor variation with εd. Except for the one being varied, parameters in (b), (c), and (d) are same as in (a).

Equations (30)

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

εm(ω)=1ωp2ω(ω+iτel1)FLωL2ω2+iτL1ωωL2,
H(r)=exp(iωt+ikx)H(z)y^.
Hinc(z)=H0exp(ikmz),km=εmk02k2,
H(z)=H0eikmz+B1eikmz,z0,H(z)=A2eikdz+B2eikdz,0<zd,H(z)=A3eikm(zd),d<z,
kd=εdk02k2,Im{kd}0.
B1=r(1e2ikdd)G,A3=(1r2)eikddG,
A2=(1+r)G,B2=re2ikdd(1+r)G,
r=εdkmεmkdεdkm+εmkd,
G=1+r2e2ikdd+r4e4ikdd+=11r2e2ikdd.
εm(ωspr)+εd=0,
1G(k,ω)=0.
|Hω|exp(x/Lsp(ω)),
Lsp=1Im{kc(ω)},
|Hk|exp(t/τsp(k)),
τsp(k)=1Im{ωc(k)},
Re{ωc}=ω0,Im{ωc}=Δω/2,
adu(t)dt+b=δ(t),
u(ω)=1iωa+b=ia1(ωωc),ωc=iba,
|u(ω0)|2=1|a|2and|u(ω0+Im{ωc})|2=12|a|2,
Re{kc}=k0,Im{kc}=Δk/2,
Lspvgτsp,
R(k,ω)=a(k,ω)+b(k,ω)G(k,ω),
A(k,ω)=1|R(k,ω)|2,ω>ck/nprism,
reκd=1,κ=Im{kd},
κd1.
ωτel1,
k=ω+iτspappvgapp.
τspapp=2τel2λp+dλp,vgapp=cεdd2λp+d,
Lspapp=vgappτspapp=2τelcεd2λp+dλpdλp.
Q=ωτsp2.

Metrics