Abstract

The characteristics of surface plasmon polaritons (SPPs) confined in a one-dimensional plasmonic crystal (1D-PlC) cavity are investigated using a cathodoluminescence (CL) detection system equipped with a 200 keV scanning transmission electron microscope (STEM). The dispersion curves of SPPs near the Γ point are derived from the angle-resolved CL spectra, and the SPP cavity modes are observed inside the band gap region. The mode number and wavenumber of the cavity modes are determined from the beam scan CL spectral images. The energy of the cavity mode depends on the cavity length and the angular distribution of the emission from the cavity changes with the mode number of the cavity mode. We also reveal that the phase shift due to the reflection at the cavity edge changes significantly with the resonant energy.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  2. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501 (2010).
    [CrossRef]
  3. T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
    [CrossRef]
  4. R. M. Gelfand, L. Bruderer, and H. Mohseni, “Nanocavity plasmonic device for ultrabroadband single molecule sensing,” Opt. Lett.34(7), 1087–1089 (2009).
    [CrossRef] [PubMed]
  5. C. Marquart, S. I. Bozhevolnyi, and K. Leosson, “Near-field imaging of surface plasmon-polariton guiding in band gap structures at telecom wavelengths,” Opt. Express13(9), 3303–3309 (2005).
    [CrossRef] [PubMed]
  6. Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007).
    [CrossRef]
  7. E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
    [CrossRef]
  8. K. Takeuchi and N. Yamamoto, “Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence,” Opt. Express19(13), 12365–12374 (2011).
    [CrossRef] [PubMed]
  9. A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
    [CrossRef]
  10. A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
    [CrossRef] [PubMed]
  11. S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
    [CrossRef]
  12. J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
    [CrossRef] [PubMed]
  13. S. Balci, E. Karademir, C. Kocabas, and A. Aydinli, “Direct imaging of localized surface plasmon polaritons,” Opt. Lett.36(17), 3401–3403 (2011).
    [CrossRef] [PubMed]
  14. J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
    [CrossRef]
  15. V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
    [CrossRef] [PubMed]
  16. D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
    [CrossRef] [PubMed]
  17. N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
    [CrossRef]
  18. N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
    [CrossRef] [PubMed]
  19. T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
    [CrossRef] [PubMed]
  20. M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
    [CrossRef]
  21. T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express17(26), 23664–23671 (2009).
    [CrossRef] [PubMed]
  22. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).
  23. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
    [CrossRef] [PubMed]
  24. M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull.37(01), 39–46 (2012).
    [CrossRef]
  25. N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett.93(9), 093114 (2008).
    [CrossRef]
  26. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
    [CrossRef] [PubMed]

2012

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
[CrossRef] [PubMed]

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull.37(01), 39–46 (2012).
[CrossRef]

2011

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

K. Takeuchi and N. Yamamoto, “Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence,” Opt. Express19(13), 12365–12374 (2011).
[CrossRef] [PubMed]

S. Balci, E. Karademir, C. Kocabas, and A. Aydinli, “Direct imaging of localized surface plasmon polaritons,” Opt. Lett.36(17), 3401–3403 (2011).
[CrossRef] [PubMed]

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
[CrossRef] [PubMed]

2010

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501 (2010).
[CrossRef]

2009

A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
[CrossRef] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

R. M. Gelfand, L. Bruderer, and H. Mohseni, “Nanocavity plasmonic device for ultrabroadband single molecule sensing,” Opt. Lett.34(7), 1087–1089 (2009).
[CrossRef] [PubMed]

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express17(26), 23664–23671 (2009).
[CrossRef] [PubMed]

2008

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett.93(9), 093114 (2008).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
[CrossRef]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
[CrossRef]

2007

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007).
[CrossRef]

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

2005

2003

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

2001

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
[CrossRef]

1996

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Adamo, G.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

Araya, K.

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
[CrossRef]

Atwater, H. A.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Aydinli, A.

S. Balci, E. Karademir, C. Kocabas, and A. Aydinli, “Direct imaging of localized surface plasmon polaritons,” Opt. Lett.36(17), 3401–3403 (2011).
[CrossRef] [PubMed]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
[CrossRef] [PubMed]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
[CrossRef]

Balci, S.

S. Balci, E. Karademir, C. Kocabas, and A. Aydinli, “Direct imaging of localized surface plasmon polaritons,” Opt. Lett.36(17), 3401–3403 (2011).
[CrossRef] [PubMed]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

Barnes, W. L.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Botton, G. A.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

Bouhelier, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

Bruderer, L.

Coenen, T.

T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
[CrossRef] [PubMed]

Colas des Francs, G.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Colliex, C.

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Couillard, M.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

Dereux, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

Devaux, E.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

Ebbesen, T. W.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

García de Abajo, F. J.

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull.37(01), 39–46 (2012).
[CrossRef]

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
[CrossRef] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
[CrossRef]

Gelfand, R. M.

Geuquet, N.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

Gong, Y.

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007).
[CrossRef]

Henrard, L.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Karademir, E.

Kawata, S.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
[CrossRef]

Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Kocabas, A.

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
[CrossRef] [PubMed]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
[CrossRef]

Kocabas, C.

S. Balci, E. Karademir, C. Kocabas, and A. Aydinli, “Direct imaging of localized surface plasmon polaritons,” Opt. Lett.36(17), 3401–3403 (2011).
[CrossRef] [PubMed]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

Kociak, M.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull.37(01), 39–46 (2012).
[CrossRef]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Koenderink, A. F.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Kumacheva, E.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

Kuttge, M.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Leosson, K.

Lezec, H. J.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Liz-Marzán, L. M.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

MacDonald, K. F.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

Markey, L.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Marquart, C.

Mohseni, H.

Myroshnychenko, V.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

Nelayah, J.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Notomi, M.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501 (2010).
[CrossRef]

Ohtani, S.

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
[CrossRef] [PubMed]

Okamoto, T.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
[CrossRef]

Pastoriza-Santos, I.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Polman, A.

T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
[CrossRef] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Rodríguez-Fernández, J.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

Rossouw, D.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

Sambles, J. R.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Senlik, S. S.

A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
[CrossRef] [PubMed]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
[CrossRef]

Simonen, J.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
[CrossRef]

Stefani, F. D.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

Stéphan, O.

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Suzuki, T.

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express17(26), 23664–23671 (2009).
[CrossRef] [PubMed]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett.93(9), 093114 (2008).
[CrossRef]

Takeuchi, K.

Taminiau, T. H.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

Taverna, D.

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Tencé, M.

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

van Hulst, N. F.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

Vesseur, E. J. R.

T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
[CrossRef] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

Vickery, J.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

Vuckovic, J.

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007).
[CrossRef]

Weeber, J.-C.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

Yamamoto, N.

K. Takeuchi and N. Yamamoto, “Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence,” Opt. Express19(13), 12365–12374 (2011).
[CrossRef] [PubMed]

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
[CrossRef] [PubMed]

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express17(26), 23664–23671 (2009).
[CrossRef] [PubMed]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett.93(9), 093114 (2008).
[CrossRef]

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
[CrossRef]

Zheludev, N. I.

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

ACS Nano

T. Coenen, E. J. R. Vesseur, and A. Polman, “Deep Subwavelength Spatial Characterization of Angular Emission from Single-Crystal Au Plasmonic Ridge Nanoantennas,” ACS Nano6(2), 1742–1750 (2012).
[CrossRef] [PubMed]

Appl. Phys. Lett.

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007).
[CrossRef]

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett.83(24), 4936–4938 (2003).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, “Localization of surface plasmon polaritons in hexagonal arrays of Moiré cavities,” Appl. Phys. Lett.98(3), 031101 (2011).
[CrossRef]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett.93(9), 093114 (2008).
[CrossRef]

MRS Bull.

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull.37(01), 39–46 (2012).
[CrossRef]

Nano Lett.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11(3), 1020–1024 (2011).
[CrossRef] [PubMed]

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer In-Plane Integrated Surface Plasmon Cavities,” Nano Lett.7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

V. Myroshnychenko, J. Nelayah, G. Adamo, N. Geuquet, J. Rodríguez-Fernández, I. Pastoriza-Santos, K. F. MacDonald, L. Henrard, L. M. Liz-Marzán, N. I. Zheludev, M. Kociak, and F. J. García de Abajo, “Plasmon Spectroscopy and Imaging of Individual Gold Nanodecahedra: A Combined Optical Microscopy, Cathodoluminescence, and Electron Energy-Loss Spectroscopy Study,” Nano Lett.12(8), 4172–4180 (2012).
[CrossRef] [PubMed]

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar Plasmonic Resonances in Silver Nanowire Antennas Imaged with a Subnanometer Electron Probe,” Nano Lett.11(4), 1499–1504 (2011).
[CrossRef] [PubMed]

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie Plasmons in Individual Silver Nanospheres near a Silver Surface,” Nano Lett.11(1), 91–95 (2011).
[CrossRef] [PubMed]

Nat. Phys.

J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B79(11), 113405 (2009).
[CrossRef]

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by a high energy electron beam,” Phys. Rev. B64(20), 205419 (2001).
[CrossRef]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B77(11), 115425 (2008).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B77(19), 195130 (2008).
[CrossRef]

Phys. Rev. B Condens. Matter

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. Kocabas, S. S. Senlik, and A. Aydinli, “Slowing down surface plasmons on a Moiré surface,” Phys. Rev. Lett.102(6), 063901 (2009).
[CrossRef] [PubMed]

Rep. Prog. Phys.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501 (2010).
[CrossRef]

Other

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

E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

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 (7)

Fig. 1
Fig. 1

(a) Schematic drawing of a one-dimensional plasmonic crystal (1D-PlC) cavity. Cavity edge is defined as the center of the terrace. (b) Schematic diagram of the dispersion curves near the Γ point of a 1D-PlC. Energy of the higher (lower) band gap edge is E + ( E ). (c) Standing wave patterns of the normal electric field component at each band edge. Surface charge distribution is also shown.

Fig. 2
Fig. 2

(a) Resonant energy calculated using Eq. (3a) (dashed lines) and Eq. (3b) (solid lines) as a function of cavity length. Values of E + and E are obtained from the experimental result shown in Fig. 4. (b) Standing wave patterns of the normal electric field component at the central energy of the band gap. Symmetric (asymmetric) standing wave arises inside cavities when n is even (odd) number.

Fig. 3
Fig. 3

(a) SEM image of a sample with a one-dimensional plasmonic crystal cavity, and a diagram of the cross-section. The grating (period = 600 nm, filling factor = 0.25, height = 100 nm) with a cavity fabricated on an InP substrate is coated with a 200 nm thick silver layer. Scale bar is 1 μm. (b) Geometry of the angle-resolved measurement with a parabolic mirror and a pinhole. Sample is tilted to detect light emitted in the surface normal direction (red line). (c) Angular distribution of the emission from the sample tilted by α = 16° in the y direction. Dashed (solid) lines indicate equi-θ (φ) lines. The pinhole is moved along the red line through the green point (the surface normal direction) to obtain the ARS patterns shown. Angle φ can be regarded as 90° in the range of θ ≤ 10°.

Fig. 4
Fig. 4

(a) ARS pattern from a 1D-PlC (without cavity). This pattern reveals the dispersion pattern of SPPs near the Γ point in a 1D-PlC. Wide plasmonic band gap arises between 1.745 and 2.021 eV. (b) BSS image taken by light emission in the surface normal direction. Cross-section of the 1D-PlC is depicted below the image.

Fig. 5
Fig. 5

ARS patterns (upper part) and BSS images (lower part) of the four cavities with different cavity lengths: (a) 450 nm, (b) 800 nm, (c) 1200 nm, and (d) 1500 nm. Mode number is deduced from the number of peaks inside each cavity. Emission at θ = 0° occurs when n is an odd number. In contrast, the emission at θ = 5-10° occurs when n is an even number. (e) BSS image over a wider area of the sample (L = 1500 nm). Cross-section of the sample is depicted below each BSS image.

Fig. 6
Fig. 6

BSS images of three cavities with the same order (n = 5) but different cavity lengths of (a) 1400 nm, (b) 1450 nm, and (c) 1500 nm. Red shift occurs as cavity length increases (black arrows). Distance between two antinodes equals the half-wavelength of the cavity mode. (d) Experimental energy of the cavity modes versus the cavity length. Theoretical curves (Fig. 2(a)) are also shown.

Fig. 7
Fig. 7

(a) Relation between energy and wavenumber of the cavity modes derived from the BSS images. Solid line indicates the dispersion curve of SPPs at the vacuum/silver interface. (b) Phase shift versus energy of the cavity mode. Solid line indicates the relation in Eq. (2). Red, green, and blue circles indicate n = 3, 4 and 5, respectively.

Equations (8)

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

k x SPP L+Φ=nπ,
Φ( E cav )= π ΔE ( E cav E ),
k x SPP = 2π Λ .
k SPP = ( k x SPP ) 2 + ( k y SPP ) 2 =Re[ E cav c ε Ag ε Ag +1 ],
k x ph = E ph c sinθsinϕ E ph c sinθ, k y ph = E ph c sinθcosϕ0,
| k x SPP k x ph |=|G|,
k y SPP k y ph =0,
E SPP = E ph ,

Metrics