Abstract

Satuby and Orenstein [Opt. Express 15, 4247–4252 (2007)] reported the discovery and numerical and experimental investigation of long-range surface plasmon-polariton eigenmodes guided by wide (6 to 12 μm) rectangular gaps in 400 nm thick gold films using excitation of vacuum wavelength λvac = 1.55 μm. In this paper, we carry out a detailed numerical analysis of the two different types of plasmonic modes in these structures. We show that no long-range eigenmodes exists for these gap plasmon waveguides, and that the reported “modes” are likely to be beams of bulk waves and surface plasmons, rather than guided modes of the considered structures.

© 2007 Optical Society of America

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  1. D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
    [CrossRef]
  2. G. Veronis and S. Fan, "Guided subwavelength plasmonic mode support by a slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005).
    [CrossRef]
  3. L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 6645-6650 (2005).
    [CrossRef] [PubMed]
  4. D. F. P. Pile and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069-1071 (2004).
    [CrossRef] [PubMed]
  5. D. K. Gramotnev and D. F. P. Pile, "Single-mode sub-wavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
    [CrossRef]
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
    [CrossRef] [PubMed]
  7. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
    [CrossRef] [PubMed]
  8. D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
    [CrossRef]
  9. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
    [CrossRef]
  10. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
    [CrossRef]
  11. Y. Satuby and M. Orenstein, "Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis," Opt. Express 15, 4247-4252 (2007).
    [CrossRef] [PubMed]
  12. D. F. P. Pile, "Compact-2D FDTD for waveguides including materials with negative dielectric permittivity, magnetic permittivity and refractive index," Appl. Phys. B 81, 607-613 (2005).
    [CrossRef]
  13. Y. Satuby and M. Orenstein, "Surface plasmon poloariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
    [CrossRef]

2007 (2)

Y. Satuby and M. Orenstein, "Surface plasmon poloariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

Y. Satuby and M. Orenstein, "Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis," Opt. Express 15, 4247-4252 (2007).
[CrossRef] [PubMed]

2006 (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

2005 (6)

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, "Compact-2D FDTD for waveguides including materials with negative dielectric permittivity, magnetic permittivity and refractive index," Appl. Phys. B 81, 607-613 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

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

G. Veronis and S. Fan, "Guided subwavelength plasmonic mode support by a slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005).
[CrossRef]

2004 (2)

D. F. P. Pile and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069-1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, "Single-mode sub-wavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

2000 (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Berini, P.

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Fan, S.

Fukui, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

Gramotnev, D. K.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069-1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, "Single-mode sub-wavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

Han, Z.

Haraguchi, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

He, S.

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Liu, L.

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Matsuzaki, Y.

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

Ogawa, T.

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Okamoto, T.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

Orenstein, M.

Y. Satuby and M. Orenstein, "Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis," Opt. Express 15, 4247-4252 (2007).
[CrossRef] [PubMed]

Y. Satuby and M. Orenstein, "Surface plasmon poloariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

Pile, D. F. P.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, "Compact-2D FDTD for waveguides including materials with negative dielectric permittivity, magnetic permittivity and refractive index," Appl. Phys. B 81, 607-613 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069-1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, "Single-mode sub-wavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

Satuby, Y.

Y. Satuby and M. Orenstein, "Surface-Plasmon-Polariton modes in deep metallic trenches- measurement and analysis," Opt. Express 15, 4247-4252 (2007).
[CrossRef] [PubMed]

Y. Satuby and M. Orenstein, "Surface plasmon poloariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

Vernon, K. C.

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

Veronis, G.

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Yamaguchi, K.

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

Appl. Phys. B (1)

D. F. P. Pile, "Compact-2D FDTD for waveguides including materials with negative dielectric permittivity, magnetic permittivity and refractive index," Appl. Phys. B 81, 607-613 (2005).
[CrossRef]

Appl. Phys. Lett. (4)

Y. Satuby and M. Orenstein, "Surface plasmon poloariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, "Single-mode sub-wavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

J. Appl. Phys. (1)

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 013101 (2006).
[CrossRef]

Nature (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon sub-wavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Gap plasmon waveguide in the form of a rectangular gap (trench) of width, w, in a metal film of thickness h. (b) Representation of the guided plasmonic modes formed by coupled wedge plasmons at the four corners of the gap. (c) Geometrical optics representation of the higher order modes formed by gap plasmon modes guided by the effective index core formed by the finite thickness of the film. (d) A typical plasmonic mode field (distribution of |E|) formed by four coupled wedge plasmons with symmetric (across the thickness of the film) and anti-symmetric (across the gap) distribution of charges; w = h = 400 nm, vacuum wavelength λ vac = 1.55 μm, the gap is made in a gold film (ε Au = - 96.90 + i10.97), the dielectric permittivity inside and outside the gap is ε d = 2.25.

Fig. 2.
Fig. 2.

(a) The dependencies of the real parts of the effective mode indices Re(neff ) = Re[kλvac/(2π)] and (b) propagation distances L = 0.5/Im(k) on the gap width w for the (sfag ) cw (asterisks) and (sfsg ) cw (circles) plasmonic modes. The dashed straight lines correspond to the effective index (a) and propagation distance (b) for the (sfag ) cw and (sfsg ) cw modes at the infinite gap width. The dotted straight line corresponds to the effective index for surface plasmons at the top and bottom interfaces of the gold film. (c,d) Representation of the charge distribution for (c) the (sfag ) cw mode (with the charge distribution symmetric across the film and antisymmetric across the gap), and (d) the (sfsg ) cw mode (with the charge distribution symmetric across the film and gap). w = 400 nm, λ vac = 1.55 μm, permittivity of the dielectric inside and outside the gap ε d = 2.25, and ε Au = - 96.90 + i10.97.

Fig. 3.
Fig. 3.

The distributions of the magnitude of the electric field |E| in (a) the (sfag ) cw mode at large gap width w = 6 μm in a gold film (ε Au = - 96.90 + i10.97, λ vac = 1.55 μm) of 400 nm thickness imbedded in the uniform dielectric medium with the permittivity ε d = 2.25, and (b) the plasmon mode guided by the two 90° coupled wedges formed by a rectangular cross-section of the gold film (i.e., at w = ∞). Note that the distributions of |E| and |H| are similar for these eignemodes, e.g. having maxima at the same locations, etc.

Fig. 4.
Fig. 4.

(a) The dependencies of the real part of the effective mode index neff on gap width w for the (sfag ) cw (asterisks), (afag ) cw (circles), (sfag ) gp1 (crosses), and (afag ) gp1 (squares) plasmonic modes. The dotted straight line corresponds to the effective index for the surface plasmon at the top and bottom interfaces of the gold film. (b-d) Charge symmetries in the gap, corresponding to the (b) (afag ) cw , (c) (sfag ) gp1, and (d) (afag ) gp1 plasmonic modes. The other structural parameters are the same as for the previous Figs.

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