Abstract

The negative dispersion of the TM1 mode of a thin plasmonic gap, occurring at frequencies exceeding the surface plasmon frequency, is assigned by causality to be a backward wave. This negative index mode, is also slow-light – having small positive group velocity and is exhibiting inverse geometrical cutoff characteristics – namely when the gap width is enhanced.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Marcuse, Theory of dielectric optical waveguides, 2’nd Ed., (Academic, San-Diego, 1991).
  2. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
    [CrossRef]
  3. E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol.  25, 2547–2562 (2007).
    [CrossRef]
  4. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
    [CrossRef] [PubMed]
  5. M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.  93, 137404, (2004).
    [CrossRef] [PubMed]
  6. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with ?/4 impedance matching,” Opt. Express 15, 6762–6767 (2007).
    [CrossRef] [PubMed]
  7. A. A. Oliner and T. Tamir, “Backward waves on isotropic plasma slabs,” J. Appl. Phys.  33, 231–233 (1962).
    [CrossRef]
  8. H. Shin and S. Fan, “All-Angle Negative Refraction for Surface Plasmon Waves Using a Metal-Dielectric-Metal Structure,” Phys. Rev. Lett.  96, 073907 (2006).
    [CrossRef] [PubMed]
  9. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
    [CrossRef] [PubMed]
  10. E. D. Palik, Handbook of optical constants of solids, 2’nd Ed. (San-Diego: Academic, 1998).
  11. H. Reather, Surface plasmon (Springer, Berlin, 1988).
  12. Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
    [CrossRef] [PubMed]
  14. V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B  71, 201101(R) (2005).

2007 (4)

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol.  25, 2547–2562 (2007).
[CrossRef]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
[CrossRef]

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with ?/4 impedance matching,” Opt. Express 15, 6762–6767 (2007).
[CrossRef] [PubMed]

2006 (2)

H. Shin and S. Fan, “All-Angle Negative Refraction for Surface Plasmon Waves Using a Metal-Dielectric-Metal Structure,” Phys. Rev. Lett.  96, 073907 (2006).
[CrossRef] [PubMed]

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
[CrossRef] [PubMed]

2005 (1)

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B  71, 201101(R) (2005).

2004 (1)

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.  93, 137404, (2004).
[CrossRef] [PubMed]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

1991 (1)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
[CrossRef]

1962 (1)

A. A. Oliner and T. Tamir, “Backward waves on isotropic plasma slabs,” J. Appl. Phys.  33, 231–233 (1962).
[CrossRef]

Arbel, D.

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

Fan, S.

H. Shin and S. Fan, “All-Angle Negative Refraction for Surface Plasmon Waves Using a Metal-Dielectric-Metal Structure,” Phys. Rev. Lett.  96, 073907 (2006).
[CrossRef] [PubMed]

Feigenbaum, E.

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol.  25, 2547–2562 (2007).
[CrossRef]

Ginzburg, P.

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with ?/4 impedance matching,” Opt. Express 15, 6762–6767 (2007).
[CrossRef] [PubMed]

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

Kaminsky, N.

Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
[CrossRef]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, Theory of dielectric optical waveguides, 2’nd Ed., (Academic, San-Diego, 1991).

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
[CrossRef]

Narimanov, E. E.

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B  71, 201101(R) (2005).

Oliner, A. A.

A. A. Oliner and T. Tamir, “Backward waves on isotropic plasma slabs,” J. Appl. Phys.  33, 231–233 (1962).
[CrossRef]

Orenstein, M.

Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
[CrossRef]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol.  25, 2547–2562 (2007).
[CrossRef]

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with ?/4 impedance matching,” Opt. Express 15, 6762–6767 (2007).
[CrossRef] [PubMed]

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids, 2’nd Ed. (San-Diego: Academic, 1998).

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

Podolskiy, V. A.

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B  71, 201101(R) (2005).

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
[CrossRef]

Reather, H.

H. Reather, Surface plasmon (Springer, Berlin, 1988).

Satuby, Y.

Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
[CrossRef]

Shin, H.

H. Shin and S. Fan, “All-Angle Negative Refraction for Surface Plasmon Waves Using a Metal-Dielectric-Metal Structure,” Phys. Rev. Lett.  96, 073907 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.  93, 137404, (2004).
[CrossRef] [PubMed]

Tamir, T.

A. A. Oliner and T. Tamir, “Backward waves on isotropic plasma slabs,” J. Appl. Phys.  33, 231–233 (1962).
[CrossRef]

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

J. Appl. Phys (1)

A. A. Oliner and T. Tamir, “Backward waves on isotropic plasma slabs,” J. Appl. Phys.  33, 231–233 (1962).
[CrossRef]

J. Lightwave Technol (1)

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol.  25, 2547–2562 (2007).
[CrossRef]

J. Opt. Soc. Am (1)

Y. Satuby, N. Kaminsky, and M. Orenstein, “Nano Optical Waveguide Modes in Gaps Embedded in Left-Hand-Metamaterial,” J. Opt. Soc. Am. B  24, A62–A68 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett (1)

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett.  31, 3288–3290 (2006).
[CrossRef] [PubMed]

Phys. Rev (2)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B  44, 13556–13572 (1991).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B  71, 201101(R) (2005).

Phys. Rev. Lett (3)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures”, Phys. Rev. Lett.  76, 4773–4776 (1996)
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.  93, 137404, (2004).
[CrossRef] [PubMed]

H. Shin and S. Fan, “All-Angle Negative Refraction for Surface Plasmon Waves Using a Metal-Dielectric-Metal Structure,” Phys. Rev. Lett.  96, 073907 (2006).
[CrossRef] [PubMed]

Science (1)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

Other (3)

E. D. Palik, Handbook of optical constants of solids, 2’nd Ed. (San-Diego: Academic, 1998).

H. Reather, Surface plasmon (Springer, Berlin, 1988).

D. Marcuse, Theory of dielectric optical waveguides, 2’nd Ed., (Academic, San-Diego, 1991).

Supplementary Material (2)

» Media 1: MOV (3595 KB)     
» Media 2: MOV (2027 KB)     

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 (5)

Fig. 1.
Fig. 1.

Waveguide tapers schematics: (a) photonic or microwave taper may exhibit a cutoff when its lateral dimension is reduced; (b) plasmonic taper supporting slow-waves and light does not exhibit a cutoff; (c) plasmonic taper supporting backward waves exhibit a cutoff when its lateral dimension is enhanced.

Fig. 2.
Fig. 2.

(a) Lossless dispersion relations of TM0 and TM1 modes in “plasmonic gap” for different gap widths- d, metal permittivity according to loss-less Drude model (λp=137nm). (b) Actual dispersion Including loss) of the first 3 anti-symmetric H-field modes for d=30nm. Metal permittivity is taken from measurements [10]. ℰD=3.52.

Fig. 3.
Fig. 3.

(a) Dispersion relations of TM1 modes in “plasmonic gap” for different gap widths, λp=137nm (b) Geometrical dispersion of the first 3 anti-symmetric modes: negative index mode reaching a cutoff (blue) and two evanescent modes (TM3 in red & TM5 in green), λ=622nm (ω=0.22ωp), Au-Dielectric-Au layers. (Metal permittivity is according to measurements [10], ℰD=3.52) (Media 1).

Fig. 4.
Fig. 4.

(a) Calculation schematics: modeling the taper as a chain of thin slices, using transfer matrix and propagation in each slice, (b) Power (Pointing vector) distribution along propagation, Sz, for a taper going from 20nm to 50nm gap width. λ=622nm, ℰD=3.52, ℰM=-86.1-i8.16.

Fig. 5.
Fig. 5.

Negative index waves in an inverted taper: snapshots of H-field distribution (FDTD simulation). λ=1.5μm, ℰD=122, din=22nm, dout=32nm, Length=0.5μm. (Media 2)

Metrics