Abstract

A circular zero-time-averaged power component, coupling the forward (dielectric) and backward (metal) power channels of Surface Plasmon Polaritons (SPPs), is shown to be the core ingredient for the slow-light characteristic of SPPs at the surface plasmon frequency, for both a lossless and lossy metal. Additional slow-light regimes emerging in configurations where few SPPs are strongly coupled, such as in a narrow plasmonic gap and slab, forming local extrema of the dispersion curve (branch points for positive and negative index branches), are also propelled by the circular motion of the plasmonic power.

© 2010 OSA

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  1. R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957).
    [CrossRef]
  2. M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
    [CrossRef]
  3. M. Orenstein, “Slow Light by Slow Waves: Plasmonics for Light Halting,” Topical Meeting on Slow and Fast Light 2007, Salt-Lake City Utah, USA (2007).
  4. A. A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity manipulation in nanowaveguides,” Phys. Rev. Lett. 97(22), 223902 (2006).
    [CrossRef] [PubMed]
  5. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
    [CrossRef] [PubMed]
  6. A. A. Oliner and T. Tamir, “Backward waves on Isotropic Plasma Slabs,” J. Appl. Phys. 33(1), 231–233 (1962).
    [CrossRef]
  7. H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
    [CrossRef] [PubMed]
  8. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
    [CrossRef] [PubMed]
  9. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  10. S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
    [CrossRef] [PubMed]
  11. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
    [CrossRef] [PubMed]
  12. E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” JLT 25, 2547–2562 (2007).
  13. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
    [CrossRef] [PubMed]
  14. 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(9), 097401 (2006).
    [CrossRef] [PubMed]
  15. E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
    [CrossRef] [PubMed]
  16. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
    [CrossRef] [PubMed]
  17. E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
    [CrossRef]
  18. G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67(3), 035109 (2003).
    [CrossRef]
  19. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
    [CrossRef]
  20. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
    [CrossRef] [PubMed]
  21. T. Tamir and A. A. Oliner, “The Spectrum of Electromagnetic Waves Guided by a Plasma Layer,” Proc. IEEE 51(2), 317–332 (1963).
    [CrossRef]

2010 (1)

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

2009 (1)

E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
[CrossRef]

2008 (1)

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

2007 (5)

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” JLT 25, 2547–2562 (2007).

M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
[CrossRef]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

2006 (4)

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

A. A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity manipulation in nanowaveguides,” Phys. Rev. Lett. 97(22), 223902 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

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(9), 097401 (2006).
[CrossRef] [PubMed]

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

2003 (1)

G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67(3), 035109 (2003).
[CrossRef]

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

1999 (1)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

1963 (1)

T. Tamir and A. A. Oliner, “The Spectrum of Electromagnetic Waves Guided by a Plasma Layer,” Proc. IEEE 51(2), 317–332 (1963).
[CrossRef]

1962 (1)

A. A. Oliner and T. Tamir, “Backward waves on Isotropic Plasma Slabs,” J. Appl. Phys. 33(1), 231–233 (1962).
[CrossRef]

1957 (1)

R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957).
[CrossRef]

Atwater, H. A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Burgos, S. P.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

de Waele, R.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[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(7), 073907 (2006).
[CrossRef] [PubMed]

Feigenbaum, E.

E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
[CrossRef]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” JLT 25, 2547–2562 (2007).

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity manipulation in nanowaveguides,” Phys. Rev. Lett. 97(22), 223902 (2006).
[CrossRef] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Kaminski, N.

E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
[CrossRef]

Kuipers, L.

M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
[CrossRef]

Kurokawa, Y.

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(9), 097401 (2006).
[CrossRef] [PubMed]

Lee, R. K.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

Miyazaki, H. T.

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(9), 097401 (2006).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Oliner, A. A.

T. Tamir and A. A. Oliner, “The Spectrum of Electromagnetic Waves Guided by a Plasma Layer,” Proc. IEEE 51(2), 317–332 (1963).
[CrossRef]

A. A. Oliner and T. Tamir, “Backward waves on Isotropic Plasma Slabs,” J. Appl. Phys. 33(1), 231–233 (1962).
[CrossRef]

Orenstein, M.

E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
[CrossRef]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” JLT 25, 2547–2562 (2007).

Podolskiy, V. A.

A. A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity manipulation in nanowaveguides,” Phys. Rev. Lett. 97(22), 223902 (2006).
[CrossRef] [PubMed]

Polman, A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

Ritchie, R. H.

R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957).
[CrossRef]

Sandtke, M.

M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
[CrossRef]

Scherer, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (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(7), 073907 (2006).
[CrossRef] [PubMed]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Shvets, G.

G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67(3), 035109 (2003).
[CrossRef]

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Tamir, T.

T. Tamir and A. A. Oliner, “The Spectrum of Electromagnetic Waves Guided by a Plasma Layer,” Proc. IEEE 51(2), 317–332 (1963).
[CrossRef]

A. A. Oliner and T. Tamir, “Backward waves on Isotropic Plasma Slabs,” J. Appl. Phys. 33(1), 231–233 (1962).
[CrossRef]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Xu, Y.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

A. A. Oliner and T. Tamir, “Backward waves on Isotropic Plasma Slabs,” J. Appl. Phys. 33(1), 231–233 (1962).
[CrossRef]

JLT (1)

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” JLT 25, 2547–2562 (2007).

Nat. Mater. (1)

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9(5), 407–412 (2010).
[CrossRef] [PubMed]

Nat. Photonics (2)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
[CrossRef]

Nature (2)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

E. Feigenbaum, N. Kaminski, and M. Orenstein, “Negative dispersion: a backward wave or fast light? Nanoplasmonic examples,” Opt. Express 17(21), 18934–18939 (2009).
[CrossRef]

Opt. Lett. (1)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Phys. Rev. (1)

R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957).
[CrossRef]

Phys. Rev. B (1)

G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67(3), 035109 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

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(9), 097401 (2006).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

A. A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity manipulation in nanowaveguides,” Phys. Rev. Lett. 97(22), 223902 (2006).
[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(7), 073907 (2006).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Proc. IEEE (1)

T. Tamir and A. A. Oliner, “The Spectrum of Electromagnetic Waves Guided by a Plasma Layer,” Proc. IEEE 51(2), 317–332 (1963).
[CrossRef]

Science (2)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Other (1)

M. Orenstein, “Slow Light by Slow Waves: Plasmonics for Light Halting,” Topical Meeting on Slow and Fast Light 2007, Salt-Lake City Utah, USA (2007).

Supplementary Material (2)

» Media 1: MPG (3662 KB)     
» Media 2: MPG (4009 KB)     

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Figures (9)

Fig. 1
Fig. 1

Circular power flow of a SPP propagating along a lossless gold (x<0) air (x>0) interface for vacuum wavelength λ 0 = 216nm; Poynting vector (small arrows) and its magnitude (contour).The circular motion is illustrated by the thick arrows inset.

Fig. 2
Fig. 2

Frequency dependence of (a) the circularity measure (green) and net power flow (purple), and (b) the coupling coefficients CD M (blue) and CM D (red) in logarithmic scale, of a SPP propagating along a lossless gold-air interface. SPP frequency – dashed gray lines.

Fig. 3
Fig. 3

(a) Schematics of a metal slab and the H-field distribution of the modes, (b) dispersion curves of TM0 S (solid) and TM1 S (dashed) for lossless gold slabs in air at various thicknesses, and (c) a close-up on the positive (green) and negative (red) index branches for the dispersion curve of TM1 S at their actual position (power is propagating to positive z direction). Black arrows in (b) indicate the direction of stronger SPP coupling (decreasing dM ). The SPP dispersion curve – dashed black; the light line in (b) – black line; SPP frequency – dashed gray lines.

Fig. 5
Fig. 5

Poynting vector (arrows) and its magnitude (contour) for TM1 S of a lossless gold slab (in air) of thickness dM = 30nm, at frequency corresponding to (a) the local maximum, and (b) near the characteristic SPP frequency.

Fig. 4
Fig. 4

(a) Net power flow, (b) dispersion curve, and (c) coupling coefficients (in logarithmic scale) CD M (dashed) and CM D (solid), for TM1 S for lossless gold slabs in air at various thicknesses. Black rectangles in (c) indicate coincidence of the coupling coefficients at the extrema for the red curves. The SPP dispersion curve in (b) – dashed black; SPP frequency – dashed gray lines; vertical black lines in (a) and (c) indicates 0 and 1 respectively.

Fig. 6
Fig. 6

Schematics of a gap of thickness dD and the H-field of the gap modes, and (b) the dispersion curves of TM0 G (solid) and TM1 G (dashed) for air gaps (in lossless gold) at various widths. SPP dispersion curve – dashed black; light line – black line; SPP frequency – dashed gray line.

Fig. 7
Fig. 7

(a) Net power flow, (b) dispersion curve, and (c) coupling coefficients (logarithmic scale) CD M (dashed) and CM D (solid), for TM1 G of air gaps (in lossless gold) at various widths. Black rectangles in (c) indicate coincidence of the coupling coefficients at the extremum for the red curves; SPP frequency – dashed gray lines; vertical black lines in (a) and (c) indicates 0 and 1 respectively.

Fig. 8
Fig. 8

Snapshots of the Poynting vector (small arrows) and magnitude (contours) of TM1 G for an air gap (in lossy gold) of width dD = 50nm at frequency ω = 0.682ωp and at times t = 0 (a,b) and t = π/4ω (c,d), for the positive (a,c, Media 1) and negative (b,d, Media 2) index branches. Propagation of the circular power trajectory (at phase velocity) is tracked by green and red ellipses for the positive and negative index branches respectively. The overall power flowing through the dielectric and metal channels is illustrated by the magnitude of the thick green and red arrows respectively, while the direction of the net power flow is positive for both branches (the direction of decreasing magnitude).

Fig. 9
Fig. 9

The (a,c) imaginary and (b) real parts the propagation constant β of TM1 G for air gaps (in lossy gold) at various widths. The curves of the positive and negative branches are in solid and dashed respectively. The SPP dispersion curve (with losses) is in dotted purple. A zoomed section of the branch point for the red curves in (b) is presented inset for clarity. The black arrows in (a) and (c) indicate the direction of increasing losses.

Equations (21)

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ε M ( ω ) = ε 0 ( 1 ω p 2 ω ( ω + j γ ) )
H y ( x , z ) = e j β z f S P P ( x ) e j β z { e κ M x ,   x < 0 e κ D x ,   x > 0
[ S x , S z ] = [ S ¯ x , S ¯ z ] + [ E S P P sin ( 2 ϕ ) , E S P P ( x ) cos ( 2 ϕ ) ] f S P P 2 ( x ) / 2
[ S ¯ x , S ¯ z ] = [ 0 , E S P P ( x ) / 2 ] f S P P 2 ( x )
C D M P P = ( κ D β ) 2
C M D P P = ( κ M β ) 2
| × S | x 0 = β κ D ω ε D
P S P P [ S x , S z ] z ^ d x = β ω κ M ε M ( 1 κ M 2 κ D 2 ) cos 2 ( ω t β z )
[ S x , S z ] T M 1 S = [ S ¯ x , S ¯ z ] T M 1 S + [ E S sin ( 2 ϕ ) f T M 0 S ( x ) f T M 1 S ( x ) , E S ( x ) cos ( 2 ϕ ) f T M 1 S 2 ( x ) ] / 2
[ S ¯ x , S ¯ z ] T M 1 S = [ 0 , E S ( x ) ] f T M 1 S 2 ( x ) / 2
P ( ω ) = β ω κ D ε D ( 1 κ D 2 κ M 2 ( 1 κ M d M sinh ( κ M d M ) ) ) cos 2 ( ω t β z )
C D M P P = ( κ D β ) 2
C M D P P = ( κ M β ) 2 ( 1 κ M d M sinh ( κ M d M ) ) 1
κ M 2 κ D 2 1 = κ M d M sinh ( κ M d M )
P ( ω ) = β ω κ M ε M ( 1 κ M 2 κ D 2 ( 1 ± κ D d D sinh ( κ D d D ) ) ) cos 2 ( ω t β z )
C D M P P = ( κ D β ) 2 ( 1 ± κ D d D sinh ( κ D d D ) ) 1
C M D P P = ( κ M β ) 2
1 κ D 2 κ M 2 = κ D d D sinh ( κ D d D )
[ S x , S z ] T M 1 S = [ S ¯ x , S ¯ z ] T M 1 S + [ Re { E G f T M 0 G f T M 1 G } sin ( 2 ϕ ) , Re { E G f T M 1 G 2 } cos ( 2 ϕ ) ] e 2 β i z / 2
  [ Im { E G f T M 0 G f T M 1 G } sin ( 2 ϕ ) , Im { E G f T M 1 G 2 } cos ( 2 ϕ ) ] e 2 β i z / 2
[ S ¯ x , S ¯ z ] T M 1 S = [ Im { ( E G f T M 0 G ) f T M 1 G } , Re { ( E G f T M 1 G ) f T M 1 G } ] e 2 β i z / 2

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