Abstract

We present a theoretical analysis of planar plasmonic waveguides that support propagation of positive and negative index modes. Particular attention is given to the modes sustained by metal-insulator-metal (MIM), insulator-metal-insulator (IMI), and insulator-insulator-metal (IIM) geometries at visible and near-infrared frequencies. We find that all three plasmonic structures are characterized by negative indices over a finite range of visible frequencies, with figures of merit approaching 20. Moreover, using finite-difference time-domain simulations, we demonstrate that visible-wavelength light propagating from free space into these waveguides can exhibit negative refraction. Refractive index and figure-of-merit calculations are presented for Ag/GaP and Ag/Si3N4 - based structures with waveguide core dimensions ranging from 5 to 50 nm and excitation wavelengths ranging from 350 nm to 850 nm. Our results provide the design criteria for realization of broadband, visible-frequency negative index materials and transformation-based optical elements for two-dimensional guided waves. These geometries can serve as basic elements of three-dimensional negative-index metamaterials.

© 2008 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  2. D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation designed optical elements," Opt. Express 15, 14772-14782 (2007).
    [PubMed]
  3. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  4. N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
    [CrossRef]
  5. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
    [CrossRef] [PubMed]
  6. Z. Jacob, L. A. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
    [CrossRef] [PubMed]
  7. N. Engheta, "Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials," Science 317, 1698-1702 (2007).
    [CrossRef] [PubMed]
  8. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
    [CrossRef]
  9. A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  10. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  11. V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2007) and references therein.
    [CrossRef]
  12. A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557-1567 (2006).
    [CrossRef] [PubMed]
  13. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
    [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. 97, 097401 (2006)
    [CrossRef]
  15. E. Verhagen, J. A. Dionne, L. (Kobus) Kuipers, H. A. Atwater, and A. Polman, "Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides," Nano Lett. 8, 2925-2929 (2008)
    [CrossRef] [PubMed]
  16. 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]
  17. G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B. 67, 035109 (2003)
    [CrossRef]
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  19. A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
    [CrossRef] [PubMed]
  20. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
    [CrossRef] [PubMed]
  21. H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative Refraction at Visible Frequencies," Science 316, 430-432 (2007).
    [CrossRef] [PubMed]
  22. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 316, 1699-1701 (2007).
    [CrossRef]
  23. A. S. Barker and R. Loudon, "Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals," Rev. Mod. Phys. 44, 18-47 (1972).
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    [CrossRef] [PubMed]
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    [CrossRef]
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2008 (2)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

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

2007 (6)

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

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 316, 1699-1701 (2007).
[CrossRef]

N. Engheta, "Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials," Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2007) and references therein.
[CrossRef]

M. Stockman, "Criteria for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98, 177404 (2007)
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation designed optical elements," Opt. Express 15, 14772-14782 (2007).
[PubMed]

2006 (9)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557-1567 (2006).
[CrossRef] [PubMed]

Z. Jacob, L. A. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
[CrossRef] [PubMed]

M. Stockman, "Slow propagation, anomalous absorption, and total external reflection of surface plasmon polaritons in nanolayer systems," Nano Lett. 6, 2604-2608 (2006).
[CrossRef] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

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]

H. T. Miyazaki and Y. Kurokawa, "Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity," Phys. Rev. Lett. 97, 097401 (2006)
[CrossRef]

2005 (3)

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
[CrossRef]

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

2003 (1)

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

2002 (1)

R. Ruppin, "Electromagnetic energy density in a dispersive and absorptive material," Phys. Lett. A 299, 309-312 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1972 (2)

A. S. Barker and R. Loudon, "Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals," Rev. Mod. Phys. 44, 18-47 (1972).

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

1968 (1)

V. G. Veselago, "Electrodynamics of Substances with Simultaneously Negative Values of Sigma and Mu," Soviet Physics Uspekhi-Ussr 10, 509-514 (1968).
[CrossRef]

Alekseyev, L. A.

Alu, A.

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]

Barker, A. S.

A. S. Barker and R. Loudon, "Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals," Rev. Mod. Phys. 44, 18-47 (1972).

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
[CrossRef] [PubMed]

Christy, R. W.

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

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 316, 1699-1701 (2007).
[CrossRef]

Dionne, J. A.

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

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

Engheta, N.

N. Engheta, "Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials," Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557-1567 (2006).
[CrossRef] [PubMed]

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

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]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 316, 1699-1701 (2007).
[CrossRef]

Ibenescu, M.

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Jacob, Z.

Joannopoulos, J. D.

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

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

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

Karalis, A.

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

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. 97, 097401 (2006)
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
[CrossRef]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
[CrossRef] [PubMed]

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]

Lidorikis, E.

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Loudon, R.

A. S. Barker and R. Loudon, "Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals," Rev. Mod. Phys. 44, 18-47 (1972).

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. 97, 097401 (2006)
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

Narimanov, E.

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation designed optical elements," Opt. Express 15, 14772-14782 (2007).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin, "Electromagnetic energy density in a dispersive and absorptive material," Phys. Lett. A 299, 309-312 (2002).
[CrossRef]

Salandrino, A.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation designed optical elements," Opt. Express 15, 14772-14782 (2007).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2007) and references therein.
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

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

Smith, D. R.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation designed optical elements," Opt. Express 15, 14772-14782 (2007).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 316, 1699-1701 (2007).
[CrossRef]

Soljacic, M.

A. Karalis, E. Lidorikis, M. Ibenescu, J. D. Joannopoulos, and M. Solja?i?, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 997-980 (2006).
[CrossRef]

Stockman, M.

M. Stockman, "Criteria for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98, 177404 (2007)
[CrossRef]

M. Stockman, "Slow propagation, anomalous absorption, and total external reflection of surface plasmon polaritons in nanolayer systems," Nano Lett. 6, 2604-2608 (2006).
[CrossRef] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
[CrossRef]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Verhagen, E.

E. Verhagen, J. A. Dionne, L. (Kobus) Kuipers, H. A. Atwater, and A. Polman, "Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides," Nano Lett. 8, 2925-2929 (2008)
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V. G. Veselago, "Electrodynamics of Substances with Simultaneously Negative Values of Sigma and Mu," Soviet Physics Uspekhi-Ussr 10, 509-514 (1968).
[CrossRef]

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Phys. Rev. Lett. 97, 073901 (2006)
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Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
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Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
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Nano Lett. (2)

E. Verhagen, J. A. Dionne, L. (Kobus) Kuipers, H. A. Atwater, and A. Polman, "Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides," Nano Lett. 8, 2925-2929 (2008)
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M. Stockman, "Slow propagation, anomalous absorption, and total external reflection of surface plasmon polaritons in nanolayer systems," Nano Lett. 6, 2604-2608 (2006).
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Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature 455, 376-379 (2008).
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Nature Photon. (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2007) and references therein.
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Phys. Rev. B. (1)

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A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
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M. Stockman, "Criteria for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98, 177404 (2007)
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R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
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J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
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N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 22, 534-537 (2005).
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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-Field Microscopy Through a SiC Superlens," Science 313, 1595 (2006).
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Soviet Physics Uspekhi-Ussr (1)

V. G. Veselago, "Electrodynamics of Substances with Simultaneously Negative Values of Sigma and Mu," Soviet Physics Uspekhi-Ussr 10, 509-514 (1968).
[CrossRef]

Other (2)

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Lumerical FDTD Solutions 6.0.

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Figures (11)

Fig. 1.
Fig. 1.

Lossless dispersion for three plasmon geometries: (a) a MIM waveguide composed of 50 nm GaP clad by Ag; (b) an IIM waveguide composed of a semi-infinite Ag film coated with 20 nm GaP; and (c) an IMI waveguide composed of 50 nm Ag clad by GaP. The dotted line indicates ωSP. Insets show the waveguide geometry and the associated Hy mode profiles for both the symmetric mode (light gray) and the antisymmetric mode (dark gray). Notice that all three geometries are characterized by regions of negative slope and hence negative indices. However, this negative index regime is single valued in kx for the MIM geometry only.

Fig. 2.
Fig. 2.

Lossy dispersion for MIM waveguides consisting of GaP clad by Ag. Three GaP thicknesses are included (d=25 nm, 17 nm, and 10 nm), and dispersion relations for both Hy field symmetric (blue hues) and antisymmetric (red hues) modes are shown. Including losses, the necessary condition for negative index modes is: sign(Real{kx }) ≠ sign(Imag{kx }). This condition is clearly satisfied for the Hy -field antisymmetric mode, which can exhibit negative indices with very low loss above the surface plasmon resonance (shown as a dotted line).

Fig. 3.
Fig. 3.

Lossy dispersion for insulator-insulator-metal waveguides composed of a semi-infinite Ag film coated with a thin layer of GaP and embedded in air. Three GaP thicknesses are included (d=25 nm, 17 nm, and 10 nm), and dispersion relations for both positive index (solid) and negative index (dotted) branches are shown. While solutions satisfying sign(Real{kx }) ≠ sign(Imag{kx }) may be found, the losses are quite high, with propagation lengths comparable to or smaller than the mode wavelength.

Fig. 4.
Fig. 4.

Lossy dispersion for insulator-metal-insulator waveguides composed of a thin Ag film clad with GaP. Three Ag thicknesses are included (d = 25 nm, 17 nm, and 10 nm), and dispersion relations for the positive and negative index branches of the Hy -field symmetric mode are shown. While solutions satisfying sign(Real{kx }) ≠ sign(Imag{kx }) may be again found, the losses of this branch always exceed those of the positive index mode.

Fig. 5.
Fig. 5.

Plots of MIM indices and figures of merit (FOM) for Ag/GaP/Ag waveguides as a function of energy and core thickness. Maps for both positive and negative index modes are shown. While the FOM for positive index modes drops to zero above the plasmon resonance frequency, it can be as high as 20 above resonance for negative index modes.

Fig. 6.
Fig. 6.

Finite difference time domain simulation of negative refraction of a 488-nm plane wave into a MIM waveguide. (a) Schematic of the simulation geometry. The plane wave is incident at an angle of 30o with respect to the xz plane and 10o with respect to the xy plane. (b) Hy field component snapshot in a plane through the waveguide core. Bloch boundary conditions are used to simulate an incident plane wave that is infinite in extent. For clarity, the color scale in the waveguide to the right differs from that in the air region to the left. The arrows depict the calculated Poynting vector directions of the incident and refracted waves.

Fig. 7.
Fig. 7.

Plots of MIM indices and figures of merit for Ag/Si3N4/Ag waveguides as a function of wavelength and core thickness. Maps for both positive and negative index modes are shown. The smaller index of Si3N4, compared with GaP, shifts the region of high FOM negative indices to shorter wavelengths, where Ag is more absorbing.

Fig. 8.
Fig. 8.

Plots of IIM indices and figures of merit for Air/GaP/Ag geometries as a function of wavelength and core thickness. Both negative and positive index branches of the dispersion diagram are shown. While the negative index modes have a high figure of merit for small GaP thicknesses above the Ag/GaP plasmon resonance, the positive index modes also have a very high FOM there, too. Note that the abrupt change in index seen for d ~20 nm is related to the cutoff thickness of the negative index modes.

Fig. 9.
Fig. 9.

Plots of IIM indices and figures of merit for Air/Si3N4/Ag geometries as a function of wavelength and core thickness. Both negative and positive index branches of the dispersion diagram are shown. As with the MIM geometries, the reduced index of Si3N4 shifts the region of high negative index FOM to shorter wavelengths. However, for this IIM geometry, the FOMs for the negative and positive index modes remain comparable in magnitude above the Ag/Si3N4 plasmon resonance.

Fig. 10.
Fig. 10.

Plots of IMI indices and figures of merit for GaP/Ag/GaP geometries as a function of wavelength and core thickness. Both negative and positive index branches of the dispersion diagram are included. Despite the large accessible negative indices, FOMs for this branch never exceed those of the positive index branch.

Fig. 11.
Fig. 11.

Plots of IMI indices and figures of merit for Si3N4/Ag/Si3N4 as a function of wavelength and core thickness. The lower index of Si3N4shifts the plasmon resonance to shorter wavelengths, reducing the accessible FOM for both negative and positive index modes. However, as with GaP-based IMI waveguides, the FOM for the negative index modes never exceeds that of the positive index mode.

Equations (12)

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λ SP = 2 π Re { k x } and n = c · Re { k x } ω .
L SP = 1 2 · Im { k x } .
E ( x , z , t ) = ( E x x ̂ + E z z ̂ ) e i ( k x x ω t )
E ( x , z , t ) = ( H y y ̂ ) e i ( k x x ω t ) .
E xj = a j e k zj z + b j e k zj z
E zj = ( i k x k zj ) ( a j e k zj z + b j e k zj z ) ,
k z 0,1,2 2 = k x 2 ε 0,1,2 ( ω c ) 2 .
det ( [ 0 1 0 0 0 0 1 1 1 1 0 0 ε 0 k z 0 ε 0 k z 0 ε 1 k z 1 ε 1 k z 1 0 0 0 0 e k z 1 d 1 e k z 1 d 1 e k z 2 d 1 e k z 2 d 1 0 0 ε 1 k z 1 e k z 1 d 1 ε 1 k z 1 e k z 1 d 1 ε 2 k z 2 e k z 2 d 1 ε 2 k z 2 e k z 2 d 1 0 0 0 0 1 0 ] ) = 0
ν E = S W
sign ( ν E ) = sign ( Imag { k x } ) .
sign ( ν p ) = sign ( Real { k x } ) .
sign ( Real { k x } ) sign ( Imag { k x } ) ,

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