Abstract

The hybrid plasmonic waveguide consists of a high-permittivity dielectric nanofiber embedded in a low-permittivity dielectric near a metal surface. This architecture is considered as one of the most perspective candidates for long-range subwavelength guiding. We present qualitative analysis and numerical results which reveal advantages of the special waveguide design when dielectric constant of the cylinder is greater than the absolute value of the dielectric constant of the metal. In this case the arbitrary subwavelength mode size can be achieved by controlling the gap width. Our qualitative analysis is based on consideration of sandwich-like conductor-gap-dielectric system. The numerical solution is obtained by expansion of the hybrid plasmonic mode over single cylinder modes and the surface plasmon-polariton modes of the metal screen and matching the boundary conditions.

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).
  2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Phot.4, 83–91 (2010).
    [CrossRef]
  3. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
    [CrossRef]
  4. V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
    [CrossRef]
  5. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express18(1), 348–363 (2010).
    [CrossRef] [PubMed]
  6. R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
    [CrossRef]
  7. R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
    [CrossRef]
  8. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).
  9. I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
    [CrossRef]
  10. A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
    [CrossRef]
  11. S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
    [CrossRef]
  12. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
    [CrossRef]
  13. D. Marcuse, Light Transmission Optics (New York: Van Nostrand Reinhold, 1972).
  14. A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).
  15. W. Zakowicz, “Two coupled dielectric cylindrical waveguides,” J. Opt. Soc. Am. A14(3), 580–587 (1997).
    [CrossRef]
  16. R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
    [CrossRef] [PubMed]
  17. I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B70, 155416 (2004).
    [CrossRef]
  18. R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
    [CrossRef]

2011 (1)

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Phot.4, 83–91 (2010).
[CrossRef]

I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express18(1), 348–363 (2010).
[CrossRef] [PubMed]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

2009 (3)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

2008 (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

2007 (1)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

2004 (1)

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B70, 155416 (2004).
[CrossRef]

1999 (1)

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

1997 (3)

W. Zakowicz, “Two coupled dielectric cylindrical waveguides,” J. Opt. Soc. Am. A14(3), 580–587 (1997).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

1996 (1)

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

1988 (1)

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).

Avrutsky, I.

I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express18(1), 348–363 (2010).
[CrossRef] [PubMed]

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B70, 155416 (2004).
[CrossRef]

Bartal, G.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Bartal, Y. W. G.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Borghi, R.

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Phot.4, 83–91 (2010).
[CrossRef]

Buchwald, W.

Bulushev, A. G.

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Dianov, E. M.

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).

Efimov, A.

S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
[CrossRef]

Elser, J.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Frezza, F.

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

Genov, D. A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Gori, F.

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Phot.4, 83–91 (2010).
[CrossRef]

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Ishikawa, A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

Kobayashi, T.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Ma, Ren-Min

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, Light Transmission Optics (New York: Van Nostrand Reinhold, 1972).

Morimoto, A.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Naik, G. V.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Nam, S. H.

S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
[CrossRef]

Okhotnikov, O. G.

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).

Oulton, R. F.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Podolskiy, V.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

Salakhutdinov, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

Santarsiero, M.

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

Schettini, G.

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

Shalaev, V. M.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Soref, R.

Sorger, V. J.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Takahara, J.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Taki, H.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Taylor, A. J.

S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
[CrossRef]

West, P. R.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).

Yamagishi, S.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Ye, Z.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

Yin, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

Zakowicz, W.

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Zhang, S.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

Zhang, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

R. Borghi, F. Frezza, M. Santarsiero, and G. Schettini, “Angular spectrum of modified cylindrical wave-functions,” Int. J. Infrared Millim. Waves20(10), 1795–1801 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. A. (2)

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A.13(3), 483–493 (1996).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A.14(7), 1500–1504 (1997).
[CrossRef]

Laser Photonics Rev. (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev.4, 795–808 (2010).
[CrossRef]

Nat. Commun. (1)

V. J. Sorger, Z. Ye, R. F. Oulton, Y. W. G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011).
[CrossRef]

Nat. Phot. (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Phot.4, 83–91 (2010).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “Hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Phot.2(8), 496–500 (2008).
[CrossRef]

Nature (1)

R. F. Oulton, V. J. Sorger, T. Zentgraf, Ren-Min Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Express. (1)

S. H. Nam, A. J. Taylor, and A. Efimov, “Subwavelength hybrid terahertz waveguides,” Opt. Express.17(25), 22890–22897 (2009).
[CrossRef]

Opt. Lett. (1)

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.82(8), 1158–1160 (1997).

Phys. Rev. B (2)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metaldi-electric multilayers,” Phys. Rev. B75(24), 241402 (2007).
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B70, 155416 (2004).
[CrossRef]

Phys. Rev. Let. (1)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep Subwavelength Terahertz Waveguides Using Gap Magnetic Plasmon”, Phys. Rev. Let.102, 043904 (2009).
[CrossRef]

Quantum Electron. (1)

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Propagation of the radiation in two identical coupled waveguides,” Quantum Electron.15, 1433–1441 (1988).

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).

D. Marcuse, Light Transmission Optics (New York: Van Nostrand Reinhold, 1972).

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Figures (7)

Fig. 1
Fig. 1

a) Geometry of the waveguide; b) Plain waveguide with the same width of the gap.

Fig. 2
Fig. 2

Effective index nCGD of the CGD-mode versus gap width h for different metal permittivity and critical gap width (εm; hc). The dielectric constants of the dielectric and gap region are εd = 5.76 and εg = 1 respectively at wavelength λ = 490nm.

Fig. 3
Fig. 3

Effective refractive index of the fundamental hybrid mode versus cylinder diameter d (coloured lines) compared with those of single fiber (black solid line) and SPP mode (lower black broken line). The upper black broken line corresponds to the refractive index of the cylinder. The dielectric constants of the cylinder, dielectric and metal are εd = 12.25 εg = 2.25 and εm = −129 +3.3i respectively at wavelength λ = 1.55μm. These parameters are chosen in accordance with the paper [3]. The critical gap width hc = 5nm. The HPP-to-CGD crossover point: d* ≈ 17μm for h = 2nm.

Fig. 4
Fig. 4

Effective refractive index of the fundamental hybrid mode versus cylinder diameter d (coloured lines) compared with those of single fiber (black solid line) and SPP mode (lower black broken line). The upper black broken line corresponds to the refractive index of the cylinder. (a) The dielectric constants of the cylinder, dielectric and metal are εd = 5.76, εg = 1 and εm = −9.2 respectively at wavelength λ = 0.49μm. These parameters are chosen in accordance with the paper [16]. The critical gap width hc = 7nm. The HPP-to-CGD crossover points are: d* ≈ 310nm for h = 2nm, d* ≈ 875nm for h = 5nm. (b) The dielectric constants of the cylinder, dielectric and metal are εd = 5.76, εg = 1 and εm = −4 respectively at wavelength λ = 0.49μm. The critical gap width hc = 13, 4nm. The HPP-to-CGD crossover points (black arrows) are: d* ≈ 40nm for h = 2nm, d* ≈ 65nm for h = 5nm, d* ≈ 220nm for h = 10nm.

Fig. 5
Fig. 5

Spatial distribution of the time-average z-component of the Poynting vector Sz(x, y) for the fundamental HPP-mode. The diameter of the cylinder is d = 120nm and the gap width is h = 2nm. The dielectric constants of the cylinder and dielectric are εd = 5.76 and εg = 1 respectively at wavelength λ = 0.49μm. (a) The dielectric permittivity of the metal is εm = −9.2, (b) εm = −4.

Fig. 6
Fig. 6

The fundamental HPP-mode’s propagation distance in dependence on cylinder diameter (coloured lines) compared with propagation distance of pure SPP-mode at metal-dielectric interface (black broken line). The dielectric constants of the cylinder, dielectric and metal are εd = 5.76, εg = 1 and εm = −4+0.1i respectively at wavelength λ = 0.49μm.

Fig. 7
Fig. 7

Reference system.

Equations (24)

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exp [ 2 h κ g ] = ( ε d κ g ε g κ d ) ( ε m κ g ε g κ m ) ( ε d κ g + ε g κ d ) ( ε m κ g + ε g κ m ) ,
h c = λ 4 π ε d ε g log ε m ε d ε g ε g ε d ε m ε m ε d ε g + ε g ε d ε m .
ε d > | ε m | > ε g ,
n CGD 1 2 k h ln ( ε d ε g ) ( ε m ε g ) ( ε d + ε g ) ( ε m + ε g ) .
n CGD 1 k h | ε m | ( 1 | ε m | ε d + i ε m | ε m | ) ,
Δ { E z H z } ( β 2 ε k 2 ) { E z H z } = 0 ,
d * 1 4 ( n CGD 2 ε d ) h k 2 .
κ g 2 / k 2 16 e 2 γ + 1 ( k d ) 2 exp { 8 ( ε d + ε g ) ε g ( ε d ε g ) ( k d ) 2 } 1 ,
{ E z ( d ) = n = 0 a n E J n ( χ d r ) cos n φ E z ( g ) = n = 0 b n E K n ( κ g r ) cos n φ + + 0 c q E exp ( Q κ g ( x D ) ) cos q κ g y d q E z ( m ) = 0 d q E exp ( Q κ m ( x D ) ) cos q κ m y d q
{ H z ( d ) = n = 0 a n H J n ( χ d r ) sin n φ H z ( g ) = n = 0 b n H K n ( κ g r ) sin n φ + + 0 c q H exp ( Q κ g ( x D ) ) sin q κ g y d q H z ( m ) = 0 d q H exp ( Q κ m ( x D ) ) sin q κ m y d q
K n ( κ g r ) cos n φ = 0 F n E ( q ) e Q κ g x cos q κ g y d q ,
K n ( κ g r ) sin n φ = 0 F n H ( q ) e Q κ g x sin q κ g y d q ,
e Q κ g x cos q κ g y = n = 0 G n E cos n φ ,
e Q κ g x sin q κ g y = n = 0 G n H sin n φ ,
F n E = ( Q + q ) n + ( Q q ) n 2 Q ,
F n H = ( Q + q ) n ( Q q ) n 2 Q ,
G n E = 2 δ 0 n 2 ( ( Q + q ) n + ( Q q ) n ) I n ( κ g r ) ,
G n H = ( ( Q + q ) n ( Q q ) n ) I n ( κ g r ) .
E z ( g ) = n = 0 b n E K n ( κ g r ) cos n φ + + n = 0 cos n φ 0 c q E G n E ( r , q ) e Q κ g D d q ,
H z ( g ) = n = 0 b n H K n ( κ g r ) sin n φ + + n = 0 sin n φ 0 c q H G n H ( r , q ) e Q κ g D d q .
E z ( g ) = 0 n = 0 b n E F n E ( q ) e Q κ g x cos q κ g y d q + + 0 c q E e Q κ g ( x D ) cos q κ g y d q ,
H z ( g ) = 0 n = 0 b n H F n H ( q ) e Q κ g x sin q κ g y d q + + 0 c q H e Q κ g ( x D ) sin q κ g y d q .
E ξ = i β β 2 ε k 2 E z ξ + i k β 2 ε k 2 H z η ,
H ξ = ε i k β 2 ε k 2 E z η i β β 2 ε k 2 H z ξ ,

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