Abstract

It is well-known that, a dielectric cylinder on a metal surface offers the advantage of not yielding singular field, which would effectively reduce the propagation loss as opposed to a rectangle-shaped waveguide on a metal surface. In this article, a novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film is presented. With the strong interaction between the dielectric cylindrical waveguide mode and long-range surface plasmon polaritons (LRSPP) mode of a thin metal film, deep-subwavelength mode confinement can be achieved. Compared with the hybrid plasmonic mode guided in only one dielectric nanowire above a metal film, a much larger propagation length as well as improved figure of merit (FoM) can be simultaneously realized. A typical propagation length is 434μm, and optical field is confined into an ultra-small area of approximately 0.0096μm2 at 1.55μm. This structure could enable various applications such as nanophotonic waveguides, high-quality nanolasers, and optical trapping and transportation of nanoparticles and biomolecules.

© 2012 OSA

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2012 (3)

2011 (5)

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express19(23), 22417–22422 (2011).
[CrossRef] [PubMed]

V. D. Ta, R. Chen, and H. D. Sun, “Wide-range coupling between surface plasmon polariton and cylindrical dielectric waveguide mode,” Opt. Express19(14), 13598–13603 (2011).
[CrossRef] [PubMed]

Y. Bian, Z. Zheng, Y. Liu, J. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett.23(13), 884–886 (2011).
[CrossRef]

2010 (4)

2009 (7)

2008 (3)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008).
[CrossRef]

2007 (1)

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

2004 (1)

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

2003 (2)

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2002 (1)

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

2001 (1)

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Agarwal, R.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003).
[CrossRef] [PubMed]

Aitchison, J. S.

Alam, M. Z.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bartal, G.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008).
[CrossRef]

Benisty, H.

H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys.108(6), 063108 (2010).
[CrossRef]

Berini, P.

Besbes, M.

H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys.108(6), 063108 (2010).
[CrossRef]

Bian, Y.

Buckley, R.

Chen, D.

Chen, L.

Chen, R.

Chen, S.

Choi, S.

J. T. Kim and S. Choi, “Hybrid plasmonic slot waveguides with sidewall slope,” IEEE Photon. Technol. Lett.24(3), 170–172 (2012).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Cui, Y.

Dai, D.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Denlinger, J.

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Duan, X. F.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003).
[CrossRef] [PubMed]

Duley, W. W.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Feick, H.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Freude, W.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett.21(6), 362–364 (2009).
[CrossRef]

Fujii, M.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett.21(6), 362–364 (2009).
[CrossRef]

Gao, D.

Garcia-Meca, C.

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

Gargas, D.

R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009).
[CrossRef]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Goldberger, J.

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

He, S.

Hu, A.

Hu, G.

Huang, M. H.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Huang, Y.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003).
[CrossRef] [PubMed]

Ji, Y.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kim, J. T.

J. T. Kim and S. Choi, “Hybrid plasmonic slot waveguides with sidewall slope,” IEEE Photon. Technol. Lett.24(3), 170–172 (2012).
[CrossRef]

Kind, H.

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Kuykendall, T.

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

Law, M.

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

Leuthold, J.

M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett.21(6), 362–364 (2009).
[CrossRef]

Li, W.

Li, X.

Lieber, C. M.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003).
[CrossRef] [PubMed]

Liu, J.

Liu, Y.

Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express19(23), 22417–22422 (2011).
[CrossRef] [PubMed]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

Y. Bian, Z. Zheng, Y. Liu, J. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett.23(13), 884–886 (2011).
[CrossRef]

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Mao, S.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Marti, J.

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

Martinez, A.

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

Messer, B.

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

Mojahedi, M.

Ortuno, R.

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

Oulton, R. F.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Pauzauskie, P. J.

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008).
[CrossRef]

Russo, R.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Salvador, R.

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
[CrossRef]

Sirbuly, D.

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

Sorger, V. J.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Sun, H. D.

Ta, V. D.

Wang, G.

Wang, Y.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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]

Weber, E.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Wen, J. Z.

Wu, Y.

M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

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Xue, X. J.

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M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001).
[CrossRef] [PubMed]

Yan, H. Q.

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

Yan, R.

R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009).
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T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

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R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009).
[CrossRef]

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[CrossRef] [PubMed]

Yang, X.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

Ye, Z.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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]

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V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
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Yun, B.

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
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V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009).
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Zhao, X.

Zhao, Y.

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Zhou, Y.

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Zhu, L.

Adv. Mater. (Deerfield Beach Fla.) (1)

H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008).
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M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett.21(6), 362–364 (2009).
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H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys.108(6), 063108 (2010).
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Nano Lett. (1)

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

Nat. Commun. (1)

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, 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. Mater. (1)

T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004).
[CrossRef] [PubMed]

Nat. Photonics (2)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

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[CrossRef]

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New J. Phys. (1)

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008).
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Figures (7)

Fig. 1
Fig. 1

Schematic of a hybrid long-range plasmonic waveguide, where two identical cylindrical Si nanowires of permittivity ε n and diameter d are placed on each side of a thin metallic film with a gap distance of h. The surrounding dielectric layer is SiO2 of permittivity ε d . ε n and ε d are 12.25 and 2.25 at λ = 1.55μm. The metallic film is silver with a permittivity of ε m = −129 + 3.3i and thickness of t = 20nm.

Fig. 2
Fig. 2

(a) Normalized modal area (Am/A0) versus the cylindrical diameter d for different gap distance h. (b-e) Electromagnetic energy distributions for [h, d] = [5, 300] nm (b), [h, d] = [10, 240] nm (c), [h, d] = [50, 240] nm (d), and [h, d] = [100, 400] nm (e).

Fig. 3
Fig. 3

Propagation length ( L m ) versus the cylindrical diameter d for different gap distance h. The propagation lengths of LRSPP modes in Si-Ag-Si and SiO2-Ag-SiO2 are denoted as black dashed line and black solid line, respectively.

Fig. 4
Fig. 4

Normalized energy density along x = 0 [vertical dashed line in the inset of (a)] at h = 5nm (a), 10nm (c), 30nm (e), 50nm (g), and 100nm (i). Normalized energy density along y = t/2 + h [horizontal dashed line in the inset of (a)] at h = 5nm (b), 10nm (d), 30nm (f), 50nm (h), and 100nm (j). The cylindrical diameter d is set at 240nm.

Fig. 5
Fig. 5

(a) The dependence of the mode effective index of the hybrid LRSPP mode, n hyb , on d for different gap distance h. As a comparison, the mode effective index of a pure cylindrical dielectric waveguides, n d , versus d is depicted in the solid black line. The dependence of the effective index of the pure LRSPP mode at SiO2-silver-SiO2 waveguides is shown in the dashed black line. (b) The mode character derived from Eq. (2). (c) The dependence of coupling strength κ on d and h.

Fig. 6
Fig. 6

The dependence of the mode size, A e , of the hybrid LRSPP waveguide and previous hybrid plasmonic waveguide on the cylindrical diameter d for h = 5nm, and 10nm. The mode size, δw , for the LRSPP mode in Si-Ag-Si and SiO2-Ag-SiO2 are denoted as black dashed line and black solid line, respectively.

Fig. 7
Fig. 7

The dependence of the figure of merit (FoM) of the present hybrid LRSPP waveguide and previous hybrid plasmonic waveguide on the cylindrical diameter d for h = 5nm, and 10nm. (a) Am is used to evaluate FoM. (b) Ae is used to evaluate FoM. (1): the present hybrid LRSPP waveguide. (2): the previous hybrid plasmonic waveguide.

Equations (4)

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A m = w m max{ w(r) } = 1 max{ w(r) } w(r )d 2 r
| a + (d,h) | 2 = n hyb ( d,h ) n L [ n hyb ( d,h ) n c (d)]+[ n hyb ( d,h ) n L ]
κ= [ n hyb (d,h) n c (d)][ n hyb (d,h) n L ]
FoM= L m 2 A m π = λ 4Im( n eff ) π A m

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