Abstract

In this paper, we present a comprehensive numerical study of the wavelength-dependence of transmission through sharp 90° bends in metallic slot waveguides with sub-wavelength localization and varying geometrical parameters. In particular, it is demonstrated that increasing the plasmon wavelength results in a significant increase (up to nearly 100%) of transmission through the bend, combined with a reduction in the mode asymmetry in the second arm of the bend. The mode asymmetry and its relaxation are explained by interference of the transmitted mode with non-propagating and leaky modes generated at the bend. Comparison with the two-dimensional case of a metal-dielectric-metal waveguide is also conducted, showing significant differences for the slot waveguides based on the presence of different non-propagating and leaky modes.

© 2010 OSA

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  1. Plasmonic Nanoguides and Circuits, S. I. Bozhevolnyi, ed. (Pan Stanford Pub. Pte. Ltd., 2009).
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    [CrossRef]
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    [CrossRef]
  4. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
    [CrossRef] [PubMed]
  5. D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
    [CrossRef]
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
    [CrossRef] [PubMed]
  7. V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
    [CrossRef]
  8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  16. K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

2009 (1)

2008 (1)

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
[CrossRef]

2007 (3)

2006 (3)

L. Chen, B. Wang, and G. P. Wang, “High efficiency 90° bending metal heterowaveguides for nanophotonic integration,” Appl. Phys. Lett. 89(24), 243120 (2006).
[CrossRef]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

2005 (7)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005).
[CrossRef] [PubMed]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005).
[CrossRef] [PubMed]

T. W. Lee and S. K. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express 13(24), 9652–9659 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005).
[CrossRef]

2004 (2)

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

2002 (1)

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

1998 (1)

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

S. I. Bozhevolnyi and K. V. Nerkararyan, “Analytic description of channel plasmon polaritons,” Opt. Lett. 34(13), 2039–2041 (2009).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Chen, L.

L. Chen, B. Wang, and G. P. Wang, “High efficiency 90° bending metal heterowaveguides for nanophotonic integration,” Appl. Phys. Lett. 89(24), 243120 (2006).
[CrossRef]

Devaux, E.

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Djurišic, A. B.

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Elazar, J. M.

Fan, S.

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
[CrossRef]

D. F. P. Pile, D. K. Gramotnev, R. F. Oulton, and X. Zhang, “On long-range plasmonic modes in metallic gaps,” Opt. Express 15(21), 13669–13674 (2007).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005).
[CrossRef] [PubMed]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Gray, S. K.

Han, Z.

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

He, S.

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Lee, T. W.

Liu, L.

Majewski, M. L.

Maradudin, A. A.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Matsuzaki, Y.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Nerkararyan, K. V.

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Oulton, R. F.

Pile, D. F. P.

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
[CrossRef]

D. F. P. Pile, D. K. Gramotnev, R. F. Oulton, and X. Zhang, “On long-range plasmonic modes in metallic gaps,” Opt. Express 15(21), 13669–13674 (2007).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005).
[CrossRef] [PubMed]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Qiu, M.

Rakic, A. D.

Vernon, K. C.

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Veronis, G.

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Wang, B.

L. Chen, B. Wang, and G. P. Wang, “High efficiency 90° bending metal heterowaveguides for nanophotonic integration,” Appl. Phys. Lett. 89(24), 243120 (2006).
[CrossRef]

Wang, G. P.

L. Chen, B. Wang, and G. P. Wang, “High efficiency 90° bending metal heterowaveguides for nanophotonic integration,” Appl. Phys. Lett. 89(24), 243120 (2006).
[CrossRef]

Yamaguchi, K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Yan, M.

Zhang, X.

Appl. Opt. (1)

Appl. Phys. Lett. (5)

L. Chen, B. Wang, and G. P. Wang, “High efficiency 90° bending metal heterowaveguides for nanophotonic integration,” Appl. Phys. Lett. 89(24), 243120 (2006).
[CrossRef]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett. 89(14), 143108 (2006).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

J. Appl. Phys. (1)

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103(3), 034304 (2008).
[CrossRef]

J. Lightwave Technol. (1)

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

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Nature (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. B (1)

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66(3), 035403 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[CrossRef] [PubMed]

Other (2)

Rsoft Design Group, RsoftFullWAVE version 8.2. http://www.rsoftdesign.com

Plasmonic Nanoguides and Circuits, S. I. Bozhevolnyi, ed. (Pan Stanford Pub. Pte. Ltd., 2009).

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Figures (5)

Fig. 1
Fig. 1

(a) The considered slot-waveguide with a 90° bend and a gap width w in a silver film of thickness h, surrounded by vacuum. (b) Top-down view of the bend with generating dipole (current source) S.

Fig. 2
Fig. 2

Relative transmissivity Tr through a 90° bend in (a) w = 50 nm and (b) w = 100 nm silver slot waveguide at various film thicknesses h = 50 nm (●), 100 nm (○) and 200 nm (∆). The relative transmissivity through a 90° bend in an MDM waveguide of the same gap width (×) is presented for comparison.

Fig. 3
Fig. 3

The distribution of the z-component of the Poynting vector (averaged over one period of the wave) at the plane A (z is normal to A; Fig. 1b) of a w = h = 100 nm slot at different excitation wavelengths λ vac = (a) 0.5 μm, (b) 0.75 μm, (c) 1.0 μm, and (d) 2.0 µm. The right wall of the slot (x > 0) corresponds to the outer wall of the bend (Fig. 1b). Scale is in microns. Red (blue) regions denote regions of maximum (minimum) intensity.

Fig. 4
Fig. 4

(a) The dependencies of the z-component of the Poynting vector (averaged over one period of the wave) at the half-height inside the slot near the outer (solid curve) and near the inner (dotted curve) slot walls on distance z from the bend into the second arm (z = w/2 corresponds to the inner corner of the bend). The structural parameters are the same as for Fig. 3 with λ vac = 750 nm. The inset shows the same dependencies for the 2D MDM waveguide with w = 100 nm at the same wavelength. (b) The same dependencies, but for the slot with w = h = 50 nm.

Fig. 5
Fig. 5

(a) Bend in the slot waveguide with the addition triangular pillar defect of side d = w/2. (b-c) Top–down view of the slot waveguide with bend and defect (b) and straight slot waveguide of equivalent length (c), showing relative positions of the planes B and A, and the source S.

Tables (1)

Tables Icon

Table 1 Comparative energy flows with and without the corner defect

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