Abstract

We introduce a kind of surface plasmonic waveguide with double elliptical air cores. The dependence of distribution of longitudinal energy flux density, effective index and propagation length of the fundamental mode supported by this waveguide on geometrical parameters and working wavelengths are analyzed using the finite-difference frequency-domain (FDFD) method. Results show that the longitudinal energy flux density distributes mainly in the two wedged corners which are formed by two elliptical air cores, and the closer to the corners the stronger the longitudinal energy flux density. The effective index and propagation length of the fundamental mode can be adjusted by the centric distance of two ellipses as well as the size of the two semiaxis. At the certain working wavelength, relative to the case of a=b, in the case of a>b, the energy in the metal is small, then the interaction of field and silver is weak, and the effective index becomes small, and the propagation length becomes large. With certain geometric parameters, relative to the case of λ=632.8nm, in the case of larger λ, the area of field distribution is large, and the energy in the metal is small, then the interaction of field and silver is weak, and the effective index becomes small, and the propagation length becomes large. This kind of hollow surface plasmonic waveguide can be applied to the field of photonic device integration and sensors.

© 2008 Optical Society of America

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    [CrossRef]

2008 (5)

2007 (6)

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434-10 (2007).
[CrossRef]

I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, "Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves," Opt. Express 15, 16596-16603 (2007).
[CrossRef] [PubMed]

M. Yan and M. Qiu, "Guided plasmon polariton at 2D metal coners," J. Opt. Soc. Am. B 24, 2333-2342 (2007).
[CrossRef]

S. A. Maier, "Plasmonics: The promise of highly integrated optical devices," IEEE J. Sel. Top. Quantum Electron. 12, 1671-1677 (2007).

2006 (3)

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

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, 508-511 (2006).
[CrossRef] [PubMed]

S. L. Chen, J. Shakya, and M. Lipson, "Subwavelength confinement in an integrated metal slot waveguide on silicon," Opt. Lett. 31, 2133-2135 (2006).
[CrossRef] [PubMed]

2005 (5)

F. Kusunokia, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101-3 (2005).
[CrossRef]

R. Gordon and A. G. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005).
[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, 261114-3 (2005).
[CrossRef]

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

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (2005).
[CrossRef]

2004 (3)

2003 (2)

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002 (1)

1999 (1)

1990 (1)

J. Q. Lu and A. A. Maradudin, "Channel plasmons," Phys. Rev. B 42, 11159-11165 (1990).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4317-4379 (1972).
[CrossRef]

1969 (1)

E. N. Economou, "Surface plasmon in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1951 (1)

W. E. Arnoldi, "The principle of minimized iteration in the solution of matrix eigenvalue problems," Q. Appl. Math. 9, 17-29 (1951).

Adato, R.

Albin, S.

Arbel, D.

Arnoldi, W. E.

W. E. Arnoldi, "The principle of minimized iteration in the solution of matrix eigenvalue problems," Q. Appl. Math. 9, 17-29 (1951).

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Berini, P.

Boltasseva, A.

Bozhevolnyi, S. I.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, "Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths," Opt. Express 16, 5252-5260 (2008).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. M. Moreno, and F. J. G. Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon polaritons," Phys. Rev. Lett. 100, 023901-4 (2008).
[CrossRef] [PubMed]

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434-10 (2007).
[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, 508-511 (2006).
[CrossRef] [PubMed]

Brolo, A. G.

Brown, T. G.

Chang, H. C.

Chen, S. L.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4317-4379 (1972).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Devaux, E.

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, 508-511 (2006).
[CrossRef] [PubMed]

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, 508-511 (2006).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, "Surface plasmon in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Fukui, M.

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (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, 261114-3 (2005).
[CrossRef]

Gordon, R.

Gramotnev, D. K.

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (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, 261114-3 (2005).
[CrossRef]

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

Guo, J.

Guo, L.

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

Guo, S.

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, 261114-3 (2005).
[CrossRef]

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (2005).
[CrossRef]

He, S.

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4317-4379 (1972).
[CrossRef]

Jung, J.

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434-10 (2007).
[CrossRef]

I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, "Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves," Opt. Express 15, 16596-16603 (2007).
[CrossRef] [PubMed]

Kim, H.

Kobayashi, T.

F. Kusunokia, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101-3 (2005).
[CrossRef]

Kusunokia, F.

F. Kusunokia, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101-3 (2005).
[CrossRef]

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, 508-511 (2006).
[CrossRef] [PubMed]

Lee, B.

Lee, I.

Lipson, M.

Liu, L.

Lu, J. Q.

J. Q. Lu and A. A. Maradudin, "Channel plasmons," Phys. Rev. B 42, 11159-11165 (1990).
[CrossRef]

Maier, S. A.

S. A. Maier, "Plasmonics: The promise of highly integrated optical devices," IEEE J. Sel. Top. Quantum Electron. 12, 1671-1677 (2007).

Maradudin, A. A.

J. Q. Lu and A. A. Maradudin, "Channel plasmons," Phys. Rev. B 42, 11159-11165 (1990).
[CrossRef]

Matsuo, S.

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (2005).
[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, 261114-3 (2005).
[CrossRef]

Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. M. Moreno, and F. J. G. Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon polaritons," Phys. Rev. Lett. 100, 023901-4 (2008).
[CrossRef] [PubMed]

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, "Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths," Opt. Express 16, 5252-5260 (2008).
[CrossRef] [PubMed]

Moreno, L. M.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. M. Moreno, and F. J. G. Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon polaritons," Phys. Rev. Lett. 100, 023901-4 (2008).
[CrossRef] [PubMed]

Nielsen, R. B.

Ogawa, T.

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (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, 261114-3 (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, 261114-3 (2005).
[CrossRef]

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (2005).
[CrossRef]

Orenstein, M.

Ozbay, E.

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Park, J.

Pile, D. F. P.

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (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, 261114-3 (2005).
[CrossRef]

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

Qiu, M.

Rodrigo, S. G.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, "Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths," Opt. Express 16, 5252-5260 (2008).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. M. Moreno, and F. J. G. Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon polaritons," Phys. Rev. Lett. 100, 023901-4 (2008).
[CrossRef] [PubMed]

Shakya, J.

Sondergaard, T.

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434-10 (2007).
[CrossRef]

Takahara, J.

F. Kusunokia, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101-3 (2005).
[CrossRef]

Tanaka, K.

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

Vernon, K. C.

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, 261114-3 (2005).
[CrossRef]

Vidal, F. J. G.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. M. Moreno, and F. J. G. Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon polaritons," Phys. Rev. Lett. 100, 023901-4 (2008).
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Volkov, V. S.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, "Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths," Opt. Express 16, 5252-5260 (2008).
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H. Wang, W. Xue, and W. Zhang, "Negative dispersion properties of photonic crystal fiber with dual core and composite lattice," Acta Optica Sinica 28, 27-30 (2008).
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Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Xue, W.

H. Wang, W. Xue, and W. Zhang, "Negative dispersion properties of photonic crystal fiber with dual core and composite lattice," Acta Optica Sinica 28, 27-30 (2008).
[CrossRef]

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

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, 261114-3 (2005).
[CrossRef]

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F. Kusunokia, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101-3 (2005).
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H. Wang, W. Xue, and W. Zhang, "Negative dispersion properties of photonic crystal fiber with dual core and composite lattice," Acta Optica Sinica 28, 27-30 (2008).
[CrossRef]

Zhou, G.

Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Zhu, Z.

Acta Optica Sinica (3)

H. Wang, W. Xue, and W. Zhang, "Negative dispersion properties of photonic crystal fiber with dual core and composite lattice," Acta Optica Sinica 28, 27-30 (2008).
[CrossRef]

L. Guo, Y. Wu, W. Xue, and G. Zhou, "Dispersion properties of photonic crystal fiber with composite hexagonal air hole lattice," Acta Optica Sinica 27, 935-939 (2007).

Y. Wu, L. Guo, W. Xue, and G. Zhou, "Photonic crystal fiber with single polarization," Acta Optica Sinica 27, 593-597 (2007).

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K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
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[CrossRef]

D. F. P. Pile and T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, and M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106-3 (2005).
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Opt. Express (9)

J. Guo, and R. Adato, "Control of 2D plasmon-polariton mode with dielectric nanolayers," Opt. Express 16, 1232-1237 (2008).
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Figures (10)

Fig. 1.
Fig. 1.

Crosssection of plasmonic waveguides with double elliptical air cores. The centric distance of two ellipses is 2c and semiaxis of two ellipses is a, b respectively.

Fig. 2.
Fig. 2.

Schematic of the fabrication steps: (1) fabricate a pair of W-suface plasmonic waveguides, (2) combine them into a surface plasmonic waveguide with double elliptical air cores

Fig. 3.
Fig. 3.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=130nm, b=170nm, c=120nm and λ=632.8nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 4.
Fig. 4.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=130nm, b=130nm, c=120nm and λ=632.8nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 5.
Fig. 5.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=130nm, b=90nm, c=120nm and λ=632.8nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 6.
Fig. 6.

Dependence of (a) Re(neff ) and (b) L prop on c when b=a-40, a,a+40 at λ=632.8nm

Fig. 7.
Fig. 7.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=b=130nm, c=120nm and λ=548.7nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 8.
Fig. 8.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=b=130nm, c=120nm and λ=705.0nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 9.
Fig. 9.

The distribution of the field of (a)Hx, (b)Hy and (c)Sz at the cross section when a=b=130nm, c=120nm and λ=800.0nm. Dashed line in (a) and (b) indicate the outline of the structure.

Fig. 10.
Fig. 10.

Dependence of (a) Re(neff ) and (b) L prop on c when a=b=120nm,130nm,140nm and λ=632.8nm, 705.0nm and 800.0nm

Equations (2)

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[ Q x x Q x y Q y x Q y y ] [ H x H y ] = β 2 [ H x H y ]
[ P x x P x y P y x P y y ] [ E x E y ] = β 2 [ E x E y ]

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