Abstract

We verify the effective refraction index approach (ERIA) developed for surface plasmon propagation in ultrathin tapered metal–dielectric–metal slot waveguides by means of comparison of exact solutions obtained within ERIA for two different profiles and different scales of tapering with finite-difference time-domain numerical simulations. We show that for smooth enough tapering, ERIA gives the plasmon field structure closely matched with numerical results. We also outline the range of the taper scales in which ERIA leads to the results different from simulations.

© 2013 Optical Society of America

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References

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    [CrossRef]
  2. M. L. Brongersma and P. G. Kik, eds., Surface Plasmon Nanophotonics (Springer-Verlag, 2007), pp. 1–11.
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007), pp. 21–34.
  4. L. Cao and M. L. Brongersma, “Active plasmonics: ultrafast developments,” Nat. Photonics 3, 12–13 (2009).
    [CrossRef]
  5. A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
    [CrossRef]
  6. S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
    [CrossRef]
  7. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef]
  8. V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
    [CrossRef]
  9. D. A. B. Miller, “Are optical transistors the next logical step?,” Nat. Photonics 4, 3–5 (2010).
    [CrossRef]
  10. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
    [CrossRef]
  11. M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
    [CrossRef]
  12. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef]
  13. D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
    [CrossRef]
  14. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
    [CrossRef]
  15. D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
    [CrossRef]
  16. G. B. Hocker and W. K. Burns, “Mode dispersion in diffused channel waveguides by the effective index method,” Appl. Opt. 16, 113–118 (1977).
    [CrossRef]
  17. S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon-polariton,” Opt. Express 14, 9467–9476 (2006).
    [CrossRef]
  18. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  19. G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
    [CrossRef]
  20. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]
  21. A. A. Zharov, N. A. Zharova, D. A. Smirnova, and A. A. Zharov, “Three-dimensional nanofocusing of light through surface plasmon scattering by lump-like defect in metal/dielectric/metal slot waveguides,” J. Opt. Soc. Am. B 30, 626–630 (2013).
    [CrossRef]
  22. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge, 1927), pp. 337–355, Part 2, “Transcendental functions”.

2013 (1)

2012 (1)

D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
[CrossRef]

2010 (5)

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
[CrossRef]

D. A. B. Miller, “Are optical transistors the next logical step?,” Nat. Photonics 4, 3–5 (2010).
[CrossRef]

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

2009 (3)

L. Cao and M. L. Brongersma, “Active plasmonics: ultrafast developments,” Nat. Photonics 3, 12–13 (2009).
[CrossRef]

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

2008 (1)

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

2007 (2)

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

2006 (1)

2005 (1)

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

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

1977 (1)

1974 (1)

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Bozhevolnyi, S. I.

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

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon-polariton,” Opt. Express 14, 9467–9476 (2006).
[CrossRef]

Brongersma, M. L.

L. Cao and M. L. Brongersma, “Active plasmonics: ultrafast developments,” Nat. Photonics 3, 12–13 (2009).
[CrossRef]

Burns, W. K.

Cao, L.

L. Cao and M. L. Brongersma, “Active plasmonics: ultrafast developments,” Nat. Photonics 3, 12–13 (2009).
[CrossRef]

Coway, J.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Deych, L. I.

V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
[CrossRef]

Drezek, R. A.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Fan, S.

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

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

Gobin, A. M.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Gramotnev, D. K.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

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

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

Halas, N. G.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Hocker, G. B.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

James, W. D.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Kaminov, I. P.

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Kocabas, S. E.

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

Lee, H.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Lee, M. H.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Lisyansky, A. A.

V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007), pp. 21–34.

Mammel, W. L.

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Menon, V. M.

V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
[CrossRef]

Miller, D.

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, “Are optical transistors the next logical step?,” Nat. Photonics 4, 3–5 (2010).
[CrossRef]

Noginov, M. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Pile, D. F. P.

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

Podolsky, V. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Ritzo, B. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Smirnov, A. I.

D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
[CrossRef]

Smirnova, D. A.

A. A. Zharov, N. A. Zharova, D. A. Smirnova, and A. A. Zharov, “Three-dimensional nanofocusing of light through surface plasmon scattering by lump-like defect in metal/dielectric/metal slot waveguides,” J. Opt. Soc. Am. B 30, 626–630 (2013).
[CrossRef]

D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
[CrossRef]

Staffaroni, M.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Tang, J.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Vedantam, S.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Veronis, G.

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

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

Vogel, M. W.

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge, 1927), pp. 337–355, Part 2, “Transcendental functions”.

Weber, H. P.

West, J. L.

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge, 1927), pp. 337–355, Part 2, “Transcendental functions”.

Yablonovich, E.

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Zhang, X.

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

Zharov, A. A.

A. A. Zharov, N. A. Zharova, D. A. Smirnova, and A. A. Zharov, “Three-dimensional nanofocusing of light through surface plasmon scattering by lump-like defect in metal/dielectric/metal slot waveguides,” J. Opt. Soc. Am. B 30, 626–630 (2013).
[CrossRef]

A. A. Zharov, N. A. Zharova, D. A. Smirnova, and A. A. Zharov, “Three-dimensional nanofocusing of light through surface plasmon scattering by lump-like defect in metal/dielectric/metal slot waveguides,” J. Opt. Soc. Am. B 30, 626–630 (2013).
[CrossRef]

D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Zharova, N. A.

Zhu, G.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

G. Veronis, S. E. Kocabas, D. Miller, and S. Fan, “Modeling of plasmon waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808 (2009).
[CrossRef]

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

JETP Lett. (1)

D. A. Smirnova, A. I. Smirnov, and A. A. Zharov, “Two-dimensional plasmonic eigenmode nanolocalization in an inhomogeneous metal-dielectric-metal slot waveguide,” JETP Lett. 96, 245–250 (2012).
[CrossRef]

Nano Lett. (2)

A. M. Gobin, M. H. Lee, N. G. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Lett. 7, 1929–1934 (2007).
[CrossRef]

S. Vedantam, H. Lee, J. Tang, J. Coway, M. Staffaroni, and E. Yablonovich, “A plasmonic dimple lens fore nanoscale focusing of light,” Nano Lett. 9, 3447–3452 (2009).
[CrossRef]

Nat. Photonics (4)

V. M. Menon, L. I. Deych, and A. A. Lisyansky, “Nonlinear optics: towards polaritonic logic circuits,” Nat. Photonics 4, 345–346 (2010).
[CrossRef]

D. A. B. Miller, “Are optical transistors the next logical step?,” Nat. Photonics 4, 3–5 (2010).
[CrossRef]

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

L. Cao and M. L. Brongersma, “Active plasmonics: ultrafast developments,” Nat. Photonics 3, 12–13 (2009).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmon by a tapered gap,” Phys. Rev. B 75, 035431 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolsky, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Other (3)

M. L. Brongersma and P. G. Kik, eds., Surface Plasmon Nanophotonics (Springer-Verlag, 2007), pp. 1–11.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007), pp. 21–34.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge, 1927), pp. 337–355, Part 2, “Transcendental functions”.

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Figures (3)

Fig. 1.
Fig. 1.

Coordinate system and types of considered MDM slot waveguides: (a) groove-like waveguide and (b) hyperbolically tapered waveguide.

Fig. 2.
Fig. 2.

(a) Profiles of the tapering of considered slot waveguides—linear groove-like (solid line) and hyperbolic (dashed line). (b) ReEz(x) at the slot axis obtained by FDTD method (solid) and ERIA (dashed) for linear groove-like slot tapering. a0=20nm, L=2500nm, tapering angle θa0/L0.46°. (c) Same as in (b) for the hyperbolically tapered waveguide slot: a0=40nm, L=500nm. The SP frequency is assumed to correspond to vacuum wavelength λ0=(2πc/ω)=1550nm. The materials parameters were taken as ωp=1.32·1016s1, ν=0.68·1014s1 for metal (silver) and εs=2.1(SiO2) for dielectric filling the waveguide slot. The parameters of the waveguides [see Fig. 1 and (b), (c)] are chosen in such a way that both slot widths decrease on the distance 0<x<2000nm in five times.

Fig. 3.
Fig. 3.

Same as in Fig. 2(b) for another waveguide slot parameters: (a) a0=30nm, L=5000nm (θ35°), (b) a0=20nm, L=1250nm (θ0.92°). FDTD—solid line, ERIA—dashed line.

Equations (17)

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CE⃗dl⃗=ik0SB⃗dS⃗,
U(x+dx)U(x)=ik0(Bzdz)dx,
dUdx=ik0Bzdz.
(×Bz)z=Byx=ik0ε(x,z)Ez.
2Ux2=k02ε(x,z)Ezdz.
2Ux2+k02εeff(x)U=0,
εeff(x)=εsa(x)+2κMa(x)+2εsεMκM=εsa(x)+2Λpωiνωa(x)2Λpεs(ωωp)2(ωiνω)3/2
Ez(x)=U(x)a(x)2Λpεs(ωωp)2(ωiνω)3/2.
a(x)=a0(1xL),x>0,
a(x)=a01+xL,x>0,
2Uξ2+{14+μξ+14m2ξ2}U=0,
ξ=2i(k0L)εs(xL1+aca03iν2ω),
μ=iΛpa0(k0L)εs(1iνω),m=12;
ξ=22Λpεsac(k0L)(1+5iν4ω){(13iν2ω)xL(a0ac1+3iν2ω)},
μ=a02εs8Λpac(1+2Λpac)(k0L)(1+iνω),m=12.
Uξ=C1Wμ,m(ξ)+C2Wμ,m(ξ)=C1Wμ,12(ξ)+C2Wμ,12(ξ),
Wμ,m(ξ)ξμexp(12ξ),|arg(ξ)|<πWμ,m(ξ)(ξ)μexp(12ξ),|arg(ξ)|<π.

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