Abstract

We have investigated the slow light and trapping effects in tapered metal-insulator-metal plasmonic waveguides. It is found that a significant reduction of group velocity (<0.01c) can be obtained when considering the intrinsic loss of realistic metal. The theoretical analysis shows that the group velocity can be further decreased, even approach zero in the lossless metallic waveguides. The perfect trapping of light is realized when an appropriate gain material is incorporated in the core layer to compensate metallic loss. The proposed ultracompact configuration may find excellent applications on nanoscale optical storages.

© 2013 Optical Society of America

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  1. M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
    [CrossRef]
  2. A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
    [CrossRef]
  3. K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
    [CrossRef]
  4. M. Sandtke and L. Kuipers, Nat. Photonics 1, 573 (2007).
    [CrossRef]
  5. Z. Ruan and M. Qiu, Appl. Phys. Lett. 90, 201906 (2007).
    [CrossRef]
  6. G. Wang, H Lu, and X. Liu, Opt. Express 20, 20902 (2012).
    [CrossRef]
  7. K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
    [CrossRef]
  8. Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
    [CrossRef]
  9. L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
    [CrossRef]
  10. D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
    [CrossRef]
  11. G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
    [CrossRef]
  12. W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
    [CrossRef]
  13. Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
    [CrossRef]
  14. M. Jang and H. Atwater, Phys. Rev. Lett. 107, 207401 (2011).
    [CrossRef]
  15. M. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef]
  16. E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
    [CrossRef]
  17. A. Govyadinov and V. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
    [CrossRef]
  18. A. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).
  19. Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
    [CrossRef]
  20. J. Park, K. Kim, I. Lee, H. Na, S. Lee, and B. Lee, Opt. Express 18, 598 (2010).
    [CrossRef]
  21. V. M. Shalaev, and S. Kawata, Nanophotonics with Surface Plasmons (Advances in Nano-Optics and Nano-Photonics) (Elsevier, 2007).
  22. S. Maier, Opt. Commun. 258, 295 (2006).
    [CrossRef]

2012 (2)

G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
[CrossRef]

G. Wang, H Lu, and X. Liu, Opt. Express 20, 20902 (2012).
[CrossRef]

2011 (4)

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

M. Jang and H. Atwater, Phys. Rev. Lett. 107, 207401 (2011).
[CrossRef]

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

2010 (3)

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

J. Park, K. Kim, I. Lee, H. Na, S. Lee, and B. Lee, Opt. Express 18, 598 (2010).
[CrossRef]

2009 (2)

Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
[CrossRef]

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

2007 (5)

K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

M. Sandtke and L. Kuipers, Nat. Photonics 1, 573 (2007).
[CrossRef]

Z. Ruan and M. Qiu, Appl. Phys. Lett. 90, 201906 (2007).
[CrossRef]

Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
[CrossRef]

2006 (2)

A. Govyadinov and V. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef]

S. Maier, Opt. Commun. 258, 295 (2006).
[CrossRef]

2004 (2)

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

M. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

Alegre, T.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Atwater, H.

M. Jang and H. Atwater, Phys. Rev. Lett. 107, 207401 (2011).
[CrossRef]

Banyal, R.

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Bartoli, F.

Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
[CrossRef]

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Boardman, A.

K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Bozhevolnyi, S.

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Casse, B.

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Chan, J.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Chang, D.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Chen, L.

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Ding, Y.

Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
[CrossRef]

Eichenfield, M.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Fan, S.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

Forsberg, E.

Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
[CrossRef]

Gan, Q.

Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
[CrossRef]

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Govyadinov, A.

A. Govyadinov and V. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef]

Gramotnev, D.

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Hamm, J.

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

Han, Z.

Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
[CrossRef]

He, S.

Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
[CrossRef]

Hess, O.

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Hill, J.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Huang, Y.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Jang, M.

M. Jang and H. Atwater, Phys. Rev. Lett. 107, 207401 (2011).
[CrossRef]

Kawata, S.

V. M. Shalaev, and S. Kawata, Nanophotonics with Surface Plasmons (Advances in Nano-Optics and Nano-Photonics) (Elsevier, 2007).

Kim, K.

Kirby, E.

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Kuipers, L.

M. Sandtke and L. Kuipers, Nat. Photonics 1, 573 (2007).
[CrossRef]

Lee, B.

Lee, I.

Lee, S.

Lin, Q.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Liu, X.

G. Wang, H Lu, and X. Liu, Opt. Express 20, 20902 (2012).
[CrossRef]

G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
[CrossRef]

Love, J. D.

A. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Lu, H

Lu, H.

G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
[CrossRef]

Lu, W.

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Maier, S.

S. Maier, Opt. Commun. 258, 295 (2006).
[CrossRef]

Min, C.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

Na, H.

Painter, O.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Park, J.

Pickering, T.

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

Podolskiy, V.

A. Govyadinov and V. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef]

Qiu, M.

Z. Ruan and M. Qiu, Appl. Phys. Lett. 90, 201906 (2007).
[CrossRef]

Ruan, Z.

Z. Ruan and M. Qiu, Appl. Phys. Lett. 90, 201906 (2007).
[CrossRef]

Safavi-Naeini, A.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Sandtke, M.

M. Sandtke and L. Kuipers, Nat. Photonics 1, 573 (2007).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, and S. Kawata, Nanophotonics with Surface Plasmons (Advances in Nano-Optics and Nano-Photonics) (Elsevier, 2007).

Snyder, A.

A. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Sridhar, S.

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Stockman, M.

M. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Tsakmakidis, K.

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Veronis, G.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

Wang, G.

G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
[CrossRef]

G. Wang, H Lu, and X. Liu, Opt. Express 20, 20902 (2012).
[CrossRef]

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Winger, M.

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Yanik, M. F.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

Appl. Phys. Lett. (4)

G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).
[CrossRef]

W. Lu, Y. Huang, B. Casse, R. Banyal, and S. Sridhar, Appl. Phys. Lett. 96, 211112 (2010).
[CrossRef]

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

Z. Ruan and M. Qiu, Appl. Phys. Lett. 90, 201906 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
[CrossRef]

Nat. Photonics (2)

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

M. Sandtke and L. Kuipers, Nat. Photonics 1, 573 (2007).
[CrossRef]

Nature (2)

K. Tsakmakidis, A. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

A. Safavi-Naeini, T. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. Hill, D. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Opt. Commun. (1)

S. Maier, Opt. Commun. 258, 295 (2006).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (2)

E. Kirby, J. Hamm, T. Pickering, K. Tsakmakidis, and O. Hess, Phys. Rev. B 84, 041103 (2011).
[CrossRef]

L. Chen, G. Wang, Q. Gan, and F. Bartoli, Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

Q. Gan, Y. Ding, and F. Bartoli, Phys. Rev. Lett. 102, 056801 (2009).
[CrossRef]

M. Jang and H. Atwater, Phys. Rev. Lett. 107, 207401 (2011).
[CrossRef]

M. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

A. Govyadinov and V. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Other (2)

V. M. Shalaev, and S. Kawata, Nanophotonics with Surface Plasmons (Advances in Nano-Optics and Nano-Photonics) (Elsevier, 2007).

A. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the tapered plasmonic waveguide: d, the core thickness of the waveguide. The light vertically illuminates the structure from the left side. (b) Dispersion curves calculated from the eigenmode equation for the TMm mode in the planar waveguide. The red and blue curves correspond to the forward-propagating and backward-propagating modes, respectively. The circle indicates the degeneracy point. The inset shows the critical thickness for different frequencies of the incident light. In the calculations, the metal is assumed as lossless with εm=1 and εd=12.25 for the wavelength of 1550 nm.

Fig. 2.
Fig. 2.

Real and imaginary part of the phase index np and the group index ng for lossless (a), (b) and lossy cases (c), (d). The red and blue curves correspond to the forward and backward modes. For both the lossless and lossy cases, the core layer has εd=12.25. The wavelength of the incident light is 1550 nm. The inset shows the field distribution of a Gaussian pulse with a width of 100 fs and central wavelength of 1550 nm propagates through the proposed plasmonic waveguide that tapered from 500 to 200 nm in an 11 μm region (Media 1). In our FDTD simulation, the spatial steps are Δx=Δy=5nm and the temporal step is Δt=Δx/2c, where c is the velocity of light in vacuum.

Fig. 3.
Fig. 3.

(a) Group index for different gain values. (b) Evolution of the factor G(ξ,ρ)/ξ in Eq. (4) with different imaginary parts of metal and gain material. (c), (d) Real and imaginary parts of the phase index and group index when incorporating gain into the core layer. In calculations, the wavelength of the incident light is 1550 nm and the metal is characterized by Drude model. The gain coefficient is about 197cm1.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

k0d=1εdnp2[mπ+2arctan(np2εmεdnp2εdεm)],
εdk0d=G(ξ,ρ).
dnpdk0=npξdξdk0+npρdρdk0.
ng=npk0εd2(1+ξ2)npdρdk01G(ξ,ρ)/ξ×ξ(np2εd)np(1+ξ2)(G(ξ,ρ)k0G(ξ,ρ)ρdρdk0).

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