Abstract

We present an effective generic method for manipulating energy flow in a metal–dielectric–metal plasmonic waveguide by spatially varying the thickness of the dielectric layer. To illustrate the utility of our method, we theoretically design a plasmonic convex lens and analyze its performance using full-wave numerical simulations. In particular, we show that such a lens is low dispersive and broadband.

© 2012 Optical Society of America

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References

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  1. S. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
  3. S. M. C. Abdulla, L. J. Kauppinen, G. J. M. Krijnen, and R. M. Ridder, Opt. Lett. 37, 2010 (2012).
    [CrossRef]
  4. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
    [CrossRef]
  5. S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).
  6. L. Cao and M. L. Brongersma, Nat. Photonics 3, 12 (2009).
  7. W. Zhu, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J. 4, 741 (2012).
  8. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 19, 206 (2011).
    [CrossRef]
  9. P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, Opt. Lett. 36, 3191 (2011).
    [CrossRef]
  10. M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media: Optical Amplifiers (Cambridge University, 2011).
  11. T. Wijesinghe and M. Premaratne, Opt. Express 20, 7151 (2012).
    [CrossRef]
  12. P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).
  13. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).
  14. W. Zhu, I. D. Rukhlenko, and M. Premaratne, J. Opt. Soc. Am. B 29, 2659 (2012).
    [CrossRef]
  15. S. I. Bozhevolnyi, Opt. Express 14, 9467 (2006).
    [CrossRef]
  16. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
  17. S. I. Bozhevolnyi and J. Jung, Opt. Express 16, 2676 (2008).
    [CrossRef]
  18. H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
    [CrossRef]
  19. A. Vakil and N. Engheta, Phys. Rev. B 85, 075434 (2012).

2012 (5)

2011 (2)

2010 (3)

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).

2009 (3)

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).

L. Cao and M. L. Brongersma, Nat. Photonics 3, 12 (2009).

2008 (2)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

S. I. Bozhevolnyi and J. Jung, Opt. Express 16, 2676 (2008).
[CrossRef]

2006 (1)

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

Abdulla, S. M. C.

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 19, 206 (2011).
[CrossRef]

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media: Optical Amplifiers (Cambridge University, 2011).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

Bozhevolnyi, S. I.

Brongersma, M. L.

L. Cao and M. L. Brongersma, Nat. Photonics 3, 12 (2009).

Cao, L.

L. Cao and M. L. Brongersma, Nat. Photonics 3, 12 (2009).

Chen, X.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Chen, Z.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

Cui, T. J.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Duyne, R. P. V.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Engheta, N.

A. Vakil and N. Engheta, Phys. Rev. B 85, 075434 (2012).

Garcia-Vidal, F. J.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Huidobro, P. A.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Inouye, Y.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).

Jiang, W. X.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

Jung, J.

Kauppinen, L. J.

Kawata, S.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).

Krijnen, G. J. M.

Liu, Y.

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, Opt. Lett. 36, 3191 (2011).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

Lu, C.

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Ma, H. F.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Maier, S.

S. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martin-Moreno, L.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Nesterov, M. L.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Premaratne, M.

T. Wijesinghe and M. Premaratne, Opt. Express 20, 7151 (2012).
[CrossRef]

W. Zhu, I. D. Rukhlenko, and M. Premaratne, J. Opt. Soc. Am. B 29, 2659 (2012).
[CrossRef]

W. Zhu, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J. 4, 741 (2012).

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 19, 206 (2011).
[CrossRef]

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media: Optical Amplifiers (Cambridge University, 2011).

Ridder, R. M.

Rukhlenko, I. D.

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Vakil, A.

A. Vakil and N. Engheta, Phys. Rev. B 85, 075434 (2012).

Verma, P.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).

Wang, S.

Wijesinghe, T.

Xu, H. S.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Yang, X. M.

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Yin, X.

Zentgraf, T.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

Zhang, P.

Zhang, X.

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, Opt. Lett. 36, 3191 (2011).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Zhu, W.

W. Zhu, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J. 4, 741 (2012).

W. Zhu, I. D. Rukhlenko, and M. Premaratne, J. Opt. Soc. Am. B 29, 2659 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

IEEE Photonics J. (1)

W. Zhu, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J. 4, 741 (2012).

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

Nano Lett. (2)

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, Nano Lett. 10, 1985 (2010).

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1985 (2010).

Nat. Mater. (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne, Nat. Mater. 7, 442 (2008).
[CrossRef]

Nat. Photonics (3)

S. Kawata, Y. Inouye, and P. Verma, Nat. Photonics 3, 388 (2009).

L. Cao and M. L. Brongersma, Nat. Photonics 3, 12 (2009).

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

A. Vakil and N. Engheta, Phys. Rev. B 85, 075434 (2012).

Other (2)

S. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media: Optical Amplifiers (Cambridge University, 2011).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of plasmonic waveguide system representing a convex lens. The system consists of two planar MDM waveguides and a gradient-index MDM waveguide. (b) and (c) show the lateral (A-A) cross section of the gradient-index MDM waveguide and trajectories of the plasmon rays refracted by the lens; w and f are the width of the gradient-index section and focal distance, respectively.

Fig. 2.
Fig. 2.

Lateral profiles of the effective-mode index (left scale) and air-gap thickness (right scale) for plasmonic convex lens operating at different wavelengths. Solid curves were obtained using Eqs. (3) and (4) for λ=1.55μm; dashed and dotted curves were obtained for λ=1.2 and 1.8 μm, respectively, using Eq. (3) and effective-mode-index profile shown by the solid curve. Insert shows the derivative of the effective mode index with respect to the wavelength for x=0, 2, and 4 μm. For other parameters refer to the text.

Fig. 3.
Fig. 3.

Snapshots of the electric field of SPP mode inside the air gap of a silver-air-silver composite waveguide shown in Fig. 1(a). In (a) and (c), SPPs are excited at 1.55 and 1.8 μm by a point source located at the left focusing point of the convex lens, while (b) and (d) show focusing of plane SPP waves of wavelengthes 1.55 and 1.2 μm incident from the y direction. For other parameters refer to the text.

Equations (5)

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

tanh(kdh2)=εdεmkmkd.
n2εd+2α2+2αεdεm+α2,
h(n)2εdεmn2εmn2εdcω.
n(x)=n01w((fw/2)2+x2f+w/2),
Lmax=2w(n0nd)[2f+w(n0nd1)].

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