Abstract

This Letter presents an analytical expression for the equivalent impedance of the fundamental mode of both 2D and 3D metal–insulator–metal (MIM) plasmonic waveguides. It also presents circuit models for passive 2D MIM waveguide components represented by additional parasitic circuit elements. Moreover, a modeling library for various 2D MIM waveguide structures is developed. The proposed analytical results have been verified and show great accuracy compared to the full-wave characterizations.

© 2013 Optical Society of America

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References

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. A. I. Csurgay and W. Porod, Int. J. Circuit Theory Appl. 32, 339 (2004).
    [CrossRef]
  6. G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  7. S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
    [CrossRef]
  8. H. Nejadi and A. Beirami, Opt. Lett. 37, 1050 (2012).
    [CrossRef]
  9. M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
    [CrossRef]
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    [CrossRef]
  11. H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
    [CrossRef]
  12. S.-I. Inoue and S. Yokoyama, Electron. Lett. 45, 1087 (2009).
    [CrossRef]
  13. Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
    [CrossRef]
  14. N. Marcuvitz, Waveguide Handbook (Peter Peregrinus, 1986).

2013

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

2012

H. Nejadi and A. Beirami, Opt. Lett. 37, 1050 (2012).
[CrossRef]

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

2010

2009

S.-I. Inoue and S. Yokoyama, Electron. Lett. 45, 1087 (2009).
[CrossRef]

2008

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

2007

H. Lezec, J. A. Dionne, and H. A. Atwater, Science 316, 430 (2007).
[CrossRef]

2006

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

S. A. Maier, IEEE J. Sel. Top. Quantum Electron. 12, 1214 (2006).
[CrossRef]

2005

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

2004

A. I. Csurgay and W. Porod, Int. J. Circuit Theory Appl. 32, 339 (2004).
[CrossRef]

Agrawal, G. P.

Atwater, H. A.

H. Lezec, J. A. Dionne, and H. A. Atwater, Science 316, 430 (2007).
[CrossRef]

Beirami, A.

Bozhevolnyi, S. I.

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

Chu, H.-S.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Conway, J.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Csurgay, A. I.

A. I. Csurgay and W. Porod, Int. J. Circuit Theory Appl. 32, 339 (2004).
[CrossRef]

Dionne, J. A.

H. Lezec, J. A. Dionne, and H. A. Atwater, Science 316, 430 (2007).
[CrossRef]

Fan, S.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Han, Z.

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

Hattori, H. T.

Inoue, S.-I.

S.-I. Inoue and S. Yokoyama, Electron. Lett. 45, 1087 (2009).
[CrossRef]

Kocabas, S. E.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

Kurniawan, O.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Lezec, H.

H. Lezec, J. A. Dionne, and H. A. Atwater, Science 316, 430 (2007).
[CrossRef]

Li, D.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Li, E.-P.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Maier, S. A.

S. A. Maier, IEEE J. Sel. Top. Quantum Electron. 12, 1214 (2006).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).

Marcuvitz, N.

N. Marcuvitz, Waveguide Handbook (Peter Peregrinus, 1986).

Miller, D.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

Nejadi, H.

Pannipitiya, A.

Porod, W.

A. I. Csurgay and W. Porod, Int. J. Circuit Theory Appl. 32, 339 (2004).
[CrossRef]

Premaratne, M.

Rukhlenko, I. D.

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

Staffaroni, M.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Tang, J.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Vedantam, S.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Veronis, G.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Yablonovitch, E.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Yokoyama, S.

S.-I. Inoue and S. Yokoyama, Electron. Lett. 45, 1087 (2009).
[CrossRef]

Zhang, W.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

Appl. Phys. Lett.

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Electron. Lett.

S.-I. Inoue and S. Yokoyama, Electron. Lett. 45, 1087 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

S. A. Maier, IEEE J. Sel. Top. Quantum Electron. 12, 1214 (2006).
[CrossRef]

IEEE Trans. Nanotechnol.

H.-S. Chu, O. Kurniawan, W. Zhang, D. Li, and E.-P. Li, IEEE Trans. Nanotechnol. 11, 731 (2012).
[CrossRef]

Int. J. Circuit Theory Appl.

A. I. Csurgay and W. Porod, Int. J. Circuit Theory Appl. 32, 339 (2004).
[CrossRef]

Mater. Today

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9(7–8), 20 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Photon. Nanostr. Fundam. Appl.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, Photon. Nanostr. Fundam. Appl. 10, 166 (2012).
[CrossRef]

Rep. Prog. Phys.

Z. Han and S. I. Bozhevolnyi, Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

Science

H. Lezec, J. A. Dionne, and H. A. Atwater, Science 316, 430 (2007).
[CrossRef]

Other

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).

N. Marcuvitz, Waveguide Handbook (Peter Peregrinus, 1986).

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Figures (6)

Fig. 1.
Fig. 1.

Electric and magnetic field distributions (red and blue color) in a MIM waveguide, and transmission line analogy with the even mode of the waveguide with the contour of the line integration (green color) to calculate the equivalent displacement current.

Fig. 2.
Fig. 2.

Error of the fundamental-mode characteristic impedance of a 2D silver–air–silver waveguide, and the same 3D waveguide with different thickness, with respect to the insulator gap width, calculated from Eq. (2) and from first-order Taylor expansion.

Fig. 3.
Fig. 3.

Equivalent circuit model of MIM waveguide discontinuities: (a) MIM waveguide bend and (b) MIM waveguide splitter.

Fig. 4.
Fig. 4.

Values of the parasitic circuit components Lb, Lj, Lin, and Cser in the MIM waveguide bend and splitter models with respect to the gap width.

Fig. 5.
Fig. 5.

Geometry of the MIM Mach–Zehnder modulator and its normalized output power with respect to the driving voltage, compared to the full-wave result and the result from the simple model from [10].

Fig. 6.
Fig. 6.

Vπ of the MIM Mach–Zehnder modulator with respect to the driving voltage, compared to the full-wave result and the result from the simple model from [10].

Tables (1)

Tables Icon

Table 1. Coefficients of the Curve Fitting Based on Full-Wave Simulation for β in 3D MIM Waveguides

Equations (4)

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

Zeven=V/I=(0Eydy)/(CHxdl),
Zeven=βωεm(ek1a+ek1a)2k1W=βωεmWsinh(k1a)k1,
Zevenβa/(ωεmW),
κ=1+Aexp[(aB1)2/2B22],

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