Abstract

We propose a closed form formulation for the impedance of the metal–insulator–metal (MIM) plasmonic transmission lines by solving the Maxwell’s equations. We provide approximations for thin and thick insulator layers sandwiched between metallic layers. In the case of very thin dielectric layer, the surface waves on both interfaces are strongly coupled resulting in an almost linear dependence of the impedance of the plasmonic transmission line on the thickness of the insulator layer. On the other hand, for very thick insulator layer, the impedance does not vary with the insulator layer thickness due to the weak-coupling/decoupling of the surface waves on each metal–insulator interface. We demonstrate the effectiveness of our proposed formulation using two test scenarios, namely, almost zero reflection in T-junction and reflection from line discontinuity in the design of Bragg reflectors, where we compare our formulation against previously published results.

© 2012 Optical Society of America

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References

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  1. J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).
  2. G. Veronis and S. Fan, Proc. SPIE 6123, JThC94 (2006).
  3. A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 15, 15280 (2007).
  4. A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
    [CrossRef]
  5. H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
    [CrossRef]
  6. Z. Han, E. Forsberg, and S. He, IEEE Photon. Technol. Lett. 19, 91 (2007).
  7. A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
    [CrossRef]
  8. G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
    [CrossRef]
  9. A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 16, 1475 (2006).
  10. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

2009 (1)

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

2008 (2)

A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
[CrossRef]

2007 (2)

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 15, 15280 (2007).

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

2006 (3)

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

G. Veronis and S. Fan, Proc. SPIE 6123, JThC94 (2006).

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 16, 1475 (2006).

2005 (1)

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

2002 (1)

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Atwater, H.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

Aussenegg, F.

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Dionne, J.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

Ditlbacher, H.

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Fan, S.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

G. Veronis and S. Fan, Proc. SPIE 6123, JThC94 (2006).

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

Forsberg, E.

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

Han, Z.

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

He, S.

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

Hosseini, A.

A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 15, 15280 (2007).

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 16, 1475 (2006).

Kocabas, S. E.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

Krenn, J.

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Leitner, A.

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Massoud, Y.

A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 15, 15280 (2007).

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 16, 1475 (2006).

Miller, D. A. B.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

Nejati, H.

A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 15, 15280 (2007).

A. Hosseini, H. Nejati, and Y. Massoud, Opt. Express 16, 1475 (2006).

Polman, A.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

Schider, G.

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Sweatlock, L.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

Veronis, G.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

G. Veronis and S. Fan, Proc. SPIE 6123, JThC94 (2006).

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

Appl. Phys. Lett. (3)

A. Hosseini, H. Nejati, and Y. Massoud, Appl. Phys. Lett. 92, 013116 (2008).
[CrossRef]

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

H. Ditlbacher, J. Krenn, G. Schider, A. Leitner, and F. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

IEEE ISCAS (1)

A. Hosseini, H. Nejati, and Y. Massoud, IEEE ISCAS 92, 2346 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

Opt. Express (2)

Phys. Rev. B (2)

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, Phys. Rev. B 79, 035120 (2009).

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006).

Proc. SPIE (1)

G. Veronis and S. Fan, Proc. SPIE 6123, JThC94 (2006).

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Figures (3)

Fig. 1.
Fig. 1.

Real (blue solid line) and imaginary (red dashed line) parts of the effective refractive index of an MIM structure (shown in the inset) as a function of the dielectric layer thickness. The operating wavelength is assumed to be 1.55 μm.

Fig. 2.
Fig. 2.

MIM characteristic impedance as a function of the thickness of the silicon layer for W=1μm. The leftmost shaded region is the strongly coupled region, where the impedance is directly proportional to the thickness of the dielectric layer. The middle and right shaded regions are the moderately coupled and the weakly coupled regions, respectively. In the weakly coupled region, the impedance is almost unvarying with the dielectric thickness and the modes are almost decoupled. The sketches of the strongly and weakly coupled regions are also shown in the bottom.

Fig. 3.
Fig. 3.

(a) Reflection coefficient as a function of the ratio of the input to the output branch thicknesses using models presented in the [8,9] (blue solid line), our proposed formulation (red dashed line), and the COMSOL results (red circles). (b) The optimized ratio as a function of the input branch thickness. Hz in a T-junction is shown in the inset.

Tables (1)

Tables Icon

Table 1. Reflection Coefficient of an Impedance Discontinuity in MIM Structure

Equations (4)

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

Z=VI=d2d2EZdzCHYdl,
Z=d2d2kxkzd(ejkzdz+ejkzdz)dzCωϵdckx(ejkzdzejkzdz)dl=2kxjWkzdωϵdtanh(jkzdd2),
Zthick2kxW|kzd|ωϵd.
ZthinkxdWωϵd.

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