Abstract

Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides (PWs). In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged from a hyperbolic metamaterial (HMM) in a HMM–Insulator–HMM (HIH) structure. We show that HMM claddings give flexibility in designing the properties of HIH waveguides. Our comparative study on 1D PWs reveals that HIH-type waveguides can have a higher performance than MIM or IMI waveguides.

© 2014 Optical Society of America

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References

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  1. Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
    [CrossRef]
  2. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
    [CrossRef]
  3. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
    [CrossRef]
  4. S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, Opt. Lett. 36, 451 (2011).
    [CrossRef]
  5. S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
    [CrossRef]
  6. P. Berini, Adv. Opt. Photon. 1, 484 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. B 73, 155108 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2014 (1)

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

2013 (3)

S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
[CrossRef]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

2012 (1)

2011 (2)

2010 (3)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

I. De Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

2009 (3)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

T. Jiang, J. Zhao, and Y. Feng, Opt. Express 17, 170 (2009).
[CrossRef]

P. Berini, Adv. Opt. Photon. 1, 484 (2009).
[CrossRef]

2008 (1)

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 77, 063836 (2008).
[CrossRef]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

2006 (6)

2005 (2)

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

2004 (1)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

1972 (1)

P. B. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1956 (1)

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Alekseyev, L. V.

Babicheva, V. E.

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

Berini, P.

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Chen, K. P.

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Christy, R.

P. B. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

De Leon, I.

I. De Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

Dong, X.

Drachev, V. P.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, Opt. Lett. 36, 451 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Du, C.

Elser, J.

Engheta, N.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Feng, Y.

Gao, H.

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Han, S.

He, S. L.

He, Y. R.

Huang, Y. J.

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 77, 063836 (2008).
[CrossRef]

Hung, Y. J.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

Ishii, S.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
[CrossRef]

X. Ni, S. Ishii, M. D. Thoreson, V. M. Shalaev, S. Han, S. Lee, and A. V. Kildishev, Opt. Express 19, 25242 (2011).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, Opt. Lett. 36, 451 (2011).
[CrossRef]

Jacob, Z.

Jiang, T.

Johnson, P. B.

P. B. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kildishev, A. V.

S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
[CrossRef]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, Opt. Lett. 36, 451 (2011).
[CrossRef]

X. Ni, S. Ishii, M. D. Thoreson, V. M. Shalaev, S. Han, S. Lee, and A. V. Kildishev, Opt. Express 19, 25242 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

Lavrinenko, A. V.

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Lee, S.

Leosson, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Lu, W. T.

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 77, 063836 (2008).
[CrossRef]

Luo, X.

Maier, S. A.

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

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

E. E. Narimanov, “Photonic hyper-crystals,” arXiv:1402.0681 (2014).

Ni, X.

X. Ni, S. Ishii, M. D. Thoreson, V. M. Shalaev, S. Han, S. Lee, and A. V. Kildishev, Opt. Express 19, 25242 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Orlov, A.

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

Podolskiy, V. A.

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. B 73, 155108 (2006).
[CrossRef]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Rytov, S. M.

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Salandrino, A.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Shalaev, V. M.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, Opt. Lett. 36, 451 (2011).
[CrossRef]

X. Ni, S. Ishii, M. D. Thoreson, V. M. Shalaev, S. Han, S. Lee, and A. V. Kildishev, Opt. Express 19, 25242 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Shi, H.

Sipe, J.

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Smolyaninov, I. I.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Sridhar, S.

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 77, 063836 (2008).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Sun, Z.

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Thoreson, M. D.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Wang, C.

Wangberg, R.

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Yang, X. D.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Yuan, H. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Zhao, J.

Zhukovsky, S. V.

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

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

Laser Photon. Rev. (1)

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, Laser Photon. Rev. 7, 265 (2013).
[CrossRef]

Nano Lett. (2)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

S. Ishii, V. M. Shalaev, and A. V. Kildishev, Nano Lett. 13, 159 (2013).
[CrossRef]

Nat. Photonics (3)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Nat. Photonics 7, 948 (2013).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).
[CrossRef]

I. De Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (2)

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 77, 063836 (2008).
[CrossRef]

S. V. Zhukovsky, A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. Sipe, Phys. Rev. A 90, 013801 (2014).

Phys. Rev. B (4)

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

P. B. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Other (2)

E. E. Narimanov, “Photonic hyper-crystals,” arXiv:1402.0681 (2014).

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

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Figures (6)

Fig. 1.
Fig. 1.

Effective anisotropic permittivities of the lamellar structures for r=0.2, 0.5, 0.8, and 1. The solid lines and dashed lines represent perpendicular and parallel components, respectively.

Fig. 2.
Fig. 2.

(a) Schematic of a symmetric HIH PW. Magnetic field amplitudes along the y axis at 1550 nm are superimposed. (b) Effective index, (c) propagation length, and (d) penetration depth of the HIH PWs at r=0.2, 0.5, 0.8, and 1.

Fig. 3.
Fig. 3.

Propagation length of (a) MIM, (b) IMI, and (c), (d) HIH PWs for three different core thicknesses (20, 50, and 100 nm). For HIH PWs, (c) εm=εAu, εd=2.25, εs=1, and r=0.5; and (d) εm=εAu, εd=2.25, εc=1.88, and r=0.2.

Fig. 4.
Fig. 4.

FoMs of HIH PWs for various r (r=0.2, 0.5, and 1) in comparison to the FoM of the IMI PWs. The HIH PW at r=1 is equivalent to the MIM PW. For all cases, the core thickness is 50 nm. (a) The permittivity of the core in the HIH PWs and of the host in the IMI PW is equal to 1. (b) The permittivity of the core the HIH PWs and of the host in the IMI PW is 2.25.

Fig. 5.
Fig. 5.

Characteristics of the HIH PWs and their comparison with MIM and IMI PW layouts at the wavelength of 1.55 μm.

Fig. 6.
Fig. 6.

Schematic drawing of an anisotropic waveguide.

Equations (16)

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

×E=μ0t(μH),
×H=ε0t(εE),
x^×(εx1x^·×H)+y^×(εy1y^·×H)+z^×(εz1z^·×H)=k02H=0.
dx=iω1εx1h(y).
h(x,x)+εy(εx1h(y))(y)+εyh=0,
e2γ2εx2d(γ1+γ2)(γ2+γ3)e2γ2εx2d(γ1γ2)(γ2γ3)=0,
tanh(2εx2γ2d)=γ2γ1+γ3γ22+γ1γ3.
tanh(2εx2γ2d)=2γ2/γ1+γ1/γ2.
tanh(γ2εx2d)=γ1/γ2
tanh(γ2εx2d)=γ2/γ1.
tanh(g2d)=g1ε2(g2ε1)1,
tanh(g2d)=g2ε1(g1ε2)1,
tan(g2d)=g2εx1(g1εx2)1,
tan(g2d)=g1εx2(g2εx1)1,
tan(k2d)=k2/k1,
tan(k2d)=k1/k2,

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