Abstract

Connecting lumped circuit elements in a conventional circuit is usually accomplished by conducting wires that act as conduits for the conduction currents with negligible potential drops. More challenging, however, is to extend these concepts to optical nanocircuit elements. Here, following our recent development of optical lumped circuit elements, we show how a special class of nanowaveguides formed by a thin core with relatively large (positive or negative) permittivity surrounded by a thin concentric shell with low permittivity may provide the required analogy to ‘wires’ for optical nano-circuits.

© 2007 Optical Society of America

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  1. R. W. Rendell, and D. J. Scalapino, "Surface plasmons confined by microstructures on tunnel junctions," Phys. Rev. B 24, 3276 (1981).
    [CrossRef]
  2. X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
    [CrossRef]
  3. D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
    [CrossRef]
  4. A. I. Csurgay, and W. Porod, "Surface plasmon waves in nanoelectronic circuits," Int. J. Circuit Theory and Applications 32, 339 (2004).
    [CrossRef]
  5. N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
    [CrossRef] [PubMed]
  6. A. Alù, A. Salandrino, and N. Engheta, "Parallel, series, and intermediate interconnections of optical nanocircuit elements - Part 2: nanocircuit and physical interpretation," submitted to J. Opt. Soc. Am. B, online at: http://arxiv.org/abs/0707.1003>.
  7. A. Alù, and N. Engheta, "Optical nano-transmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23, 571-583 (2006).
    [CrossRef]
  8. A. Alù, and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
    [CrossRef]
  9. M. G. Silveirinha, A. Alù, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," under review, online at: http://arxiv.org/abs/cond-mat/0703600>.
  10. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, 1985).
  11. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).
  12. CST Studio Suite2006B, www.cst.com>.
  13. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  14. A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
    [CrossRef]
  15. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
    [CrossRef]

2007 (2)

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

2006 (2)

A. Alù, and N. Engheta, "Optical nano-transmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23, 571-583 (2006).
[CrossRef]

A. Alù, and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
[CrossRef]

2005 (1)

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

2004 (2)

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

A. I. Csurgay, and W. Porod, "Surface plasmon waves in nanoelectronic circuits," Int. J. Circuit Theory and Applications 32, 339 (2004).
[CrossRef]

2003 (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

1989 (1)

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

1981 (1)

R. W. Rendell, and D. J. Scalapino, "Surface plasmons confined by microstructures on tunnel junctions," Phys. Rev. B 24, 3276 (1981).
[CrossRef]

Alù, A.

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

A. Alù, and N. Engheta, "Optical nano-transmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23, 571-583 (2006).
[CrossRef]

A. Alù, and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Bergman, D. J.

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

Bilotti, F.

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

Csurgay, A. I.

A. I. Csurgay, and W. Porod, "Surface plasmon waves in nanoelectronic circuits," Int. J. Circuit Theory and Applications 32, 339 (2004).
[CrossRef]

Engheta, N.

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

A. Alù, and N. Engheta, "Optical nano-transmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23, 571-583 (2006).
[CrossRef]

A. Alù, and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Genov, D. A.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

Hui, P. M.

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Porod, W.

A. I. Csurgay, and W. Porod, "Surface plasmon waves in nanoelectronic circuits," Int. J. Circuit Theory and Applications 32, 339 (2004).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Rendell, R. W.

R. W. Rendell, and D. J. Scalapino, "Surface plasmons confined by microstructures on tunnel junctions," Phys. Rev. B 24, 3276 (1981).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Sarychev, A. K.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

Scalapino, D. J.

R. W. Rendell, and D. J. Scalapino, "Surface plasmons confined by microstructures on tunnel junctions," Phys. Rev. B 24, 3276 (1981).
[CrossRef]

Shalaev, V. M.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Stroud, D.

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

Vegni, L.

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

Wei, A.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Zeng, X. C.

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, "Theory and simulations of a conformal omni-directional sub-wavelength metamaterial leaky-wave antenna," IEEE Trans. Antennas Propag. 55, 1698-1708 (2007).
[CrossRef]

Int. J. Circuit Theory and Applications (1)

A. I. Csurgay, and W. Porod, "Surface plasmon waves in nanoelectronic circuits," Int. J. Circuit Theory and Applications 32, 339 (2004).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

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

Nano Lett. (1)

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancement from metal nanoparticle arrays," Nano Lett. 4, 153 (2004).
[CrossRef]

Phys. Rev. B (4)

A. Alù, and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern," Phys. Rev. B 75, 155410 (2007).
[CrossRef]

R. W. Rendell, and D. J. Scalapino, "Surface plasmons confined by microstructures on tunnel junctions," Phys. Rev. B 24, 3276 (1981).
[CrossRef]

X. C. Zeng, P. M. Hui, D. J. Bergman, and D. Stroud, "Correlation and clustering in the optical properties of composites: a numerical study," Phys. Rev. B 39, 13224 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Other (5)

A. Alù, A. Salandrino, and N. Engheta, "Parallel, series, and intermediate interconnections of optical nanocircuit elements - Part 2: nanocircuit and physical interpretation," submitted to J. Opt. Soc. Am. B, online at: http://arxiv.org/abs/0707.1003>.

M. G. Silveirinha, A. Alù, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," under review, online at: http://arxiv.org/abs/cond-mat/0703600>.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, 1985).

CST Studio Suite2006B, www.cst.com>.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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Figures (6)

Fig. 1.
Fig. 1.

(Color online) The cross-section of an optical wire composed of an EVL core and an ENZ shell. Electric (a) and magnetic (b) field distribution, snapshot in time, as calculated from full-wave simulations using CST Studio Suite [12] and consistent with Eq. (1) for a nanowire with acore =25nm, ashell = acore /0.6 , εENZ =(0.01 + i0.01)ε 0, εEVL =50ε 0 at a background wavelength of λ 0 = 500nm. Arrows are drawn in scale and darker colors correspond to larger field amplitudes.

Fig. 2.
Fig. 2.

(Color online) Calculated region of guidance (between the black solid and the red dashed lines) for the waveguide of Fig. 1 in terms of its geometrical parameters.

Fig. 3.
Fig. 3.

(Color online) Dispersion of the guided wave number as a function of εEVL varying εENZ for ashell = acore /0.8 and acore = λ 0/20.

Fig. 4.
Fig. 4.

(Color online) Dispersion of the guided wave number for a nanowire with ashell = acore /0.8 and acore = 25nm considering the frequency dispersion of plasmonic materials. Solid black lines refer to the real part of β and dashed red lines to its imaginary part.

Fig. 5.
Fig. 5.

(Color online) Full-wave simulations (snapshots in time) of: (a) distribution of the optical displacement current density on a transverse cross section of a straight nanowire as in Fig. 1; (b) distribution of the optical magnetic field for a bent nanowire with the geometry of Fig. 1 (the length of the straight section is λ 0 and the radius of curvature of the bend is λ 0/2). Darker (brighter) colors correspond to higher values.

Fig. 6.
Fig. 6.

(Color online) Full-wave simulations (snapshots in time) of (a) electric (tangential to the plane of the figure) and (b) magnetic (orthogonal to the plane of the figure) field distribution for the finite-length straight nanowire of Fig. 5(a). In both scenarios the length of the nanowire section depicted in the figure is about 850nm.

Equations (6)

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

H = φ ̂ A z 1 ( k 2 β 2 ρ ) e iβz
E = ρ ̂ A β ω ε z 1 ( k 2 β 2 ρ ) e iβz +
+ i z ̂ A k 2 β 2 ω ε z 0 ( k 2 β 2 ρ ) e iβz
β 2 = k ENZ 2 2 ln a shell / a core [ i π 2 J 0 ( k EVL a core ) k EVL a core J 1 ( k EVL a core ) ln ( k 0 2 a core 2 4 ) 2 γ ] ,
2 J 0 ( k EVL a core ) k EVL a core J 1 ( k EVL a core ) + ln ( k 0 2 a core 2 4 ) + 2 γ < 0 ,
Z wire ( iπω ε EVL a 1 2 ) 1 .

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