Abstract

We study propagation of electromagnetic waves in a nano-coaxial waveguide for frequencies around and below the surface plasmon frequency. We show, that for frequencies sufficiently lower than the surface plasmon frequency, the waveguide supports a plasmon polariton mode that resembles, and indeed reduces to the conventional TEM mode of the conventional coaxial transmission line, known in the radiotechnology.

© 2008 Optical Society of America

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References

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  1. J. Rybczynski, K. Kempa, A. Herczynski, Y. Wang, M. J. Naughton, and Z. F. Ren, Z. P. Huang, D. Cai, M. Giersig, "Subwavelength waveguide for visible light," Appl. Phys. Lett. 90, 021104 (2007).
    [CrossRef]
  2. D. M. Pozar, Microwave Engineering, 3rd edition, (John Wiley & Sons, Inc. 2005).
  3. "Neuerung in dem Verfahren zur Herstellung isolirter Leitungen," (Siemens & Halske, Berlin), Kaiserliches Patentamt, Patentschrift Nummer 28978, Berlin, September 3, 1884.
  4. M. S. Kushwaha1 and B. Djafari-Rouhani, "Green-function theory of confined plasmons in coaxial cylindrical geometries: Zero magnetic field," Phys. Rev. B 67, 245320 (2003).
    [CrossRef]
  5. M. S. Kushwaha1 and B. Djafari-Rouhani, "Plasma excitations in multicoaxial cables," Phys. Rev. B 71, 153316 (2005).
    [CrossRef]
  6. S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli1, "Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis," Phys. Rev. B 70, 245406 (2004).
    [CrossRef]
  7. F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
    [CrossRef]
  8. N. Garcia and Ming Bai, "Theory of transmission of light by sub-wavelength cylindrical holes in metallic films," Opt. Express 14, 10028 (2006).
    [CrossRef] [PubMed]
  9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett. 22, 475 (1997).
    [CrossRef] [PubMed]
  10. X. Wang and K. Kempa, "Plasmon polaritons in slot waveguides: Simple model calculations and a full nonlocal quantum mechanical treatment," Phys. Rev. B 75, 245426 (2007).
    [CrossRef]
  11. X. Wang and K. Kempa, "Negative refraction and subwavelength lensing in a polaritonic crystal," Phys. Rev. B 71, 233101 (2005).
    [CrossRef]
  12. K. Kempa, X. Wang, Z. F. Ren and M. J. Naughton, to be published

2007 (2)

J. Rybczynski, K. Kempa, A. Herczynski, Y. Wang, M. J. Naughton, and Z. F. Ren, Z. P. Huang, D. Cai, M. Giersig, "Subwavelength waveguide for visible light," Appl. Phys. Lett. 90, 021104 (2007).
[CrossRef]

X. Wang and K. Kempa, "Plasmon polaritons in slot waveguides: Simple model calculations and a full nonlocal quantum mechanical treatment," Phys. Rev. B 75, 245426 (2007).
[CrossRef]

2006 (2)

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

N. Garcia and Ming Bai, "Theory of transmission of light by sub-wavelength cylindrical holes in metallic films," Opt. Express 14, 10028 (2006).
[CrossRef] [PubMed]

2005 (2)

X. Wang and K. Kempa, "Negative refraction and subwavelength lensing in a polaritonic crystal," Phys. Rev. B 71, 233101 (2005).
[CrossRef]

M. S. Kushwaha1 and B. Djafari-Rouhani, "Plasma excitations in multicoaxial cables," Phys. Rev. B 71, 153316 (2005).
[CrossRef]

2004 (1)

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli1, "Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis," Phys. Rev. B 70, 245406 (2004).
[CrossRef]

2003 (1)

M. S. Kushwaha1 and B. Djafari-Rouhani, "Green-function theory of confined plasmons in coaxial cylindrical geometries: Zero magnetic field," Phys. Rev. B 67, 245320 (2003).
[CrossRef]

1997 (1)

Appl. Phys. Lett. (1)

J. Rybczynski, K. Kempa, A. Herczynski, Y. Wang, M. J. Naughton, and Z. F. Ren, Z. P. Huang, D. Cai, M. Giersig, "Subwavelength waveguide for visible light," Appl. Phys. Lett. 90, 021104 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (6)

M. S. Kushwaha1 and B. Djafari-Rouhani, "Green-function theory of confined plasmons in coaxial cylindrical geometries: Zero magnetic field," Phys. Rev. B 67, 245320 (2003).
[CrossRef]

M. S. Kushwaha1 and B. Djafari-Rouhani, "Plasma excitations in multicoaxial cables," Phys. Rev. B 71, 153316 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli1, "Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis," Phys. Rev. B 70, 245406 (2004).
[CrossRef]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

X. Wang and K. Kempa, "Plasmon polaritons in slot waveguides: Simple model calculations and a full nonlocal quantum mechanical treatment," Phys. Rev. B 75, 245426 (2007).
[CrossRef]

X. Wang and K. Kempa, "Negative refraction and subwavelength lensing in a polaritonic crystal," Phys. Rev. B 71, 233101 (2005).
[CrossRef]

Other (3)

K. Kempa, X. Wang, Z. F. Ren and M. J. Naughton, to be published

D. M. Pozar, Microwave Engineering, 3rd edition, (John Wiley & Sons, Inc. 2005).

"Neuerung in dem Verfahren zur Herstellung isolirter Leitungen," (Siemens & Halske, Berlin), Kaiserliches Patentamt, Patentschrift Nummer 28978, Berlin, September 3, 1884.

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Figures (3)

Fig. 1.
Fig. 1.

Geometry of the nanocoax.

Fig. 2.
Fig. 2.

Dispersion of the selected nanocoax modes. (a) Frequency ω (real) vs real part of the wave vector k z. “TEM-like” mode dispersion is represented by crosses (from Eq. 2), and open circles (FDTD simulation). The solid circles represent dispersion of the plasmonic gapped mode. (b) Imaginary part of k z vs ω for the TEM-like mode (solid squares) obtained from Eq. (2). The inset is the zoomed-in section of this curve for very small ω, with solid curve from Eq. (2), and dashed from the formula for macroscopic coax (Eq. 4).

Fig. 3.
Fig. 3.

Distribution of the electric field E ρ inside the nanocoax for the two modes of Fig. 2(a). The left distribution is for the “TEM-like” mode, and the right for the plasmonic gapped mode. The color intensity is proportional to the field amplitude, and color change represents the sign (field direction) change. k z=0.005 nm-1. The inset shows E ρ vs. ρ (solid line), and E ρ ρ vs. ρ (dashed line).

Equations (5)

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ε 1 = ε 3 = ε b ω p 2 ( ω 2 + i ωγ )
( K 0 ( k 2 b ) I 0 ( k 2 a ) ε 1 I 1 ( k 1 a ) I 0 ( k 2 b ) k 1 I 0 ( K 1 a ) ε 2 k 2 K 1 ( k 2 a ) K 0 ( k 2 a ) ε 1 I 1 ( k 1 a ) k 1 I 0 ( k 1 a ) K 0 ( k 2 b ) ε 2 I 1 ( k 2 a ) k 2 I 0 ( k 2 b ) ) ( ε 3 k 3 K 1 ( k 3 b ) K 0 ( k 3 b ) ε 2 k 2 I 1 ( k 2 b ) I 0 ( k 2 b ) )
( K 0 ( k 3 b ) ε 2 k 2 I 1 ( k 2 a ) I 0 ( k 2 b ) K 0 ( k 3 b ) I 0 ( k 2 a ) I 0 ( k 2 b ) ε 1 k 1 I 1 ( k 1 a ) I 0 ( k 1 a ) ) ( ε 2 k 2 K 1 ( k 2 b ) + K 0 ( k 2 b ) ε 2 k 2 I 1 ( k 2 b ) I 0 ( k 2 b ) ) = F ( ω , k x ) = 0
( ε 2 k 2 K 1 ( k 2 a ) K 0 ( k 2 a ) ε 1 k 1 I 1 ( k 1 a ) I 0 ( k 1 a ) ) = 0
Im ( k z ) = 1 2 σδ ε 0 μ 0 ( 1 a + 1 b ) ln ( b a ) = 1 2 ω p 2 ( 1 a + 1 b ) ln ( b a ) γω

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