Abstract

A theory for treating terahertz (THz) surface wave propagation and focusing on conical metal wire waveguides is presented. According to the theory, the surface wave propagation and focusing on the conical copper wire waveguide is investigated by the numerical calculation, and the results show the theory agrees with experimental measurement result obtained by Ji et al. The theory presented provides a basis for describing surface wave propagation and focusing on conical metal wire waveguides and, importantly, the theory suggests that a simple conical metal wire can be used for subwavelength energy concentration and superfocusing.

© 2008 Optical Society of America

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  1. C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
    [CrossRef] [PubMed]
  2. R. Mendis and D. Grischkowsky, "Undistorted guided-wave propagation of subpicosecond terahertz pulses," Opt. Lett. 26, 846-848 (2001).
    [CrossRef]
  3. H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
    [CrossRef]
  4. K. Wang and D. M. Mittleman, "Metal wires for terahertz waveguiding," Nature 432, 376-379 (2004).
    [CrossRef] [PubMed]
  5. T. -I. Jeon, J. Zhang, and D. Grischkowsky, "THz Sommerfeld wave propagation on a single metal wire," Appl. Phys. Lett. 86, 161904 (2005).
    [CrossRef]
  6. K. Wang and D. M. Mittleman, "Guided propagation of terahertz pulses on metal wires," J. Opt. Soc. Am. B 22, 2001-2008 (2005).
    [CrossRef]
  7. M. Wächter, M. Nagel, and H. Kurz, "Frequency-dependent characterization of THz Sommerfeld wave propagation on single wires," Opt. Express 13, 10815-10822 (2005).
    [CrossRef] [PubMed]
  8. K. Wang and D. M. Mittleman, "Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range," Phys. Rev. Lett. 96, 157401 (2006).
    [CrossRef] [PubMed]
  9. Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes," Ann. Phys. u.Chemie 67, 233 - 290 (1899).
  10. J. A. Deibel, N. Berndsen, K. Wang, D. M. Mittleman, N. C. J. van der Valk, and P. C. M. Planken, "Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires," Opt. Express 14, 8772-8778 (2006).
    [CrossRef] [PubMed]
  11. P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
    [CrossRef]
  12. Y. B. Ji, E. S. Lee, J. S. Jang, and T. -I. Jeon, "Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide," Opt. Express 16, 271-278 (2008).
    [CrossRef] [PubMed]
  13. G. Goubau, "Surface waves and their application to transmission lines," J. Appl. Phys. 21, 1119-1128 (1950).
    [CrossRef]
  14. M. J. King and J. C. Wiltse, "Surface-wave propagation on coated and uncoated metal wires at millimeter wavelengths," IRE Trans. Antennas Propag. 10, 246-254 (1962).
    [CrossRef]
  15. X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
    [CrossRef]
  16. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
    [CrossRef] [PubMed]

2008 (2)

P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
[CrossRef]

Y. B. Ji, E. S. Lee, J. S. Jang, and T. -I. Jeon, "Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide," Opt. Express 16, 271-278 (2008).
[CrossRef] [PubMed]

2006 (4)

J. A. Deibel, N. Berndsen, K. Wang, D. M. Mittleman, N. C. J. van der Valk, and P. C. M. Planken, "Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires," Opt. Express 14, 8772-8778 (2006).
[CrossRef] [PubMed]

X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

K. Wang and D. M. Mittleman, "Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range," Phys. Rev. Lett. 96, 157401 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

K. Wang and D. M. Mittleman, "Metal wires for terahertz waveguiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

2002 (1)

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

2001 (1)

2000 (1)

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

1962 (1)

M. J. King and J. C. Wiltse, "Surface-wave propagation on coated and uncoated metal wires at millimeter wavelengths," IRE Trans. Antennas Propag. 10, 246-254 (1962).
[CrossRef]

1950 (1)

G. Goubau, "Surface waves and their application to transmission lines," J. Appl. Phys. 21, 1119-1128 (1950).
[CrossRef]

1899 (1)

Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes," Ann. Phys. u.Chemie 67, 233 - 290 (1899).

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

Berndsen, N.

Cao, J.

X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
[CrossRef]

Cho, M.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Deibel, J. A.

Feng, S.

X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
[CrossRef]

Garcia-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

Goubau, G.

G. Goubau, "Surface waves and their application to transmission lines," J. Appl. Phys. 21, 1119-1128 (1950).
[CrossRef]

Grischkowsky, D.

T. -I. Jeon, J. Zhang, and D. Grischkowsky, "THz Sommerfeld wave propagation on a single metal wire," Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

R. Mendis and D. Grischkowsky, "Undistorted guided-wave propagation of subpicosecond terahertz pulses," Opt. Lett. 26, 846-848 (2001).
[CrossRef]

Han, H.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

He, X.

X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
[CrossRef]

Imbriale, W.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Jamnejad, V.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Jang, J. S.

Jeon, T. -I.

Y. B. Ji, E. S. Lee, J. S. Jang, and T. -I. Jeon, "Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide," Opt. Express 16, 271-278 (2008).
[CrossRef] [PubMed]

T. -I. Jeon, J. Zhang, and D. Grischkowsky, "THz Sommerfeld wave propagation on a single metal wire," Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Ji, Y. B.

Kim, J.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

King, M. J.

M. J. King and J. C. Wiltse, "Surface-wave propagation on coated and uncoated metal wires at millimeter wavelengths," IRE Trans. Antennas Propag. 10, 246-254 (1962).
[CrossRef]

Kurz, H.

Lee, E. S.

Luiten, O. J.

P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
[CrossRef]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

Manshadi, F.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Martin-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

Mendis, R.

Mittleman, D. M.

Nagel, M.

Park, H.

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Planken, P. C. M.

Root, W. P. E. M. O.

P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
[CrossRef]

Shimabukuro, F.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Smorenburg, P. W.

P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
[CrossRef]

Sommerfeld,

Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes," Ann. Phys. u.Chemie 67, 233 - 290 (1899).

Stanton, P.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

van der Valk, N. C. J.

Wächter, M.

Wang, K.

Wiltse, J. C.

M. J. King and J. C. Wiltse, "Surface-wave propagation on coated and uncoated metal wires at millimeter wavelengths," IRE Trans. Antennas Propag. 10, 246-254 (1962).
[CrossRef]

Yeh, C.

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Zhang, J.

T. -I. Jeon, J. Zhang, and D. Grischkowsky, "THz Sommerfeld wave propagation on a single metal wire," Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

H. Han, H. Park, M. Cho, and J. Kim, "Terahertz pulse propagation in a plastic photonic crystal fiber," Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

T. -I. Jeon, J. Zhang, and D. Grischkowsky, "THz Sommerfeld wave propagation on a single metal wire," Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Chemie (1)

Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes," Ann. Phys. u.Chemie 67, 233 - 290 (1899).

Chin. Phys. Lett. (1)

X. He, J. Cao, and S. Feng, "Simulation of the propagation property of metal wires terahertz waveguides," Chin. Phys. Lett. 23, 2066-2069 (2006).
[CrossRef]

IRE Trans. Antennas Propag. (1)

M. J. King and J. C. Wiltse, "Surface-wave propagation on coated and uncoated metal wires at millimeter wavelengths," IRE Trans. Antennas Propag. 10, 246-254 (1962).
[CrossRef]

J. Appl. Phys. (1)

G. Goubau, "Surface waves and their application to transmission lines," J. Appl. Phys. 21, 1119-1128 (1950).
[CrossRef]

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

Nature (2)

K. Wang and D. M. Mittleman, "Metal wires for terahertz waveguiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

C. Yeh, F. Shimabukuro, P. Stanton, V. Jamnejad, W. Imbriale, and F. Manshadi, "Communication at millimeter- submillimetre wavelengths using a ceramic ribbon," Nature 404, 584-588 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

P. W. Smorenburg, W. P. E. M. O. Root, and O. J. Luiten, "Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches," Phys. Rev. B 78, 115415 (2008)
[CrossRef]

Phys. Rev. Lett. (2)

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, "Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires," Phys. Rev. Lett. 97, 176805 (2006)
[CrossRef] [PubMed]

K. Wang and D. M. Mittleman, "Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range," Phys. Rev. Lett. 96, 157401 (2006).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Configuration of the conical metal wire waveguide

Fig. 2.
Fig. 2.

Ratio of the E field component versus the frequency with a=30µm

Fig. 3.
Fig. 3.

Ratio of the E field component versus the end-tip diameter with a=0µm

Fig. 4.
Fig. 4.

Ratio of the E field component versus the frequency with a=0µm

Fig. 5.
Fig. 5.

Superfocusing of the conical metal wire

Fig. 6.
Fig. 6.

Normalized amplitude of E field versus the radial distance for the cylindrical wire

Equations (20)

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E r = j A ( z ) h ( z ) γ ( z ) Z 1 ( γ ( z ) r ) e j ( ω t h ( z ) z ) ,
E z = A ( z ) Z 0 ( γ ( z ) r ) e j ( ω t h ( z ) z ) ,
H φ = j A ( z ) k 2 ω μ γ ( z ) Z 1 ( γ ( z ) r ) e j ( ω t h ( z ) z ) ,
inside : k c = ( ω μ c σ c ) 1 2 e j π 4 ;
outside : k = ω ( ε μ ) 1 2
γ c 2 = k c 2 h 2 ;
γ 2 = k 2 h 2 .
N ( z ) = Re [ a z 2 π r E r ( z ) H φ * ( z ) dr ] .
Re [ a 0 2 π r E r ( 0 ) H φ * ( 0 ) dr ] = Re [ a z 2 π r E r ( z ) H φ * ( z ) dr ] .
Re [ a 0 2 π r A ( 0 ) A * ( 0 ) ( j h ( 0 ) γ ( 0 ) H 1 ( 1 ) ( γ ( 0 ) r ) ) ( j k 2 ω μ γ ( 0 ) H 1 ( 1 ) ( γ ( 0 ) r ) ) * dr ]
= Re [ a z 2 π r A ( z ) A * ( z ) ( j h ( z ) γ ( z ) H 1 ( 1 ) ( γ ( z ) r ) ) ( j k 2 ω μ γ ( z ) H 1 ( 1 ) ( γ ( z ) r ) ) * dr ] .
A ( z ) A ( 0 ) = γ ( z ) γ ( 0 ) ×
{ Re [ ( h ( 0 ) γ ( 0 ) a 0 H 1 ( 2 ) ( γ * ( 0 ) a 0 ) H 0 ( 1 ) ( γ ( 0 ) a 0 ) h ( 0 ) γ * ( 0 ) a 0 H 1 ( 1 ) ( γ ( 0 ) a 0 ) H 0 ( 2 ) ( γ * ( 0 ) a 0 ) ) ( γ 2 ( z ) γ * 2 ( z ) ) ] / Re [ ( h ( z ) γ ( z ) a z H 1 ( 2 ) ( γ * ( z ) a z ) H 0 ( 1 ) ( γ ( z ) a z ) h ( z ) γ * ( z ) a z H 1 ( 1 ) ( γ ( z ) a z ) H 0 ( 2 ) ( γ * ( z ) a z ) ) ( γ 2 ( 0 ) γ * 2 ( 0 ) ) ] } 1 2 .
H φ ( z ) H φ ( 0 ) a = j A ( z ) j A ( 0 ) k 2 ω μ γ ( z ) H 1 ( 1 ) ( γ ( z ) ( a z + a ) ) k 2 ω μ γ ( 0 ) H 1 ( 1 ) ( γ ( 0 ) ( a 0 + a ) )
= A ( z ) γ ( 0 ) A ( 0 ) γ ( z ) H 1 ( 1 ) ( γ ( z ) ( a z + a ) ) H 1 ( 1 ) ( γ ( 0 ) ( a 0 + a ) ) ,
E r ( z ) E r ( 0 ) a = j A ( z ) j A ( 0 ) h ( z ) γ ( z ) H 1 ( 1 ) ( γ ( z ) ( a z + a ) ) h ( 0 ) γ ( 0 ) H 1 ( 1 ) ( γ ( 0 ) ( a 0 + a ) )
= A ( z ) h ( z ) γ ( 0 ) A ( 0 ) h ( 0 ) γ ( z ) H 1 ( 1 ) ( γ ( z ) ( a z + a ) ) H 1 ( 1 ) ( γ ( 0 ) ( a 0 + a ) ) .
E r ( z ) E r ( 0 ) a H φ ( z ) H φ ( 0 ) a =
{ Re [ ( h ( 0 ) γ ( 0 ) a 0 H 1 ( 2 ) ( γ * ( 0 ) a 0 ) H 0 ( 1 ) ( γ ( 0 ) a 0 ) h ( 0 ) γ * ( 0 ) a 0 H 1 ( 1 ) ( γ ( 0 ) a 0 ) H 0 ( 2 ) ( γ * ( 0 ) a 0 ) ) ( γ 2 ( z ) γ * 2 ( z ) ) ] / Re [ ( h ( z ) γ ( z ) a z H 1 ( 2 ) ( γ * ( z ) a z ) H 0 ( 1 ) ( γ ( z ) a z ) h ( z ) γ * ( z ) a z H 1 ( 1 ) ( γ ( z ) a z ) H 0 ( 2 ) ( γ * ( z ) a z ) ) ( γ 2 ( 0 ) γ * 2 ( 0 ) ) ] } 1 2 ×
H 1 ( 1 ) ( γ ( z ) ( a z + a ) ) H 1 ( 1 ) ( γ ( 0 ) ( a 0 + a ) ) .

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