Abstract

An analytical recurrence formula for the zeroth-order metal wire plasmon of terahertz waves is presented. In the derivation, the property that the relative permittivity of a metal in the spectral region of terahertz wave is huge, the property that the effective index is about 1, some properties of modified Bessel functions, and a suitable Taylor expansion are employed. The recurrence formula is numerically tested for 11 nonmagnetic metals for the whole spectral region of terahertz waves and for the wide radius range from 10μm to infinity. We find that the relative deviation for the effective index always becomes smaller than 2.1×106 after only four recurrences if a suitable initial input is used. Some related problems, such as the connection to the Newton method and the dependence of the accuracy on frequency, are also discussed.

© 2010 Optical Society of America

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2009 (2)

J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express 17, 20806–20815 (2009).
[CrossRef] [PubMed]

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

2008 (7)

2007 (2)

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

M. Wächter, M. l. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90, 061111 (2007).
[CrossRef]

2006 (9)

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14, 9944–9954 (2006).
[CrossRef] [PubMed]

L. Chen, H. Chen, T. Kao, J. Lu, and C. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31, 308–310 (2006).
[CrossRef] [PubMed]

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]

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14, 279–290 (2006).
[CrossRef] [PubMed]

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]

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13021–13029 (2006).
[CrossRef] [PubMed]

C. Themistos, B. M. Azizur Rahman, M. Rajarajan, V. Rakocevic, and K. T. V. Grattan, “Finite element solutions of surface-plasmon modes in metal-clad dielectric waveguides at THz frequency,” J. Lightwave Technol. 24, 5111–5118 (2006).
[CrossRef]

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]

2005 (6)

2004 (4)

M. J. Fitch and R. Osiander, “Terahertz waves for commu-nications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[CrossRef] [PubMed]

J. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express 12, 5263–5268 (2004).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

2003 (1)

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

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)

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

2000 (3)

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
[CrossRef]

1999 (1)

1996 (1)

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

1995 (1)

1988 (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

1985 (2)

1978 (1)

1975 (1)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

1974 (1)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

1950 (1)

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

Abbott, D.

Alexander, R. W.

Andrews, S. R.

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]

Atakaramians, S.

Azizur Rahman, B. M.

Bartal, G.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

Bell, R. J.

Berndsen, N.

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

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]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Cao, H.

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]

Cao, Q.

Chai, L.

Chen, H.

Chen, L.

Chen, Y.

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]

Chuen, M. O. L.

Deibel, J. A.

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14, 279–290 (2006).
[CrossRef] [PubMed]

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]

Dereux, A.

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Ding, Y. J.

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

Dupuis, A.

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Escarra, M.

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

Escarra, M. D.

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]

Fischer, B. M.

Fitch, M. J.

M. J. Fitch and R. Osiander, “Terahertz waves for commu-nications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

Freeman, M. R.

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87, 261107 (2005).
[CrossRef]

Gallot, G.

Garcia-Vidal, F. J.

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]

Genov, D. A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

George, R.

Gong, Y.

Goubau, G.

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

Grattan, K. T. V.

Grischkowsky, D.

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

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000).
[CrossRef]

R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of THz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24, 1431–1433 (1999).
[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]

Harrington, J.

Hassani, A.

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]

Hegmann, F. A.

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87, 261107 (2005).
[CrossRef]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Hu, B. B.

Hu, J.

Hu, M.

Ishikawa, A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

Jahns, J.

Jamison, S. P.

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
[CrossRef]

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000).
[CrossRef]

Jang, J.

Jeon, T.-I.

Y. Ji, E. Lee, J. 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.-Q. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Ji, Y.

Kao, T.

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]

Kurz, H.

Lee, E.

Li, Y.

Liang, H.

Long, L. L.

Lu, J.

Luiten, O. J.

P. W. Smorenburg, W. P. E. M. Op’t 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, A.

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]

Marchewka, A.

Marcuse, D.

Martin-Moreno, L.

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]

McGowan, R. W.

Mendis, R.

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

Mittleman, D. M.

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

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]

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14, 279–290 (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]

K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
[CrossRef]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[CrossRef] [PubMed]

Monro, T. M.

Mueller, E.

Nagel, M.

Nagel, M. l.

M. Wächter, M. l. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90, 061111 (2007).
[CrossRef]

Nahata, A.

H. Cao and A. Nahata, “Coupling of terahertz pulses onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005).
[CrossRef] [PubMed]

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Ngai, K. L.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Nuss, M. C.

Op’t Root, W. P. E. M.

P. W. Smorenburg, W. P. E. M. Op’t 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]

Ordal, M. A.

Osiander, R.

M. J. Fitch and R. Osiander, “Terahertz waves for commu-nications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

Palik, E. D.

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

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]

Paulose, V.

Pedersen, P.

Pfeiffer, C. A.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Planken, P. C. M.

Querry, M. R.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

Rajarajan, M.

Rakocevic, V.

Ren, G.

Ruan, S.

Schröter, U.

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Shahraam, A. V.

Shi, W.

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

Shum, P.

Skorobogatiy, M.

Smorenburg, P. W.

P. W. Smorenburg, W. P. E. M. Op’t 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]

Song, Z.

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Sun, C.

Themistos, C.

van der Valk, N. C. J.

Wächter, M.

M. Wächter, M. l. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90, 061111 (2007).
[CrossRef]

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]

Walther, M.

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87, 261107 (2005).
[CrossRef]

Wang, C.

Wang, G.

Wang, K.

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

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]

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]

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14, 279–290 (2006).
[CrossRef] [PubMed]

K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
[CrossRef]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[CrossRef] [PubMed]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Xing, Q.

Yang, J.

Yu, X.

Zhang, J.-Q.

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

Zhang, M.

Zhang, S.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

Zhang, X.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

Zhang, Z.

Zhou, C.

Appl. Opt. (1)

Appl. Phys. Lett. (7)

M. Wächter, M. l. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90, 061111 (2007).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
[CrossRef]

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87, 261107 (2005).
[CrossRef]

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

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett. 76, 1987–1989 (2000).
[CrossRef]

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]

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82, 4435–4437 (2003).
[CrossRef]

C. R. Phys. (1)

J. A. Deibel, K. Wang, M. Escarra, N. Berndsen, and D. M. Mittleman, “The excitation and emission of terahertz surface plasmon polaritons on metal wire waveguides,” C. R. Phys. 9, 215–231 (2008).
[CrossRef]

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]

IEEE Photon. Technol. Lett. (1)

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” IEEE Photon. Technol. Lett. 95, 1624–1640 (2007).

J. Appl. Phys. (2)

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

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

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Johns Hopkins APL Tech. Dig. (1)

M. J. Fitch and R. Osiander, “Terahertz waves for commu-nications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).

Nature (1)

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[CrossRef] [PubMed]

Opt. Express (14)

Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005).
[CrossRef] [PubMed]

H. Cao and A. Nahata, “Coupling of terahertz pulses onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005).
[CrossRef] [PubMed]

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]

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14, 279–290 (2006).
[CrossRef] [PubMed]

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]

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14, 13021–13029 (2006).
[CrossRef] [PubMed]

H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express 16, 18241–18248 (2008).
[CrossRef] [PubMed]

Y. Ji, E. Lee, J. 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]

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14, 9944–9954 (2006).
[CrossRef] [PubMed]

A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss terahertz guiding,” Opt. Express 16, 6340–6351 (2008).
[CrossRef] [PubMed]

G. Ren, Y. Gong, P. Shum, X. Yu, J. Hu, G. Wang, M. O. L. Chuen, and V. Paulose, “Low-loss air-core polarization maintaining terahertz fiber,” Opt. Express 16, 13593–13598 (2008).
[CrossRef] [PubMed]

S. Atakaramians, A. V. Shahraam, B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
[CrossRef] [PubMed]

J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express 17, 20806–20815 (2009).
[CrossRef] [PubMed]

J. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express 12, 5263–5268 (2004).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. B (3)

P. W. Smorenburg, W. P. E. M. Op’t 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]

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102, 043904 (2009).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

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]

Other (3)

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

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

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Figures (5)

Fig. 1
Fig. 1

(a) Comparison between the calculated values κ a , 4 and the exact values κ a for copper and 0.5 THz . The dashed curve is Im ( κ a ) , and the plus signs show Im ( κ a , 4 ) . The solid curve is Re ( κ a ) and the open circles show Re ( κ a , 4 ) . (b) Relative deviation of κ a , 4 . The solid curve represents the relative deviation of Re ( κ a , 4 ) and the dashed curve the relative deviation of Im ( κ a , 4 ) .

Fig. 2
Fig. 2

(a) Comparison between the calculated values n eff , 4 and the exact values n eff for copper and 0.5 THz . The dashed curve is Im ( n eff ) and the plus signs show Im ( n eff , 4 ) . The solid curve is Re ( n eff ) 1 and the open circles show Re ( n eff ) 1 . (b) Relative deviation of n eff , 4 . The solid curve represents the relative deviation of Re ( n eff , 4 ) and the dashed curve the relative deviation of Im ( n eff , 4 ) .

Fig. 3
Fig. 3

(a) Comparison between the calculated values n eff , 4 and the exact values n eff for copper and 0.1 THz . The dashed curve is Im ( n eff ) and the plus signs show Im ( n eff , 4 ) . The solid curve is Re ( n eff ) 1 and the open circles show Re ( n eff , 4 ) 1 . (b) Relative deviation of n eff , 4 . The solid curve represents the relative deviation of Re ( n eff , 4 ) and the dashed curve the relative deviation of Im ( n eff , 4 ) .

Fig. 4
Fig. 4

(a) Comparison between the calculated values n eff , 4 and the exact values n eff for copper and 10 THz . The dashed curve is Im ( n eff ) and the plus signs show Im ( n eff , 4 ) . The solid curve is Re ( n eff ) 1 and the open circles show Re ( n eff , 4 ) 1 . (b) Relative deviation of n eff , 4 . The solid curve represents the relative deviation of Re ( n eff , 4 ) and the dashed curve the relative deviation of Im ( n eff , 4 ) .

Fig. 5
Fig. 5

(a) Comparison between the calculated values n eff , 4 and the exact values n eff for copper and 0.5 THz . The dashed curve is Im ( n eff ) and the plus signs show Im ( n eff , 4 ) . The solid curve is Re ( n eff ) 1 and the open circles show Re ( n eff , 4 ) 1 . (b) Relative deviation of ( n eff , 4 1 ) . The solid curve represents the relative deviation of Re ( n eff , 4 ) 1 and the dashed curve the relative deviation of Im ( n eff , 4 )

Equations (11)

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ϵ m κ m I 1 ( k 0 κ m R ) I 0 ( k 0 κ m R ) + 1 κ a K 1 ( k 0 κ a R ) K 0 ( k 0 κ a R ) = 0 ,
a ϵ m 1 ϵ m I 1 ( k 0 R 1 ϵ m ) I 0 ( k 0 R 1 ϵ m ) .
f ( u ) = K 1 ( u ) K 0 ( u ) .
a κ a + f ( u ) = 0 .
a κ a , n + f ( u n 1 ) + f ( u n 1 ) ( u n u n 1 ) = 0 ,
f ( u n 1 ) = K 1 2 ( u n 1 ) K 0 2 ( u n 1 ) K 1 ( u n 1 ) K 0 ( u n 1 ) u n 1 1 .
κ a , n = f ( u n 1 ) u n 1 f ( u n 1 ) a + f ( u n 1 ) k 0 R ,
u n = k 0 κ a , n R .
κ a r = 1 1 4 a c 2 a ,
u r = k 0 κ a r R .
n eff , n = κ a , n 2 + 1 .

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