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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 18550–18557
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Theory for terahertz plasmons of metallic nanowires with sub-skin-depth diameters

Jie Yang, Qing Cao, and Changhe Zhou  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 18550-18557 (2010)
http://dx.doi.org/10.1364/OE.18.018550


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Abstract

We investigate the propagation properties of terahertz plasmon of a metallic nanowire with sub-skin-depth diameter. By taking the small radius and the huge relative permittivity into account, we establish an approximate analytical description for this kind of surface plasmon. It is shown that the main propagation properties are closely related to the product of the radius of the metallic nanowire and the complex wave number of the metal. In addition, when the radius of the metal wire is smaller than the skin-depth, the size of the modal field is simply proportional to the radius of the metal wire. We also carefully verify these analytical predictions with rigorous numerical simulations.

© 2010 OSA

1. Introduction

Terahertz (THz) wave, locating between the infrared and microwave bands of the electromagnetic spectrum, is one of the hot research topics. It is normally defined as the range from 0.1 to 10 THz (or correspondingly, from 30 μm to 3 mm in wavelength). In recent years, terahertz technology has shown potential applications in many fields, such as in sensing, imaging, and spectroscopy [1

1. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995). [CrossRef] [PubMed]

3

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

]. Among those research works, THz waveguides have attracted more and more interests [4

4. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef] [PubMed]

43

43. L. Martin-Moreno, “Terahertz technology: Mind the gap,” Nat. Photonics 3(3), 131–132 (2009). [CrossRef]

]. In 2004, Wang and Mittleman [4

4. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef] [PubMed]

] reported that a simple metal wire can effectively guide THz wave. It was quickly shown that the THz waveguide effect of metal wire comes from the azimuthally polarized surface plasmon [5

5. Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]

]. Up to now, many interesting theoretical and experimental works on metal wire THz waveguide have been carried out [5

5. Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]

27

27. V. Astley, R. Mendis, and D. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett. 95(3), 031104 (2009). [CrossRef]

].

A very important size for a plasmon in the spectral region of terahertz wave is the skin-depth. Recently, some research works on metallic nano-slit with sub-skin-depth width have been carried out [42

42. M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]

,43

43. L. Martin-Moreno, “Terahertz technology: Mind the gap,” Nat. Photonics 3(3), 131–132 (2009). [CrossRef]

]. It was reported that terahertz field can be enhanced by a metallic nano-slit. However, until now, only few papers have touched the topics of terahertz plasmon of a metal nanowire with a sub-skin-depth diameter [24

24. H. Liang, S. Ruan, M. Zhang, and H. Su, “Nanofocusing of terahertz wave on conical metal wire waveguides,” Opt. Commun. 283(2), 262–264 (2010). [CrossRef]

]. The investigation on this kind of plasmon is just at the very beginning. Therefore, a lot of research works are needed to be done in this interesting area.

2. Approximate analytical description for THz plasmon of a metallic nanowire with a sub-skin-depth diameter

Consider a cylindrical metal wire surrounded by air. We are interested in the axially symmetric eigenmode. Namely, the relations ∂E/∂φ = 0 and ∂H/∂φ = 0 always hold. For TM polarization of a nonmagnetic metal, by substituting the above-mentioned relations into Maxwell’s equations [44

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

] and using the continuities of Ez and Hφ at the interface, one can get the following eigen-equation [5

5. Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]

,23

23. J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express 17(23), 20806–20815 (2009). [CrossRef] [PubMed]

,25

25. J. Yang, Q. Cao, and C. Zhou, “An analytical recurrence formula for the zero-order metal wire plasmon of terahertz wave,” J. Opt. Soc. Am. A 27(7), 1608–1612 (2010). [CrossRef]

,45

45. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

,46

46. U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64(12), 125420 (2001). [CrossRef]

]:
εmκmI1(k0κmR)I0(k0κmR)+1κaK1(k0κaR)K0(k0κaR)=0,
(1)
where κa = [(neff)2-1]1/2, κm = [(neff)2m]1/2, neff is the effective index of the eigenmode, εm denotes the relative permittivity of the metal. I0(.), K0(.), I1(.) and K1(.) are modified Bessel functions. k0 = 2π/λ0, where λ0 and k0 denote wavelength and wave number in free space, respectively, and R is the radius of the metal wire.

The effective index neff is an important parameter for the plasmon. It is hidden in Eq. (1). We now derive an approximate expression for the effective index neff. By use of the property |neff 2|<<|εm|, one can get κm≈(-εm)1/2. In addition, the relation K1(k0κaR)≈(k0κaR)−1 holds for small R. Substituting these two approximations into Eq. (1), one can further get
κa2K0(k0Rκa)=a,
(2)
where

a=1k0RεmI0(k0Rεm)I1(k0Rεm).
(3)

The left-hand side of Eq. (2) has two factors, one is κa 2, the other is K0(k0κaR). The former factor κa 2 changes fast and the latter factor K0(k0κaR) changes very slowly. Basically, the factor K0(k0κaR) changes as slowly as a logarithmic function. By use of these properties, we develop the following recurrence formula
κa,n2K0(k0Rκa,n1)=a,
(4)
where n = 1,2,3…, κa,n is the corresponding approximate value for κa after n times recurrences. The recurrence solution κa,n of Eq. (4) is simply given by

κa,n=aK0(k0Rκa,n1),
(5)

To implement the recurrence formula of Eq. (5), one needs an initial input κa,0. Simply letting the factor K0(k0κaR) of Eq. (2) be 1, one can get the initial rough value κa,0, which is given by

κa,0=a.
(6)

For many important analyses, one does not need a highly accurate κa,n value with a large n. As we shall show below, the approximate value κa,2 is actually good enough for this kind of analysis. After two times uses of Eq. (5), one can get
κa,2=a[K0(k0RaK0(k0Ra     ))]1/2,
(7)
where K0(.) is a modified Bessel function. The corresponding approximate value neff,2 can be further obtained from the relation

neff,2=κa,22+1.
(8)

3. Numerical tests

To get an intuitive impression on the capability of our analytical expression, we calculate the approximate values neff,2 and the exact values neff in the radius range from 5 nm to 500 nm. The metal is chosen to be copper, and the frequency is chosen to be 0.5 THz (i.e., λ0 = 0.6 mm). The corresponding εm value is εm = −6.3 × 105 + j2.77 × 106 according to a fitted Drude formula for copper [47

47. M. A. Ordal, R. J. Bell, R. W. Alexander Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). [CrossRef] [PubMed]

]. The approximate neff,2 values and the exact neff values are shown in Fig. 1(a)
Fig. 1 (a) Comparison between the approximate values neff,2 and the exact values neff, for metal copper and 0.5 THz. The dashed curve is Im(neff) and the signs “+” show Im(neff,2). The solid curve is Re(neff) and the signs “o” show Re(neff,2). (b) The relative deviation of neff,2. The solid curve represents the relative deviations of Re(neff,2), and the dashed curve is the relative deviations of Im(neff,2).
. And the relative deviations for the real part and the imaginary part of neff,2 are shown in Fig. 1(b). One can see that the maximum relative deviation of neff,2 is less than 1% in the considered radius range. It should be pointed out that the radius R = 500 nm is already far larger than the skin depth δ, which is 72.5 nm according to the definition of δ = λ0/[2πIm(εm 1/2)].

We also test the applicability of the approximate formula for neff,2 for other nonmagnetic metals mentioned in Ref [47

47. M. A. Ordal, R. J. Bell, R. W. Alexander Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). [CrossRef] [PubMed]

]. We find that the approximate formula for neff,2 performs also well for all other nonmagnetic metals of Al, Ag, Au, Mo, W, Pd, Ti, Pb, Pt, V. The maximum relative deviation of the formula neff,2 is always less than 3% for all 11 tested nonmagnetic metals in the whole spectral region of THz wave when the radius of metal wire is in the wide range from 5 nm to 500 nm.

4. Conclusions and discussions

It is worth mentioning that Ref [24

24. H. Liang, S. Ruan, M. Zhang, and H. Su, “Nanofocusing of terahertz wave on conical metal wire waveguides,” Opt. Commun. 283(2), 262–264 (2010). [CrossRef]

]. has touched the topics of terahertz plasmon of a metal nanowire with a sub-skin-depth diameter before our current work. However, the main contents of our current work are quite different from those of Ref [24

24. H. Liang, S. Ruan, M. Zhang, and H. Su, “Nanofocusing of terahertz wave on conical metal wire waveguides,” Opt. Commun. 283(2), 262–264 (2010). [CrossRef]

]. The new results of our current paper are mainly as follows.

  • 1) We derive an elegant approximate formula for the effective index neff of the terahertz plasmon of a metal nanowire with a sub-skin-depth diameter. Simply substituting the parameters λ0, R and εm into Eqs. (7) and (8), one can immediately obtain the effective index neff with a good accuracy.
  • 2) We show that the main propagation properties of a sub-skin-depth plasmon of a terahertz wave are closely related to the product of the radius of the metallic nanowire and the complex wave number of the metal. This important result is very helpful for understanding the physical mechanism of a sub-skin-depth plasmon.
  • 3) We show that the FWHM of the model field is simply equal to 1.5R. This result presents an intuitive and quantitative picture for the width of the modal field.

For potential practical applications, the excitation, coupling and detection of sub-skin-depth plasmon are also important. Recently, Refs [26

26. M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett. 94(5), 051107 (2009). [CrossRef]

,27

27. V. Astley, R. Mendis, and D. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett. 95(3), 031104 (2009). [CrossRef]

]. experimentally investigated the excitation, coupling and detection of subwavelength plasmon. We guess that the methods developed in Refs [26

26. M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett. 94(5), 051107 (2009). [CrossRef]

,27

27. V. Astley, R. Mendis, and D. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett. 95(3), 031104 (2009). [CrossRef]

]. might be also valid for the excitation, coupling and detection of sub-skin-depth plasmon. In particular, we strongly suggest the use of radially polarized beam as the input beam to increase the coupling efficiency because this kind of beam matches well the polarization of the terahertz plasmon of a metallic nanowire [5

5. Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]

].

Acknowledgment

The authors are indebted to the reviewer for the comments and suggestions for improving the paper, in particular for the suggestion of differentiating our current work from that of Ref. [24

24. H. Liang, S. Ruan, M. Zhang, and H. Su, “Nanofocusing of terahertz wave on conical metal wire waveguides,” Opt. Commun. 283(2), 262–264 (2010). [CrossRef]

].

References and links

1.

B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995). [CrossRef] [PubMed]

2.

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(16), 2321 (1996). [CrossRef]

3.

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

4.

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef] [PubMed]

5.

Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]

6.

M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87(26), 261107 (2005). [CrossRef]

7.

T.-I. Jeon, J.-Q. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005). [CrossRef]

8.

H. Cao and A. Nahata, “Coupling of terahertz pulses onto a single metal wire waveguide using milled grooves,” Opt. Express 13(18), 7028–7034 (2005). [CrossRef] [PubMed]

9.

M. Wächter, M. Nagel, and H. Kurz, “Frequency-dependent characterization of THz Sommerfeld wave propagation on single-wires,” Opt. Express 13(26), 10815–10822 (2005). [CrossRef] [PubMed]

10.

K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22(9), 2001–2008 (2005). [CrossRef]

11.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006). [CrossRef] [PubMed]

12.

K. Wang and D. M. Mittleman, “Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range,” Phys. Rev. Lett. 96(15), 157401 (2006). [CrossRef] [PubMed]

13.

J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman, “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Opt. Express 14(1), 279–290 (2006). [CrossRef] [PubMed]

14.

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(19), 8772–8778 (2006). [CrossRef] [PubMed]

15.

Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C. Y. Wang, “Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves,” Opt. Express 14(26), 13021–13029 (2006). [CrossRef] [PubMed]

16.

C. Themistos, B. M. A. 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(12), 5111–5118 (2006). [CrossRef]

17.

X. He, J. Cao, and S. Feng, “Simulation of the propagation property of metal wires terahertz waveguides,” Chin. Phys. Lett. 23(8), 2066–2069 (2006). [CrossRef]

18.

J. A. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite-element method simulations of guided wave phenomena at terahertz frequencies,” Proc. IEEE 95(8), 1624–1640 (2007). [CrossRef]

19.

H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express 16(22), 18241–18248 (2008). [CrossRef] [PubMed]

20.

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(1), 271–278 (2008). [CrossRef] [PubMed]

21.

P. W. Smorenburg, W. Op ’t Root, and O. J. Luiten, “Direct generation of terahertz surface plasmon polaritons on a wire using electron bunches’,” Phys. Rev. B 78(11), 115415 (2008). [CrossRef]

22.

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(2), 215–231 (2008). [CrossRef]

23.

J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express 17(23), 20806–20815 (2009). [CrossRef] [PubMed]

24.

H. Liang, S. Ruan, M. Zhang, and H. Su, “Nanofocusing of terahertz wave on conical metal wire waveguides,” Opt. Commun. 283(2), 262–264 (2010). [CrossRef]

25.

J. Yang, Q. Cao, and C. Zhou, “An analytical recurrence formula for the zero-order metal wire plasmon of terahertz wave,” J. Opt. Soc. Am. A 27(7), 1608–1612 (2010). [CrossRef]

26.

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett. 94(5), 051107 (2009). [CrossRef]

27.

V. Astley, R. Mendis, and D. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett. 95(3), 031104 (2009). [CrossRef]

28.

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30.

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31.

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33.

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34.

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35.

R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of terahertz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24(20), 1431–1433 (1999). [CrossRef]

36.

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88(7), 4449 (2000). [CrossRef]

37.

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000). [CrossRef]

38.

W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. 82(25), 4435 (2003). [CrossRef]

39.

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006). [CrossRef] [PubMed]

40.

M. Wächter, M. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90(6), 061111 (2007). [CrossRef]

41.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009). [CrossRef] [PubMed]

42.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]

43.

L. Martin-Moreno, “Terahertz technology: Mind the gap,” Nat. Photonics 3(3), 131–132 (2009). [CrossRef]

44.

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

45.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

46.

U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64(12), 125420 (2001). [CrossRef]

47.

M. A. Ordal, R. J. Bell, R. W. Alexander Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(260.3090) Physical optics : Infrared, far
(260.3910) Physical optics : Metal optics

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 7, 2010
Revised Manuscript: July 23, 2010
Manuscript Accepted: July 27, 2010
Published: August 16, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Jie Yang, Qing Cao, and Changhe Zhou, "Theory for terahertz plasmons of metallic nanowires with sub-skin-depth diameters," Opt. Express 18, 18550-18557 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18550


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References

  1. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995). [CrossRef] [PubMed]
  2. 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(16), 2321 (1996). [CrossRef]
  3. M. J. Fitch and R. Osiander, “Terahertz waves for communications and sensing,” Johns Hopkins APL Tech. Dig. 25, 348–355 (2004).
  4. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef] [PubMed]
  5. Q. Cao and J. Jahns, “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13(2), 511–518 (2005). [CrossRef] [PubMed]
  6. M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87(26), 261107 (2005). [CrossRef]
  7. T.-I. Jeon, J.-Q. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005). [CrossRef]
  8. H. Cao and A. Nahata, “Coupling of terahertz pulses onto a single metal wire waveguide using milled grooves,” Opt. Express 13(18), 7028–7034 (2005). [CrossRef] [PubMed]
  9. M. Wächter, M. Nagel, and H. Kurz, “Frequency-dependent characterization of THz Sommerfeld wave propagation on single-wires,” Opt. Express 13(26), 10815–10822 (2005). [CrossRef] [PubMed]
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