Abstract

We experimentally demonstrate complete two-dimensional (2-D) confinement of terahertz (THz) energy in finite-width parallel-plate waveguides, defying conventional wisdom in the century-old field of microwave waveguide technology. We find that the degree of energy confinement increases exponentially with decreasing plate separation. We propose that this 2-D confinement is mediated by the mutual coupling of plasmonic edge modes, analogous to that observed in slot waveguides at optical wavelengths. By adiabatically tapering the width and the separation, we focus THz waves down to a size of 10 μm (≈λ/260) by 18 μm (≈λ/145), which corresponds to a mode area of only 2.6 × 10−5 λ2.

©2010 Optical Society of America

1. Introduction

Much attention has been paid to the subwavelength confinement of electromagnetic waves using wave-guiding techniques [19], for applications in high-resolution imaging and localized sensing. Here we discuss the use of a parallel-plate waveguide (PPWG) for terahertz (THz) waves, and experimentally demonstrate subwavelength confinement not only normal to the plates, as could be expected [3], but also parallel to the plates where there is no physical boundary, defying conventional wisdom in the century-old field of microwave-waveguide technology [1017]. We achieve this complete two-dimensional (2-D) confinement by employing a finite plate-width along with a reduced plate separation. Remarkably, we find that the 2-D energy confinement within the finite-width PPWG increases exponentially as the plate separation is reduced. By adiabatically tapering the width and the separation, we focus a single-cycle pulse having a peak spectral component of 0.115 THz down to a size of 10 μm (≈λ/260) by 18 μm (≈λ/145). This corresponds to a mode area of only 2.6 × 10−5 λ2, the smallest fractional mode area ever experimentally demonstrated using a wave-guiding technique at any wavelength.

This 2-D confinement is analogous to what has been observed in slot (or gap plasmon) waveguides [18,19] at optical wavelengths. These optical waveguides are geometrically similar to finite-width PPWGs, consisting of two metallic plates immersed in a homogenous dielectric medium such as air. However, the two situations are electro-dynamically distinct, since metals exhibit a strong plasmonic response at optical frequencies, but a much weaker response in the THz range. In the optical case, the 2-D confinement has been attributed to the excitation of plasmonic edge modes at the corners of the plate edges, and in particular to their mutual coupling across the gap between the two metal surfaces [18]. Our measurements of the spatial mode pattern at the output face of the PPWG suggest the relevance of these edge modes even at THz frequencies. As a result, we hypothesize that a similar mechanism mediates the observed 2-D confinement. This work opens the door to a paradigm shift in the conventional understanding of the PPWG. Furthermore, since the highly confined propagating mode exhibits no cutoff, this mode confinement suffers from no bandwidth limitations, and can therefore enable broadband subwavelength THz imaging and sensing [20].

2. Two-dimensional confinement in parallel-plate waveguides

To explore the efficiency of lateral confinement, we first study the behavior of an untapered PPWG with a plate width of w = 1 cm as in Fig. 1(a) , fabricated of two highly polished aluminum plates of length 25 cm. Using a THz time-domain spectroscopy setup, we focus a beam of single-cycle broadband THz pulses onto the input facet of the waveguide, centered on the air gap. The spot size of the input beam is chosen to have a 1/e diameter of 1 cm, matching the waveguide width. The polarization is along the y axis, perpendicular to the inner plate surfaces, to excite the TEM mode of the waveguide [21,22]. Using a fiber-coupled photoconductive receiver, we measure the spatial distribution and temporal waveforms of the radiation emerging from the output facet for several different plate separations. A 1 mm-diameter aperture held directly in front of the receiver improves the spatial resolution.

 

Fig. 1 Measurement schematic. (a) A schematic of the field measurements for untapered PPWGs. The field is directly detected using a fiber-coupled photoconductive antenna, with an aperture in front of the substrate lens to improve the spatial resolution. The antenna is oriented so as to be sensitive to the y component of the field. (b) A schematic of the measurement scheme for tapered PPWGs. In this case, an aperture-based method provides inadequate spatial resolution, so a scattering-probe technique is employed. Here, the measurement is sensitive to the z component of the field. The field can be characterized by scanning the position of the probe. The parameters describing the size of the output aperture, wout, the plate width, and bout, the plate separation, are shown. (c) A close-up photograph of the setup illustrated in (b).

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Figures 2(a) and 2(b) show the spatially resolved two-dimensional profiles of the transverse electric field (E y) measured in the plane of the output facet of the PPWG with plate separations of b = 10 mm and b = 5 mm, respectively. These field maps show a surprisingly high degree of field confinement along the x axis (the unshielded direction). Moreover, there is evidence of field enhancement at the four sharp corners. This is clearer in Fig. 2(c), which shows the line profiles corresponding to the two vertical black dotted lines in Fig. 2(a). The field near the corners is ~35% larger than near the flat surfaces at x = 0. These field enhancements may be an important indication of the lateral confinement mechanism. They are probably related to plasmonic edge modes, coupled electromagnetic and electronic excitations that propagate along the metal edge. Calculations have indicated that, when two edges are in close proximity, these modes can couple to each other resulting in higher energy confinement within the plates [18]. A smaller plate separation leads to a stronger coupling, and therefore improved mode confinement.

 

Fig. 2 Characterization of the output mode in untapered PPWGs. Two-dimensional profiles of the THz electric field measured at the output facet of the 1 cm-wide PPWG with plate separation (a) b = 10 mm and (b) 5 mm. (c) Vertical line profiles along the dotted black lines in (a), showing the field enhancements near the corners. (d) Horizontal line profiles for three different plate separations, including the two shown in (a) and (b). The horizontal dashed white lines indicate the locations along which these scans have been extracted, centered between the two plates. The line profile for a 10 cm-wide PPWG is also shown for comparison (green curve).

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We can experimentally quantify the degree of mode confinement as a function of the plate separation b. Figure 2(d) shows line profiles of the measured spatial distributions along the x axis, for three different values of b. These field profiles depend strongly on the value of b. This is in contrast to the case of a much wider (10-cm) PPWG, where the field profiles are always Gaussian and independent of b [see green curve in Fig. 2(d)]. For the narrower PPWG, the departure from a Gaussian profile becomes more pronounced as b decreases. We emphasize that the curves in Fig. 2(d) are measured at the center of the air gap (i.e., at y = 0), which is as far as possible from the sharp metal corners (at y = ± b/2). Yet, for values of b less than about 5 mm, we observe a field enhancement at the waveguide edges even in the middle of the air gap. This suggests that the edge modes couple more strongly to each other as b decreases.

We define an energy confinement factor as the ratio of the total THz energy within the waveguide to the total THz energy in the plane of the output facet. This confinement factor exhibits an exponential dependence on b, converging to unity at b = 0 (see Fig. 3 ). This remarkable result indicates that the energy in the propagating mode is increasingly confined within the waveguide as b decreases.

 

Fig. 3 Mode confinement as a function of plate separation. The confinement factor as a function of the separation between the two metal surfaces at the output facet. The insets schematically illustrate how this confinement factor is defined. The curve is a fit to an exponential dependence, showing the convergence to unity at zero plate separation.

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3. Subwavelength confinement using tapered parallel-plate waveguides

With this new understanding of the crucial role of the plate separation b, we can now explore the possibility of subwavelength confinement in 2-D by adiabatically tapering the plate width and separation b [2325]. As before, we use a waveguide of 25 cm length, but now the last 20 cm tapers uniformly from an initial width of win = 1 cm down to a final width, wout, which is less than the free-space wavelength λ. We study several waveguides with different value of wout, ranging down to 10 μm. For these waveguides, the plate separation also decreases uniformly from bin = 1 mm (at the input end) down to a final value of bout, which is as small as 18 μm.

In order to study the field distribution at the end of these tapered PPWGs, a 1 mm spatial resolution is inadequate. Instead of direct detection through an aperture, we employ scattering-probe imaging [9,26], which is similar to apertureless near-field microscopy [2628]. A tapered metal probe with a point diameter of either 2 μm or 10 μm (depending on wout) is held at the end of the waveguide, parallel to the z axis. This probe scatters the field emerging from the waveguide, where it is measured via lock-in detection [see Figs. 1(b) and 1(c)]. This technique provides subwavelength spatial resolution of the z component of the field at the probe’s apex [9].

We map Ez at the output facet of the tapered PPWGs by scanning the location of the scattering probe. Figure 4 shows typical time-domain waveforms at the output of a tapered PPWG with wout = 10 μm and bout = 18 μm (black and blue curves), along with an equivalent measurement on an untapered waveguide for comparison (red curve). All of these waveforms have similar temporal structure, indicating that the taper does not distort the time-domain signals. The right inset compares the amplitude spectra for the tapered and untapered cases. These are nearly identical, which demonstrates that the extreme subwavelength tapering does not impose any bandwidth restriction. It should be noted that these output spectra mimic the input spectrum, except for a broadband loss. The left inset shows a 2-D field map at the output facet of a tapered PPWG with wout = 40 μm and bout = 25 μm. This map, along with the waveforms, indicates a polarity reversal for E z between the regions near the upper and lower plates of the waveguide. This polarity flip is similar to that associated with the symmetric plasmon mode of slot waveguides [23,25,29].

 

Fig. 4 Time-domain waveforms detected via scattering-probe imaging. Waveforms measured at the output facet of a tapered (wout = 10 μm, bout = 18 μm) and untapered waveguide. These are measured using identical methods so that the waveforms can be compared. The similarity of the red (untapered case; wout = 1 cm) and black (tapered case) curves indicates that the waveguide taper has little effect on the shape of the time-domain signal. The right inset compares the normalized amplitude spectra, showing no bandwidth restrictions even though wout is much smaller than the free-space wavelength in the tapered case. The left inset shows a two-dimensional field map (xy plane) at the output of a tapered waveguide (wout = 40 μm, bout = 25 μm) which exhibits a polarity flip between the two metal surfaces. This polarity flip, also evident in comparisons of the time-domain waveforms measured at the upper and lower plate surfaces (blue and black curves), establishes that we are observing the symmetric plasmon mode described in previous studies [23,25,29].

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By controlling both wout and bout, we can effectively confine this broadband THz output field to an area far below λ2. Figure 5 shows line scans along the x axis, for three different PPWGs with decreasing values of wout and bout. In each case, the FWHM (full-width-half-max) is roughly equal in size to wout. Since the z component is intimately coupled to the additional y component of the field via Maxwell’s equations, this is a good indication of the confinement of the resultant field at the output. This is a dramatic demonstration of the importance of plasmonic effects at THz frequencies: even though there is no material boundary along the x direction, the field is still squeezed along x to a subwavelength size. For the narrowest wout (black dots), the x-confinement is about λ/260, corresponding to a mode area of only 2.6 × 10−5 of λ2. To the best of our knowledge, this is the smallest fractional mode area ever experimentally demonstrated using a wave-guiding technique at any wavelength.

 

Fig. 5 Normalized line scans at the output of tapered PPWGs, in close proximity to the edge of the upper plate. These line scans (along the x axis, which is the unshielded direction) show the degree of localization of the THz field at the output facet of three different waveguides, with decreasing values of wout and bout. In each case, the smallest achievable field confinement is approximately equal to wout, the size of the output width. The smallest width (black data points) gives the best confinement, with a FWHM of only 10 μm. Using the peak spectral component (0.115 THz) of the broadband THz pulse, this corresponds to ≈λ/260, with a mode area of 2.6 × 10−5 λ2.

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4. Conclusion

In summary, we have measured the mode profile at the output of PPWGs in the THz regime. We show that it is possible to achieve confinement even parallel to the plates, defying conventional wisdom in microwave waveguide technology. (This lateral confinement is fundamentally different to what can be achieved via an index-mismatch, provided by a high-index dielectric sandwiched between the plates [30].) We apply this result to achieve extreme subwavelength 2-D confinement of THz waves in tapered PPWGs. We propose that this confinement is mediated by the coupling of plasmonic edge modes across the air gap, in analogy to the confinement mechanism for slot waveguides at optical frequencies. This result emphasizes the importance of controlling both the plate separation and the plate width in achieving subwavelength confinement, and dramatically illustrates the influence of plasmonic effects for metals at THz frequencies. Incidentally, we note that the higher energy confinement could possibly result in a higher ohmic dissipation, and thus, a higher propagation loss. Although in the THz range these losses are probably several orders of magnitude less than those at optical frequencies, this issue still remains to be examined.

Acknowledgements

This work was funded in part by the National Science Foundation and by the Air Force Office of Scientific Research through the CONTACT program.

References and links

1. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003). [CrossRef]   [PubMed]  

2. A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004). [CrossRef]   [PubMed]  

3. M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005). [CrossRef]  

4. 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]  

5. T. Monro, “Optical fibres: Beyond the diffraction limit,” Nat. Photonics 1(2), 89–90 (2007). [CrossRef]  

6. M. B. Johnston, “Superfocusing of terahertz waves,” Nat. Photonics 1(1), 14–15 (2007). [CrossRef]  

7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]  

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

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

10. J. J. Thomson, Notes on Recent Researches in Electricity and Magnetism, (Clarendon, Oxford, 1893).

11. L. Rayleigh, “On the passage of electric waves through tubes, or the vibrations of dielectric cylinders,” Philos. Mag. 43, 125–132 (1897).

12. J. C. Slater, Microwave Transmission, (McGraw-Hill, New York, 1942).

13. D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950). [CrossRef]   [PubMed]  

14. S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957). [CrossRef]  

15. N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955). [CrossRef]  

16. K. S. Packard, “The origin of waveguides: a case of multiple rediscovery,” IEEE Trans. Microw. Theory Tech. 32(9), 961–969 (1984). [CrossRef]  

17. N. Marcuvitz, Waveguide Handbook, (Peregrinus, London, 1993).

18. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007). [CrossRef]  

19. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]  

20. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007). [CrossRef]  

21. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]  

22. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]  

23. A. Rusina, M. Durach, K. A. Nelson, and M. I. Stockman, “Nanoconcentration of terahertz radiation in plasmonic waveguides,” Opt. Express 16(23), 18576–18589 (2008). [CrossRef]  

24. N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005). [CrossRef]  

25. D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006). [CrossRef]  

26. V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009). [CrossRef]  

27. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999). [CrossRef]  

28. A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008). [CrossRef]   [PubMed]  

29. M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009). [CrossRef]  

30. N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005). [CrossRef]  

References

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  1. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
    [Crossref] [PubMed]
  2. A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
    [Crossref] [PubMed]
  3. M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005).
    [Crossref]
  4. 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]
  5. T. Monro, “Optical fibres: Beyond the diffraction limit,” Nat. Photonics 1(2), 89–90 (2007).
    [Crossref]
  6. M. B. Johnston, “Superfocusing of terahertz waves,” Nat. Photonics 1(1), 14–15 (2007).
    [Crossref]
  7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [Crossref]
  8. M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett. 94(5), 051107 (2009).
    [Crossref]
  9. V. Astley, R. Mendis, and D. M. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett. 95(3), 031104 (2009).
    [Crossref]
  10. J. J. Thomson, Notes on Recent Researches in Electricity and Magnetism, (Clarendon, Oxford, 1893).
  11. L. Rayleigh, “On the passage of electric waves through tubes, or the vibrations of dielectric cylinders,” Philos. Mag. 43, 125–132 (1897).
  12. J. C. Slater, Microwave Transmission, (McGraw-Hill, New York, 1942).
  13. D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950).
    [Crossref] [PubMed]
  14. S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957).
    [Crossref]
  15. N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955).
    [Crossref]
  16. K. S. Packard, “The origin of waveguides: a case of multiple rediscovery,” IEEE Trans. Microw. Theory Tech. 32(9), 961–969 (1984).
    [Crossref]
  17. N. Marcuvitz, Waveguide Handbook, (Peregrinus, London, 1993).
  18. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
    [Crossref]
  19. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
    [Crossref]
  20. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
    [Crossref]
  21. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
    [Crossref]
  22. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001).
    [Crossref]
  23. A. Rusina, M. Durach, K. A. Nelson, and M. I. Stockman, “Nanoconcentration of terahertz radiation in plasmonic waveguides,” Opt. Express 16(23), 18576–18589 (2008).
    [Crossref]
  24. N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
    [Crossref]
  25. D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006).
    [Crossref]
  26. V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
    [Crossref]
  27. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
    [Crossref]
  28. A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
    [Crossref] [PubMed]
  29. M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
    [Crossref]
  30. N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
    [Crossref]

2009 (4)

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

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

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

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

2008 (3)

A. Rusina, M. Durach, K. A. Nelson, and M. I. Stockman, “Nanoconcentration of terahertz radiation in plasmonic waveguides,” Opt. Express 16(23), 18576–18589 (2008).
[Crossref]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

2007 (4)

T. Monro, “Optical fibres: Beyond the diffraction limit,” Nat. Photonics 1(2), 89–90 (2007).
[Crossref]

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
[Crossref]

M. B. Johnston, “Superfocusing of terahertz waves,” Nat. Photonics 1(1), 14–15 (2007).
[Crossref]

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

2006 (2)

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006).
[Crossref]

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]

2005 (4)

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

2004 (1)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[Crossref] [PubMed]

2003 (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

2001 (2)

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001).
[Crossref]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[Crossref]

1999 (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

1984 (1)

K. S. Packard, “The origin of waveguides: a case of multiple rediscovery,” IEEE Trans. Microw. Theory Tech. 32(9), 961–969 (1984).
[Crossref]

1957 (1)

S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957).
[Crossref]

1955 (1)

N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955).
[Crossref]

1950 (1)

D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950).
[Crossref] [PubMed]

1897 (1)

L. Rayleigh, “On the passage of electric waves through tubes, or the vibrations of dielectric cylinders,” Philos. Mag. 43, 125–132 (1897).

Aizpurua, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Andrews, S. R.

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]

Astley, V.

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

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Awad, M.

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

Awad, M. M.

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005).
[Crossref]

Baird, D. H.

D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950).
[Crossref] [PubMed]

Brown, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[Crossref] [PubMed]

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Cheville, R. A.

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005).
[Crossref]

Deibel, J.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Durach, M.

Fan, S.

Fristrom, R. M.

D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950).
[Crossref] [PubMed]

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

García-Vidal, F. J.

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]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Gramotnev, D. K.

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006).
[Crossref]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Grischkowsky, D.

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[Crossref]

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001).
[Crossref]

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[Crossref] [PubMed]

Hillenbrand, R.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Huber, A. J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Johnston, M. B.

M. B. Johnston, “Superfocusing of terahertz waves,” Nat. Photonics 1(1), 14–15 (2007).
[Crossref]

Kadlec, F.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Keilmann, F.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Klein, N.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Knoll, B.

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Kuipers, L.

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

Kurz, H.

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

Kuzel, P.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Kužel, P.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Lahl, P.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[Crossref] [PubMed]

Maier, S. A.

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]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Marshall, S. A.

S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957).
[Crossref]

Martín-Moreno, L.

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]

Matsuzaki, Y.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Mendis, R.

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

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001).
[Crossref]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[Crossref]

Mittleman, D. M.

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

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

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Monro, T.

T. Monro, “Optical fibres: Beyond the diffraction limit,” Nat. Photonics 1(2), 89–90 (2007).
[Crossref]

Nagel, M.

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

Nelson, K. A.

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Packard, K. S.

K. S. Packard, “The origin of waveguides: a case of multiple rediscovery,” IEEE Trans. Microw. Theory Tech. 32(9), 961–969 (1984).
[Crossref]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006).
[Crossref]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Poppe, U.

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

Rayleigh, L.

L. Rayleigh, “On the passage of electric waves through tubes, or the vibrations of dielectric cylinders,” Philos. Mag. 43, 125–132 (1897).

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[Crossref] [PubMed]

Rusina, A.

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing millimeter waves into microns,” Phys. Rev. Lett. 92(14), 143904 (2004).
[Crossref] [PubMed]

Sirvetz, M. H.

D. H. Baird, R. M. Fristrom, and M. H. Sirvetz, “Stark effect absorption cells for microwave spectroscopy,” Rev. Sci. Instrum. 21(10), 881 (1950).
[Crossref] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Spasenovic, M.

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

Stockman, M. I.

van Oosten, D.

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

Verhagen, E.

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

Vernon, K. C.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Veronis, G.

Weber, J.

S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957).
[Crossref]

Wild, N. R.

N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955).
[Crossref]

Wittborn, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Yamaguchi, K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

Zhan, H.

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

Zhang, X.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Appl. Phys. Lett. (6)

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005).
[Crossref]

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

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

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[Crossref]

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguide,” Appl. Phys. Lett. 89(4), 041111 (2006).
[Crossref]

M. Spasenović, D. van Oosten, E. Verhagen, and L. Kuipers, “Measurements of modal symmetry in subwavelength plasmonic slot waveguides,” Appl. Phys. Lett. 95(20), 203109 (2009).
[Crossref]

IEEE Microw. Wirel. Compon. Lett. (1)

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

K. S. Packard, “The origin of waveguides: a case of multiple rediscovery,” IEEE Trans. Microw. Theory Tech. 32(9), 961–969 (1984).
[Crossref]

IRE Trans. Microwave Theor. Tech. (1)

N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955).
[Crossref]

J. Appl. Phys. (3)

V. Astley, H. Zhan, R. Mendis, and D. M. Mittleman, “A study of background signals in terahertz apertureless near-field microscopy and their use for scattering-probe imaging,” J. Appl. Phys. 105(11), 113117 (2009).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kužel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

N. Klein, P. Lahl, U. Poppe, F. Kadlec, and P. Kuzel, “A metal-dielectric antenna for terahertz near-field imaging,” J. Appl. Phys. 98(1), 014910 (2005).
[Crossref]

J. Lightwave Technol. (1)

Nano Lett. (1)

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile charge carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
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Figures (5)

Fig. 1
Fig. 1 Measurement schematic. (a) A schematic of the field measurements for untapered PPWGs. The field is directly detected using a fiber-coupled photoconductive antenna, with an aperture in front of the substrate lens to improve the spatial resolution. The antenna is oriented so as to be sensitive to the y component of the field. (b) A schematic of the measurement scheme for tapered PPWGs. In this case, an aperture-based method provides inadequate spatial resolution, so a scattering-probe technique is employed. Here, the measurement is sensitive to the z component of the field. The field can be characterized by scanning the position of the probe. The parameters describing the size of the output aperture, wout , the plate width, and bout , the plate separation, are shown. (c) A close-up photograph of the setup illustrated in (b).
Fig. 2
Fig. 2 Characterization of the output mode in untapered PPWGs. Two-dimensional profiles of the THz electric field measured at the output facet of the 1 cm-wide PPWG with plate separation (a) b = 10 mm and (b) 5 mm. (c) Vertical line profiles along the dotted black lines in (a), showing the field enhancements near the corners. (d) Horizontal line profiles for three different plate separations, including the two shown in (a) and (b). The horizontal dashed white lines indicate the locations along which these scans have been extracted, centered between the two plates. The line profile for a 10 cm-wide PPWG is also shown for comparison (green curve).
Fig. 3
Fig. 3 Mode confinement as a function of plate separation. The confinement factor as a function of the separation between the two metal surfaces at the output facet. The insets schematically illustrate how this confinement factor is defined. The curve is a fit to an exponential dependence, showing the convergence to unity at zero plate separation.
Fig. 4
Fig. 4 Time-domain waveforms detected via scattering-probe imaging. Waveforms measured at the output facet of a tapered (wout = 10 μm, bout = 18 μm) and untapered waveguide. These are measured using identical methods so that the waveforms can be compared. The similarity of the red (untapered case; wout = 1 cm) and black (tapered case) curves indicates that the waveguide taper has little effect on the shape of the time-domain signal. The right inset compares the normalized amplitude spectra, showing no bandwidth restrictions even though wout is much smaller than the free-space wavelength in the tapered case. The left inset shows a two-dimensional field map (xy plane) at the output of a tapered waveguide (wout = 40 μm, bout = 25 μm) which exhibits a polarity flip between the two metal surfaces. This polarity flip, also evident in comparisons of the time-domain waveforms measured at the upper and lower plate surfaces (blue and black curves), establishes that we are observing the symmetric plasmon mode described in previous studies [23,25,29].
Fig. 5
Fig. 5 Normalized line scans at the output of tapered PPWGs, in close proximity to the edge of the upper plate. These line scans (along the x axis, which is the unshielded direction) show the degree of localization of the THz field at the output facet of three different waveguides, with decreasing values of wout and bout . In each case, the smallest achievable field confinement is approximately equal to wout , the size of the output width. The smallest width (black data points) gives the best confinement, with a FWHM of only 10 μm. Using the peak spectral component (0.115 THz) of the broadband THz pulse, this corresponds to ≈λ/260, with a mode area of 2.6 × 10−5 λ2.

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