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 OSA

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

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. 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]

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]

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]

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]

2007 (4)

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

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

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

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

2006 (2)

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]

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]

2005 (4)

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]

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

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, 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]

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. 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]

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. 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]

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.

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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).
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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).
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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]

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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]

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

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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).
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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).
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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).
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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).
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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]

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S. A. Marshall and J. Weber, “Plane parallel plate transmission line stark microwave spectrograph,” Rev. Sci. Instrum. 28(2), 134–137 (1957).
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N. R. Wild, “Photoetched microwave transmission lines,” IRE Trans. Microwave Theor. Tech. 3(2), 21–30 (1955).
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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).
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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]

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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]

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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).
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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).
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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).
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[CrossRef]

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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).
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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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