Abstract

An tapered hyperbolic metal waveguide is suggested for the nanofocusing of terahertz waves. We numerically show that, at the frequency of 1 THz, the focal spot can be as small as only 5 nm, which is smaller than that of a plate waveguide by 2 orders of magnitude. Correspondingly, the longitudinal component of the energy flow density is stronger than that of a plate waveguide by 3 orders of magnitude for the same input. It is shown that these significant improvements come from the small imaginary part of the effective index of the hyperbolic metal waveguide.

© 2014 Optical Society of America

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References

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2014 (3)

2013 (3)

D. M. Mittleman, “Frontiers in terahertz sources and plasmonics,” Nat. Photonics 7(9), 666–669 (2013).
[Crossref]

A. Edelmann, L. Moeller, and J. Jahns, “Coupling of terahertz radiation to metallic wire using end-fire technique,” Electron. Lett. 49(14), 884–886 (2013).
[Crossref]

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

2012 (3)

M. Misra, S. R. Andrews, and S. A. Maier, “Waveguide artefacts in terahertz near field imaging,” Appl. Phys. Lett. 100(19), 191109 (2012).
[Crossref]

A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

H. Duan, A. I. Fernández-Domínguez, M. Bosman, S. A. Maier, and J. K. Yang, “Nanoplasmonics: classical down to the nanometer scale,” Nano Lett. 12(3), 1683–1689 (2012).
[Crossref] [PubMed]

2011 (3)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[Crossref] [PubMed]

M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28(3), 558–566 (2011).
[Crossref]

2010 (5)

2009 (6)

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]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbsen, “Nanofocusing with channel plasmon polaritons,” Nano Lett. 9(3), 1278–1282 (2009).
[Crossref] [PubMed]

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]

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, “Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial,” Opt. Express 17(5), 3826–3834 (2009).
[Crossref] [PubMed]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft x-ray microscopy,” Opt. Express 17(20), 17669–17677 (2009).
[Crossref] [PubMed]

2008 (7)

E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57 (2008).
[Crossref] [PubMed]

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]

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] [PubMed]

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[Crossref] [PubMed]

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol. 9(12), 929–943 (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]

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

2007 (2)

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–63 (2007).
[Crossref] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[Crossref] [PubMed]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

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

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

2005 (1)

2004 (3)

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

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

2003 (2)

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]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
[Crossref] [PubMed]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1998 (1)

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58(23), 15419–15421 (1998).
[Crossref]

1985 (1)

1983 (1)

1957 (1)

R. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106(5), 874–881 (1957).
[Crossref]

Ahn, J. S.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

Ahn, K. J.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[Crossref] [PubMed]

Alexander, R. W.

Alonso-González, P.

M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

Anderson, E. H.

Andrews, S. R.

M. Misra, S. R. Andrews, and S. A. Maier, “Waveguide artefacts in terahertz near field imaging,” Appl. Phys. Lett. 100(19), 191109 (2012).
[Crossref]

Arzubiaga, L.

M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

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]

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–63 (2007).
[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]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bartal, G.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

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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]

Park, H. R.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

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]

Park, I. Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Park, N.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

Park, N. K.

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]

Park, Q. H.

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]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Pelton, M.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Piao, X.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

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]

Planken, P. C. M.

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).
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Polman, A.

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
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Querry, M. R.

Raschke, M. B.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
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Reichel, K.

Rekawa, S.

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).
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R. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106(5), 874–881 (1957).
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E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
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V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbsen, “Nanofocusing with channel plasmon polaritons,” Nano Lett. 9(3), 1278–1282 (2009).
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C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
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Rusina, A.

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M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
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Schröter, U.

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58(23), 15419–15421 (1998).
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Seo, M. A.

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).
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Shu, J.

Sorger, V. J.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[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]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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Stockman, M. I.

Suwal, O. K.

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).
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Teng, D.

Thoman, A.

Ting, A. Y.

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol. 9(12), 929–943 (2008).
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Verhagen, E.

Volkov, V. S.

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Walther, M.

Wang, K.

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).
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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).
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K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
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C. H. Liang, X. W. Wang, and X. Chen, “Inverse Joukowski mapping,” Prog. Electromagnetics Res. Lett. 19, 113–125 (2010).

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Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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Xu, Q.

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Yang, J. K.

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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
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Zhan, H.

Zhang, M.

Zhang, X.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
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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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Zhou, C.

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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Appl. Opt. (2)

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

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C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
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H. Duan, A. I. Fernández-Domínguez, M. Bosman, S. A. Maier, and J. K. Yang, “Nanoplasmonics: classical down to the nanometer scale,” Nano Lett. 12(3), 1683–1689 (2012).
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Nat. Commun. (1)

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commun. 4, 2361 (2013).

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M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
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Nat. Rev. Mol. Cell Biol. (1)

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol. 9(12), 929–943 (2008).
[Crossref] [PubMed]

Nature (4)

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
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S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
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Opt. Express (11)

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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).
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H. Zhan, R. Mendis, and D. M. Mittleman, “Superfocusing terahertz waves below λ/250 using plasmonic parallel-plate waveguides,” Opt. Express 18(9), 9643–9650 (2010).
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H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express 16(22), 18241–18248 (2008).
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A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, “Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial,” Opt. Express 17(5), 3826–3834 (2009).
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W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft x-ray microscopy,” Opt. Express 17(20), 17669–17677 (2009).
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J. Shu, W. Gao, K. Reichel, D. Nickel, J. Dominguez, I. Brener, D. M. Mittleman, and Q. Xu, “High-Q terahertz Fano resonance with extraordinary transmission in concentric ring apertures,” Opt. Express 22(4), 3747–3753 (2014).
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H. Pahlevaninezhad, T. E. Darcie, and B. Heshmat, “Two-wire waveguide for terahertz,” Opt. Express 18(7), 7415–7420 (2010).
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Phys. Rev. (1)

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Phys. Rev. B (1)

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58(23), 15419–15421 (1998).
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Phys. Rev. Lett. (5)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
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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).
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E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
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Figures (7)

Fig. 1
Fig. 1 The geometry of the adiabatically tapered hyperbolic metal waveguide (ATHMWG) along axis z. (a) Two silver parts with permittivity εm are separated by air, the boundary lines of each cross-section are the branches of hyperbola with fixed θ = 45°, θ is the intersection angle between asymptote and axis x. (b) Semi-transverse axis a varies, qualitatively, along the optical axis z, a gradually decreases from a1 to a2. (c) The input plane with semi-transverse axis a1 = 1 μm. (d) The output plane with semi-transverse axis a2 = 1 nm. The frequency is 1 THz (λ≈300 μm), the permittivity of silver is εm = −2.39 × 105 + j1.04 × 106 at this frequency [31], and the permittivity εa of air is 1.
Fig. 2
Fig. 2 (color) The electric field distributions and the polarization at the input and the output plane. (a) At the input plane. (b) At the output plane. These fields are normalized against the electric field in the center of the input plane E0.
Fig. 3
Fig. 3 Change of effective index neff with semi-transverse axis a of HMWG and PPWG. (a) The real part Re(neff) - 1, (b) the imaginary part Im(neff). The horizontal dash line in (b) shows that the HMWG with semi-transverse axis a = 1 nm has the same Im(neff) as the PPWG with a = 193 nm.
Fig. 4
Fig. 4 The tapered curve of the ATHMWG and its adiabatic parameter. (a) Change of the semi-transverse axis a with the axis z derived from Eq. (3). (b) The corresponding waveguide gradient (δ1 = |da/dz|) and adiabatic parameter (δ2 = |d(kz-1)/dz|) with respect to a, the δ1 and δ2 are set strictly no more than 0.05 to ignore scattering and reflection approximately. Before a critical point a = 0.4677 μm, δ1 >δ2, and δ1 is fixed to 0.05; after the critical point, δ1<δ2, and δ2 is fixed to 0.05.
Fig. 5
Fig. 5 Terahertz light intensity enhancement in ATHMWG and an ATPPWG. The intensity enhancement of the ATHMWG continuously increases and reaches about 104 at the output plane, while the intensity enhancement of the ATPPWG gradually decreases after reaching its peak at about a≈75 nm.
Fig. 6
Fig. 6 Comparison of the center intensity enhancement of the ATHMWG from a = 1 μm to 10 nm between the WKB approximation and a full field COMSOL 3D simulation. The enhancement profile from the 3D simulation agrees well with that from the WKB approximation but has a slight deviation, which is of about 15% at a = 10 nm. The WKB approximation is still valid since the center intensity enhancement is of a same magnitude. The drop of the enhancement comes from the reflection and mode scattering of the tapered structure.
Fig. 7
Fig. 7 Change of phase effective index np (dashed line, in the form of np-1) and group effective index ng (solid line, in the form of ng-1) of HMWG with wavelength from 30 μm (~10 THz) to 600 μm (~0.5 THz). The upper two lines denote the change of both np and ng with wavelength when a = 1 nm, while the lower two denote the change of both np and ng with wavelength when a = 1 μm.

Equations (7)

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E x = 2 c 2 ( x 2 + y 2 + c 2 ) 2 4 x 2 c 2 × x 2 + y 2 + c 2 + ( x 2 + y 2 + c 2 ) 2 4 x 2 c 2 ,
E y = 2 xyc ( x 2 + y 2 + c 2 ) 2 4 x 2 c 2 × 1 x 2 + y 2 + c 2 + ( x 2 + y 2 + c 2 ) 2 4 x 2 c 2 ,
δ 1 =| da dz |<<1 δ 2 =| d( k z 1 ) dz |=| d ( k 0 n eff ) 1 da da dz |<<1,
max( δ 1 , δ 2 )=0.05,
P( z )=P( 0 )exp{ 2 k 0 0 z Im[ n eff ( z ) ]dz },
A( z )= P( z ) S z ( 0,0,z ) = S z ( x,y,z ) S z ( 0,0,z ) dxdy .
S z (0,0,z) S z (0,0,0) = A(0) A(z) exp{ 2 k 0 0 z Im[ n eff ( z ) ]dz }.

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