Abstract

In this paper we explore the existence of electromagnetic surface bound modes on a perfect metal wire milled with arrays of subwavelength grooves. The surface modes are axially symmetric transverse magnetic (TM) waves and have the same polarization state with the dominant propagating surface plasmon polaritons on the real metal wires. The dispersion of the fundamental surface mode has close resemblance with the dispersion of the surface plasmon polaritons. Moreover, we note that for TM polarization this metallic structure can be equivalent to a dielectric coated metal wire with defined geometrical parameters and effective refractive index of the dielectric coating. This metallic structure is expected to have some potential applications in the optical research in microwave or THz region.

© 2006 Optical Society of America

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  1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).
  2. H. Raether, Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [Crossref]
  4. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
    [Crossref] [PubMed]
  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, 2845 (1999).
    [Crossref]
  6. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
    [Crossref] [PubMed]
  7. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
    [Crossref]
  8. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
    [Crossref] [PubMed]
  9. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997).
    [Crossref] [PubMed]
  10. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface” Opt. Lett. 29, 1069–1071 (2004).
    [Crossref] [PubMed]
  11. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
    [Crossref]
  12. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
    [Crossref] [PubMed]
  13. T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
    [Crossref]
  14. T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
    [Crossref]
  15. H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)
  16. L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
    [Crossref]
  17. R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).
  18. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
    [Crossref] [PubMed]
  19. M. Qiu “Photonic band structures for surface waves on structured metal surfaces” Opt. Express 13, 7583–7588 (2005).
    [Crossref] [PubMed]
  20. F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
    [Crossref] [PubMed]
  21. F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
    [Crossref]
  22. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
    [Crossref] [PubMed]
  23. A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
    [Crossref] [PubMed]
  24. G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119–1128 (1950).
    [Crossref]
  25. Q. Cao and J. Jahns “Azimuthally polarized surface plasmons as effective terahertz waveguides,” Opt. Express 13, 511–518 (2005).
    [Crossref] [PubMed]
  26. K. Wang and D. M. Mittleman, “Guided propagation of terahertz pulses on metal wires,” J. Opt. Soc. Am. B 22, 2001–2008 (2005).
    [Crossref]
  27. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, Oxford, 1975).
  28. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
    [Crossref]
  29. U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
    [Crossref]
  30. K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
    [Crossref] [PubMed]
  31. The surface plasmon frequency ωsp is determined by ωsp=ωpεair+1 where ωp is the bulk plasma frequency of metal
  32. T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
    [Crossref]
  33. R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).
  34. S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
    [Crossref]
  35. J. A. Deibel, K. Wang, M. D. Escarra, and D. M. Mittleman “Enhanced coupling of terahertz radiation to cylindrical wire waveguides,” Optical Express. 14, 279–290 (2006).
    [Crossref]
  36. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
    [Crossref] [PubMed]
  37. A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13, 3535–3542 (2005).
    [Crossref] [PubMed]
  38. H. Cao and A. Nahata, “Coupling of terahertz pulsed onto a single metal wire waveguide using milled grooves,” Opt. Express 13, 7028–7034 (2005).
    [Crossref] [PubMed]
  39. S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
    [Crossref]
  40. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
    [Crossref] [PubMed]
  41. Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

2006 (4)

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

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

2005 (12)

H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
[Crossref] [PubMed]

A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13, 3535–3542 (2005).
[Crossref] [PubMed]

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

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

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

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
[Crossref]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[Crossref] [PubMed]

M. Qiu “Photonic band structures for surface waves on structured metal surfaces” Opt. Express 13, 7583–7588 (2005).
[Crossref] [PubMed]

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
[Crossref]

2004 (4)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

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

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[Crossref] [PubMed]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface” Opt. Lett. 29, 1069–1071 (2004).
[Crossref] [PubMed]

2001 (2)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

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

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, 2845 (1999).
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

1997 (1)

1996 (2)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

1984 (1)

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

1974 (1)

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

1954 (1)

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

1950 (1)

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

1948 (1)

L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
[Crossref]

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

Agrawal, A.

Andrews, S. R.

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Barlow, H. M.

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

Barnes, W. L.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

Born, M.

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

Brillouin, L.

L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
[Crossref]

Cao, H.

Cao, Q.

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[Crossref] [PubMed]

Collin, R.

R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).

Cullen, A. L.

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

Davis, C. C.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

de Abajo, F. J. Garcia

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

Deibel, J. A.

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

Dereux, A.

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

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Economou, E. N.

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

Elliott, R. S.

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

Escarra, M. D.

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

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[Crossref] [PubMed]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
[Crossref]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

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

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Goubau, G.

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

Gramotnev, D. K.

Grischkowsky, D.

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[Crossref] [PubMed]

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Jacobsen, S. C.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

Jahns, J.

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

Kitson, S. C.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

Kobayashi, T.

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Lopez-Rios, T.

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

Maier, S. A.

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Maier, S.A.

Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

Martin-Moreno, L

F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
[Crossref]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Mittleman, D. M.

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

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

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

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

Morimoto, A.

Nahata, A.

Ngai, K. L.

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

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

Pendry, J B

F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
[Crossref]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

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

Pfeiffer, C. A.

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

Pile, D. F. P.

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, 2845 (1999).
[Crossref]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

Qiu, M.

Qu, D.

Raether, H.

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

Saenz, J. J.

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

Sambles, J. R.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

Sambles, J. Roy

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Schröter, U.

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

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[Crossref] [PubMed]

Takahara, J.

Taki, H.

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Veronis, G.

Wang, K.

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

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

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

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

Wells, D. L.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

Wirgin, A.

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

Wolf, E.

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

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Wood, J. E.

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

Yamagishi, S.

Zhang, J.

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

Zhang, W.

Appl. Phys. Lett. (3)

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904–161906 (2005).
[Crossref]

T.-I. Jeon and D. Grischkowsky “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113–061115 (2006).
[Crossref]

S. A. Maier and S. R. Andrews “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88, 251120–251122 (2006).
[Crossref]

IRE Trans (1)

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans AP-2, 71–81 (1954).

J. Appl. Phys (1)

L. Brillouin, “Wave guides for slow waves,” J. Appl. Phys 19, 1023–1041 (1948).
[Crossref]

J. Appl. Phys. (1)

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

J. Opt. A: Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L Martin-Moreno, and J B Pendry “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7, S97–S101 (2005).
[Crossref]

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

Nature (2)

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

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Optical Express. (1)

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

Phys. Rev. B (3)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

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

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

Phys. Rev. Lett. (6)

K. Wang and D. M. Mittleman “Dispersion of Surface Plasmon Polaritons on metal wires in the Terahertz frequency range” Phys. Rev. Lett. 96, 157401 (2006).
[Crossref] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “A full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).
[Crossref] [PubMed]

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

F. J. Garcia de Abajo and J. J. Saenz “Electromagnetic Surface Modes in Structured Perfect-Conductor Surfaces” Phys. Rev. Lett. 95, 233901 (2005).
[Crossref] [PubMed]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[Crossref] [PubMed]

Proc. R. Soc. London (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902).

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal “Mimicking Surface Plasmons with Structured Surfaces” Science 305, 847–848 (2004).
[Crossref] [PubMed]

A. P. Hibbins, B. R. Evans, and J. Roy Sambles “Experimental verification of designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Solid State Commun. (1)

T. Lopez-Rios and A. Wirgin, “Role of waveguide and surface plasmon resonances in surface-enhanced Raman scattering at coldly evaporated metallic films,” Solid State Commun. 52, 197–201 (1984).
[Crossref]

Other (8)

R. Collin, Field Theory of Guided Waves. (New York: McGraw-Hill, 1960).

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

S. C. Jacobsen, D. L. Wells, C. C. Davis, and J. E. Wood, “Fabrication of micro-structures using nonplanar lithography (NPL),” presented at the IEEE Micro Electro Mechanical Systems Nara, Japan, 1991. http://ieeexplore.ieee.org/iel4/5306/14399/00659766.pdf?arnumber=659766
[Crossref]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett., in press (2006), arXiv:physics/0610012. http://arxiv.org/abs/physics/0610012
[Crossref] [PubMed]

Note: After submitting our manuscript to Optics Express on 09/18/2006, we found that S.A. Maier et al. proposed basically the same structure but focusing on different aspects other than those in our manuscript. We think that the excellent work proposed by S. A. Maier et al. will open up possibilities to important applications in the THz optical research, and it is very necessary to incorporate their work into our paper in order to enrich our contents and emphasize the potential applications of this metallic structure in the optical research.

The surface plasmon frequency ωsp is determined by ωsp=ωpεair+1 where ωp is the bulk plasma frequency of metal

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

H. M. Barlow and A. L. Cullen, Proc. IEE10, 329 (1953). & R. Collin, Field Theory of Guided Waves (Wiley, NewYork, ed. 2, 1990)

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Figures (5)

Fig. 1.
Fig. 1.

The metal wire milled with periodic array of subwavelength grooves

Fig. 2.
Fig. 2.

The dispersion relation ω(kz ) of the surface bound states supported by a metal wire milled with arrays of sub-wavelength grooves obtained from Eq. (8). The geometrical Parameters are d/p=0.1, b/p=2.6, a/b=1.3.

Fig. 3.
Fig. 3.

The metal wire milled with array of subwavelength grooves (a) and its equivalent dielectric coated wire (b). The geometrical parameters of the equivalent dielectric coated wire have the relations a = a n 2 1 and b = b n 2 1 . The effective refractive index n = p d is defined for the dielectric coating.

Fig. 4.
Fig. 4.

Dispersion curves of the first two surface modes (TM00 and TM01) in the first Brillouin zone. The black lines represent the surface modes of the structured metal wire; the red lines represent the modes of equivalent dielectric coated wire. The dashed lines are the light lines in vacuum and in the dielectric coating, respectively. b/p=1.7, a/b=2. (a) p/d=2.5; (b) p/d=20.

Fig. 5.
Fig. 5.

Profile view of the Hφ field distributions of the fundamental surface modes of the metellic structure [shown in (a)] and the corresponding dielectric coated wire [shown in (b)] for b/p=1.7, a/b=2,the effective refractive index of the dielectric coating is n=p/d=2.5. The fundamental surface modes in these two systems are azimuthally symmetric TM waves, the red color indicates the positive amplitude, and the blue color indicates the negative amplitude. The black lines in (a) and (b) show the interface between the guided systems and their ambient environment (vacuum). The normalized excitation frequency is ω=0.05 in units of 2 π C p . The arrows indicate the modal wavelength (the periodicity of the modal field) of the surface waves.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

H φ m ( r , z ) = [ A m ( z ) H ν ( 1 ) ( ω c r ) + B m ( z ) H ν ( 2 ) ( ω c r ) ]
for z m p d 2 b r a
H φ outside ( r , z ) = n = C n K 0 ( i τ n r ) e i β n z
for r a
H z = H r = 0
H φ = i μ k 0 ( E r z E z r )
E φ = 0
E z = i ε k 0 1 r ( r H φ ) r
E r = i ε k 0 H φ z
1 i ψ = [ J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) J 1 ( ω c a ) N 0 ( ω c b ) N 1 ( ω c a ) J 0 ( ω c b ) ]
ψ = n = f ( ω c ) · K 1 ( i τ n a ) τ n K 0 ( i τ n a ) · g n 2
J 1 ( ω c a ) N 0 ( ω c b ) N 1 ( ω c a ) J 0 ( ω c b ) J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) = 0
1 i ϕ = [ J 0 ( T a ) N 0 ( T b ) N 0 ( T a ) J 0 ( T b ) J 1 ( T a ) N 0 ( T b ) N 1 ( T a ) J 0 ( T b ) ]
ϕ = n 0 2 T K 1 ( τ a ) n 2 τ K 0 ( τ a )
J 0 ( T a ) N 0 ( T b ) N 0 ( T a ) J 0 ( T b ) = 0
J 0 ( ω c a ) N 0 ( ω c b ) N 0 ( ω c a ) J 0 ( ω c b ) = 0

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