Abstract

We discuss the conditions in which guided modes exist in a circular waveguide with an anisotropic, uniaxial metamaterial cladding. These hollow-core waveguides can guide modes at deep subwavelength dimensions, with core diameters more than 20 times smaller than the operating wavelength.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  7. K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
    [CrossRef]
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  9. Z. Y. Xiao and Z. H. Wang, “Dispersion characteristics of asymmetric double-negative material slab waveguides,” J. Opt. Soc. Am. B 23, 1757–1760 (2006).
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  10. J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).
  33. P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  41. J. Dong, “Guided and surface modes in chiral nihility fiber,” Opt. Commun. 283, 532–536 (2010).
    [CrossRef]
  42. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).
  43. M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
    [CrossRef]
  44. K. Y. Kim, “Comparative analysis of guided modal properties of double-positive and double-negative metamaterial slab waveguides,” Radioengineering 18, 117–123 (2009).
  45. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
    [CrossRef]
  46. S. Atakaramians, S. Afshar V., B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
    [CrossRef]
  47. S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
    [CrossRef]
  48. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. 1, 58–106 (2009).
    [CrossRef]
  49. C. H. Lai, Y. C. Hsueh, H. W. Chen, Y. J. Huang, H. C. Chang, and C. K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34, 3457–3459 (2009).
    [CrossRef]

2012 (1)

2011 (2)

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19, 16480–16490 (2011).
[CrossRef]

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

2010 (3)

J. Dong, “Guided and surface modes in chiral nihility fiber,” Opt. Commun. 283, 532–536 (2010).
[CrossRef]

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[CrossRef]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

2009 (7)

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

L. F. Shen and Z. H. Wang, “Guided modes in fiber with left-handed materials,” J. Opt. Soc. Am. A 26, 754–759 (2009).
[CrossRef]

M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
[CrossRef]

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

K. Y. Kim, “Comparative analysis of guided modal properties of double-positive and double-negative metamaterial slab waveguides,” Radioengineering 18, 117–123 (2009).

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. 1, 58–106 (2009).
[CrossRef]

C. H. Lai, Y. C. Hsueh, H. W. Chen, Y. J. Huang, H. C. Chang, and C. K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34, 3457–3459 (2009).
[CrossRef]

2008 (2)

S. Atakaramians, S. Afshar V., B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
[CrossRef]

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

2007 (2)

K. Y. Kim, “Fundamental guided electromagnetic dispersion characteristics in lossless dispersive metamaterial clad circular air-hole waveguides,” J. Opt. A 9, 1062–1069 (2007).
[CrossRef]

L. F. Shen and S. Xu, “Guided modes characteristics in a fiber with left-handed material,” Microw. Opt. Technol. Lett. 49, 1039–1041 (2007).
[CrossRef]

2006 (4)

A. V. Novitsky, “Negative-refractive-index fibres: TEM modes,” J. Opt. A 8, 864–866 (2006).
[CrossRef]

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wireless Compon. Lett. 16, 96–98 (2006).
[CrossRef]

Z. Y. Xiao and Z. H. Wang, “Dispersion characteristics of asymmetric double-negative material slab waveguides,” J. Opt. Soc. Am. B 23, 1757–1760 (2006).
[CrossRef]

2005 (8)

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

M. M. B. Suwailiam and Z. Chen, “Surface waves on a grounded double-negative (DNG) slab waveguide,” Microw. Opt. Technol. Lett. 44, 494–498 (2005).
[CrossRef]

G. DAguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Y. He, Z. Cao, and Q. Shen, “Guided optical modes in asymmetric left-handed waveguides,” Opt. Commun. 245, 125–135 (2005).
[CrossRef]

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microw. Opt. Technol. Lett. 44, 31–35 (2005).
[CrossRef]

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A 7, S51–S56 (2005).
[CrossRef]

K. Y. Kim, J. H. Lee, Y. K. Cho, and H-S. Tae, “Electromagnetic wave propagation through doubly dispersive subwavelength metamaterial hole,” Opt. Express 13, 3653–3665 (2005).
[CrossRef]

M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
[CrossRef]

2004 (3)

Y. Xu, “A study of waveguides filled with anisotropic metamaterials,” Microw. Opt. Technol. Lett. 41, 426–431 (2004).
[CrossRef]

R. Ruppin, “Surface polaritons and extinction properties of a left-handed material cylinder,” J. Phys. Condens. Matter 16, 5991–5998 (2004).
[CrossRef]

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

2003 (7)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

H. Cory and A. Barger, “Surface-wave propagation along a metamaterial slab,” Microw. Opt. Technol. Lett. 38, 392–395 (2003).
[CrossRef]

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

A. C. Peacock and N. G. R. Broderick, “Guided modes in channel waveguides with a negative index of refraction,” Opt. Express 11, 2502–2510 (2003).
[CrossRef]

L. Hu and Z. Lin, “Imaging properties of uniaxially anisotropic negative refractive index materials,” Phys. Lett. A 313, 316–324 (2003).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

2001 (1)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter 13, 1811–1818 (2001).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

1983 (1)

1976 (1)

J. R. Cozens, “Propagation in cylindrical fibres with anisotropic crystal cores,” Electron. Lett. 12, 413–415 (1976).
[CrossRef]

1961 (1)

Abbott, D.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

S. Atakaramians, S. Afshar V., B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
[CrossRef]

Afshar V., S.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

S. Atakaramians, S. Afshar V., B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
[CrossRef]

Anthony, J.

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

Argyros, A.

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Atakaramians, S.

Awai, I.

M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
[CrossRef]

Baccarelli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Bang, O.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

Barger, A.

H. Cory and A. Barger, “Surface-wave propagation along a metamaterial slab,” Microw. Opt. Technol. Lett. 38, 392–395 (2003).
[CrossRef]

Barkovsky, L. M.

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A 7, S51–S56 (2005).
[CrossRef]

Bartal, G.

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

Belov, P. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Bendavid, A.

Bloemer, M. J.

G. DAguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Blum, T.

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microw. Opt. Technol. Lett. 44, 31–35 (2005).
[CrossRef]

Broderick, N. G. R.

Broll, M.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Burghignoli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Cao, Z.

Y. He, Z. Cao, and Q. Shen, “Guided optical modes in asymmetric left-handed waveguides,” Opt. Commun. 245, 125–135 (2005).
[CrossRef]

Chang, H. C.

Chen, H. W.

Chen, Z.

M. M. B. Suwailiam and Z. Chen, “Surface waves on a grounded double-negative (DNG) slab waveguide,” Microw. Opt. Technol. Lett. 44, 494–498 (2005).
[CrossRef]

Cho, Y. K.

Constable, E.

Cory, H.

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microw. Opt. Technol. Lett. 44, 31–35 (2005).
[CrossRef]

H. Cory and A. Barger, “Surface-wave propagation along a metamaterial slab,” Microw. Opt. Technol. Lett. 38, 392–395 (2003).
[CrossRef]

Cozens, J. R.

J. R. Cozens, “Propagation in cylindrical fibres with anisotropic crystal cores,” Electron. Lett. 12, 413–415 (1976).
[CrossRef]

DAguanno, G.

G. DAguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Demetriadou, A.

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

Dong, J.

J. Dong, “Guided and surface modes in chiral nihility fiber,” Opt. Commun. 283, 532–536 (2010).
[CrossRef]

Feit, M. D.

Fischer, B. M.

Fleck, J. A.

Fleming, S. C.

Forester, D. W.

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Frezza, F.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Galli, A.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Gattass, R. R.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Genov, D. A.

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

Grzegorczyk, T. M.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

Hano, M.

M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
[CrossRef]

He, J.

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wireless Compon. Lett. 16, 96–98 (2006).
[CrossRef]

He, S.

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wireless Compon. Lett. 16, 96–98 (2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

He, Y.

Y. He, Z. Cao, and Q. Shen, “Guided optical modes in asymmetric left-handed waveguides,” Opt. Commun. 245, 125–135 (2005).
[CrossRef]

Heitmann, D.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Hermann, C.

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

Hess, O.

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

Heyn, C.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Hotta, M.

M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
[CrossRef]

Hsueh, Y. C.

Hu, J.

Hu, L.

L. Hu and Z. Lin, “Imaging properties of uniaxially anisotropic negative refractive index materials,” Phys. Lett. A 313, 316–324 (2003).
[CrossRef]

Huang, Y. J.

Ishikawa, A.

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

Jamois, C.

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

Kim, K. Y.

K. Y. Kim, “Comparative analysis of guided modal properties of double-positive and double-negative metamaterial slab waveguides,” Radioengineering 18, 117–123 (2009).

K. Y. Kim, “Fundamental guided electromagnetic dispersion characteristics in lossless dispersive metamaterial clad circular air-hole waveguides,” J. Opt. A 9, 1062–1069 (2007).
[CrossRef]

K. Y. Kim, J. H. Lee, Y. K. Cho, and H-S. Tae, “Electromagnetic wave propagation through doubly dispersive subwavelength metamaterial hole,” Opt. Express 13, 3653–3665 (2005).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Klaedtke, A.

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

Kong, J. A.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).

Krohn, A.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Kuhlmey, B. T.

Lai, C. H.

Lampariello, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Large, M. C. J.

Lee, J. H.

Leonhardt, R.

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

Lewis, R. A.

Lin, Z.

L. Hu and Z. Lin, “Imaging properties of uniaxially anisotropic negative refractive index materials,” Phys. Lett. A 313, 316–324 (2003).
[CrossRef]

Liu, Z.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[CrossRef]

Loschilpo, P. F.

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Lou, J.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Lovat, G.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

Lwin, R.

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19, 16480–16490 (2011).
[CrossRef]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

Marques, R.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Maslovski, S. I.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Mattiucci, N.

G. DAguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Mazur, E.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Medgyesi-Mitschang, L. N.

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Mei, Y.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[CrossRef]

Mendach, S.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Menyuk, C. R.

Min, S. S.

Monro, T. M.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

S. Atakaramians, S. Afshar V., B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16, 8845–8854 (2008).
[CrossRef]

Monzon, C.

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Mortensen, N. A.

Nagel, M.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

Nefedov, I. S.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Novitsky, A. V.

A. V. Novitsky, “Negative-refractive-index fibres: TEM modes,” J. Opt. A 8, 864–866 (2006).
[CrossRef]

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A 7, S51–S56 (2005).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Paulotto, S.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

Peacock, A. C.

Pendry, J. B.

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Pogson, E. M.

Pope, B.

Rasmussen, H. K.

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Ruppin, R.

R. Ruppin, “Surface polaritons and extinction properties of a left-handed material cylinder,” J. Phys. Condens. Matter 16, 5991–5998 (2004).
[CrossRef]

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter 13, 1811–1818 (2001).
[CrossRef]

Scalora, M.

G. DAguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Schelleng, J.

J. Schelleng, C. Monzon, P. F. Loschilpo, D. W. Forester, and L. N. Medgyesi-Mitschang, “Characteristics of waves guided by a grounded left-handed material slab of finite extent,” Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Schmidt, O. G.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Schwaiger, S.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shen, L. F.

L. F. Shen and Z. H. Wang, “Guided modes in fiber with left-handed materials,” J. Opt. Soc. Am. A 26, 754–759 (2009).
[CrossRef]

L. F. Shen and S. Xu, “Guided modes characteristics in a fiber with left-handed material,” Microw. Opt. Technol. Lett. 49, 1039–1041 (2007).
[CrossRef]

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Shen, Q.

Y. He, Z. Cao, and Q. Shen, “Guided optical modes in asymmetric left-handed waveguides,” Opt. Commun. 245, 125–135 (2005).
[CrossRef]

Silveirinha, M.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Simovski, C. R.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Smith, E. J.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[CrossRef]

Snitzer, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

Stark, Y.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Stemmann, A.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Stickler, D.

S. Schwaiger, M. Broll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Sun, C. K.

Suwailiam, M. M. B.

M. M. B. Suwailiam and Z. Chen, “Surface waves on a grounded double-negative (DNG) slab waveguide,” Microw. Opt. Technol. Lett. 44, 494–498 (2005).
[CrossRef]

Tae, H-S.

Tong, L.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Tsakmakidid, K. L.

K. L. Tsakmakidid, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73, 085104 (2006).
[CrossRef]

Tuniz, A.

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Wang, A.

A. Tuniz, B. Pope, A. Wang, M. C. J. Large, S. Atakaramians, S. S. Min, E. M. Pogson, R. A. Lewis, A. Bendavid, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Spatial dispersion in three-dimensional drawn magnetic metamaterials,” Opt. Express 20, 11924–11935 (2012).
[CrossRef]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

Wang, Z. H.

Wu, B. I.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

Xiao, Z. Y.

Xu, S.

L. F. Shen and S. Xu, “Guided modes characteristics in a fiber with left-handed material,” Microw. Opt. Technol. Lett. 49, 1039–1041 (2007).
[CrossRef]

Xu, Y.

Y. Xu, “A study of waveguides filled with anisotropic metamaterials,” Microw. Opt. Technol. Lett. 41, 426–431 (2004).
[CrossRef]

Yan, M.

Zhang, S.

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

Zhang, X.

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

Zhang, Y.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (2)

S. Atakaramians, S. Afshar V., M. Nagel, H. K. Rasmussen, O. Bang, T. M. Monro, and D. Abbott, “Direct probing of evanescent field for characterization of porous terahertz fibers,” Appl. Phys. Lett. 98, 121104 (2011).
[CrossRef]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010).
[CrossRef]

Electron. Lett. (1)

J. R. Cozens, “Propagation in cylindrical fibres with anisotropic crystal cores,” Electron. Lett. 12, 413–415 (1976).
[CrossRef]

IEEE Microw. Wireless Compon. Lett. (1)

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wireless Compon. Lett. 16, 96–98 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, “Fundamental modal properties of surface waves on metamaterial grounded slabs,” IEEE Trans. Microw. Theory Tech. 53, 1431–1442 (2005).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084(1999).

IEICE Trans. Electron. (1)

M. Hotta, M. Hano, and I. Awai, “Surface waves along a boundary of single negative material,” IEICE Trans. Electron. E88-C, 275–278 (2005).
[CrossRef]

J. Appl. Phys. (1)

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,” J. Appl. Phys. 93, 9386–9388 (2003).
[CrossRef]

J. Opt. A (3)

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A 7, S51–S56 (2005).
[CrossRef]

A. V. Novitsky, “Negative-refractive-index fibres: TEM modes,” J. Opt. A 8, 864–866 (2006).
[CrossRef]

K. Y. Kim, “Fundamental guided electromagnetic dispersion characteristics in lossless dispersive metamaterial clad circular air-hole waveguides,” J. Opt. A 9, 1062–1069 (2007).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

J. Phys. Condens. Matter (4)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter 13, 1811–1818 (2001).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

MTM-cladding waveguide structure: (a) hollow-core circular waveguide with an infinite uniaxial MTM cladding; (b) schematic cross section of one possible implementation for a hollow-core circular waveguide assembled using split-ring resonators fabricated by drawing techniques [29].

Fig. 2.
Fig. 2.

Schematic of the type (CW and/or SPP) of hybrid modes (m>0) guided in a hollow-core uniaxial MTM-clad waveguide (a) β2<k02μrϵr and (b) β2>k02μrϵr. The horizontal axis is the square of the normalized propagation constant (β¯2), and the shaded region represents the radiation mode region. Note that the conditions for TM and TE are relaxed—no condition on μrμz and ϵrϵz for TM and TE modes, respectively.

Fig. 3.
Fig. 3.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr>0, ϵz<0, μr>0, and μz<0 (first row of the Table 1). Note that all the vertical axes use a linear scale, except part (h), which uses a log scale.

Fig. 4.
Fig. 4.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr<0, ϵz>0, μr<0, and μz>0 (second row of the Table 1). Note that all the vertical axes use a linear scale, except part (h), which uses a log scale.

Fig. 5.
Fig. 5.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr>0, ϵz>0, μr>0, and μz>0 (third row of the Table 1).

Fig. 6.
Fig. 6.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr>0, ϵz>0, μr<0, and μz<0 (fourth row of Table 1). Note that the vertical axes of parts (a), (b), (e), and (f) use a log scale, and parts (c), (d), (g), and (h) use a linear scale.

Fig. 7.
Fig. 7.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr<0, ϵz<0, μr>0, and μz>0 (fifth row of the Table 1). Note that the vertical axes of parts (a), (c), (e), and (g) use a log scale, and parts (b), (d), (f), and (h) use a linear scale.

Fig. 8.
Fig. 8.

Normalized propagation constant of a uniaxial MTM-clad hollow circular waveguide as a function of normalized diameter when ϵr<0, ϵz<0, μr<0, and μz<0 (sixth row of the Table 1).

Tables (1)

Tables Icon

Table 1. Existence Condition for Hybrid Modes (m>0) of a Hollow-Core Uniaxial MTM-Clad Waveguidea

Equations (52)

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μ¯¯2=μ0(μr000μϕ=μr000μz),
ϵ¯¯2=ϵ0(ϵr000ϵϕ=ϵr000ϵz),
·E⃗=(1ϵzϵr)Ezz,
·H⃗=(1μzμr)Hzz.
E⃗=E⃗(r,ϕ)ei(βzωt),
H⃗=H⃗(r,ϕ)ei(βzωt),
2Ezr2+1rEzr+1r22Ezϕ2β2ϵzϵrEz+ω2μ0μrϵ0ϵzEz=0,
2Hzr2+1rHzr+1r22Hzϕ2β2μzμrHz+ω2ϵ0ϵrμ0μzHz=0.
2Ezr2+1rEzr+1r22Ezϕ2+{(k02β2)Ez=0ra(k02μrϵzϵzϵrβ2)Ez=0r>a,
2Hzr2+1rHzr+1r22Hzϕ2+{(k02β2)Hz=0ra(k02μzϵrμzμrβ2)Hz=0r>a.
Er=ik02μrϵrβ2[βEzr+ωμrrHzϕ],
Eϕ=ik02μrϵrβ2[βrEzϕωμrHzr],
Hr=ik02μrϵrβ2[βHzrωϵrrEzϕ],
Hϕ=ik02μrϵrβ2[βrHzϕ+ωϵrEzr].
Ez={AXm(κ1r)cos(mϕ+ψ)raAXm(κ1a)Km(κ2Ea)Km(κ2Er)cos(mϕ+ψ)r>a,
Hz={CXm(κ1r)sin(mϕ+ψ)raCXm(κ1a)Km(κ2Ha)Km(κ2Hr)sin(mϕ+ψ)r>a,
κ12={k02β2β<k0,i.e., CW guided modesβ2k02β>k0,i.e., SPP guided modes,
κ2E2=ϵzϵrβ2k02μrϵz,
κ2H2=μzμrβ2k02μzϵr.
[μ0κ1k02β2Xm(κ1a)Xm(κ1a)μ0μrκ2Hk02μrϵrβ2Km(κ2Ha)Km(κ2Ha)][ϵ0κ1k02β2Xm(κ1a)Xm(κ1a)ϵ0ϵrκ2Ek02μrϵrβ2Km(κ2Ea)Km(κ2Ea)]=(mβaω)2(1k02μrϵrβ21k02β2)2.
[ϵ0κ1k02β2X0(κ1a)X0(κ1a)ϵ0ϵrκ2Ek02μrϵrβ2K0(κ2Ea)K0(κ2Ea)]=0TM mode,
[μ0κ1k02β2X0(κ1a)X0(κ1a)μ0μrκ2Hk02μrϵrβ2K0(κ2Ha)K0(κ2Ha)]=0TE mode.
ϵz(β2ϵrk02μr)>0,
μz(β2μrk02ϵr)>0.
β2<k02μrϵr{ϵr>0,ϵz<0for TM modesμr>0,μz<0for TE modes,
β2>k02μrϵr{ϵr<0,ϵz<0for TM modesμr<0,μz<0for TE modes.
P12(μrQH+ϵrQE)=±(G2+14(μrQHϵrQE)2)1/2,
P=κ1k02β2{Jm(κ1a)Jm(κ1a)for CW modesIm(κ1a)Im(κ1a)for SPP modes,
QH=κ2Hk02μrϵrβ2Km(κ2Ha)Km(κ2Ha),
QE=κ2Ek02μrϵrβ2Km(κ2Ea)Km(κ2Ea),
G=1μ0ϵ0(mβaω)2(1k02μrϵrβ21k02β2)2.
|μz|aκ2HKm(aκ2H)Km(aκ2H)|ϵz|aκ2EKm(aκ2E)Km(aκ2E)=0.
lima0κ1a=lima0(β2k02)1/2a=πγ,
lima0κ2Ea=lima0(ϵzϵrβ2k02μrϵz)1/2a=πγϵzϵr,
lima0κ2Ha=lima0(μzμrβ2k02μzϵr)1/2a=πγμzμr.
limUIm(U)Im(U)=1,
limUKm(U)Km(U)=1,
β¯2(1ϵrϵz)>ϵr(μrϵz)SHE0modes,
β¯2(1μrμz)>μr(ϵrμz)SEH0modes.
1>ϵrϵzSHE0modes,
1>μrμzSEH0modes.
1>ϵrϵz>0SHE0modes,
1>μrμz>0SEH0modes.
β¯TM2ϵr(μrϵz)(1ϵrϵz)(SHE0),
β¯TE2μr(ϵrμz)(1μrμz)(SEH0).
β¯TM2ϵ2(μ2ϵ2)(1ϵ22)(SHE0),
β¯TE2μ2(ϵ2μ2)(1μ22)(SEH0),
κ12=k02,
κ2E2=k02μrϵz,
κ2H2=k02μzϵr.
Jm(k0a)Jm(k0a)μrϵzμrKm(k0aμrϵz)Km(k0aμrϵz)=0,
Jm(k0a)Jm(k0a)μzϵrϵrKm(k0aμzϵr)Km(k0aμzϵr)=0.

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