Abstract

We present a comprehensive study of the effect of material dispersion on the guided modes of a circular waveguide with an anisotropic, uniaxial metamaterial cladding, including in particular claddings with dispersive hyperbolic or indefinite material properties, both magnetic and electric. We show that the transverse components of material parameters have dominating effects compared to that of the longitudinal material components. We derive the condition for the existence of frequencies at which propagation constants diverge and study the modes’ behavior around such points. In particular we show these modes can be strongly confined in an air core with significantly subwavelength dimensions.

© 2013 Optical Society of America

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  1. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  2. J. Schelleng, C. Monzon, P. F. Loschialpo, 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]
  3. 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]
  4. 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]
  5. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter 13, 1811–1819 (2001).
    [CrossRef]
  6. H. Cory and A. Barger, “Surface-wave propagation along a metamaterial slab,” Microw. Opt. Technol. Lett. 38, 392–395 (2003).
    [CrossRef]
  7. 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]
  8. L. Hu and Z. Lin, “Imaging properties of uniaxially anisotropic negative refractive index materials,” Phys. Lett. A 313, 316–324 (2003).
    [CrossRef]
  9. Y. Xu, “A study of waveguides filled with anisotropic metamaterials,” Microw. Opt. Technol. Lett. 41, 426–431 (2004).
    [CrossRef]
  10. R. Ruppin, “Surface polaritons and extinction properties of a left-handed material cylinder,” J. Phys. Condens. Matter 16, 5991–5998 (2004).
    [CrossRef]
  11. H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microw. Opt. Technol. Lett. 44, 31–35 (2005).
    [CrossRef]
  12. A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A 7, S51–S56 (2005).
    [CrossRef]
  13. A. V. Novitsky, “Negative-refractive-index fibres: TEM modes,” J. Opt. A 8, 864–866 (2006).
    [CrossRef]
  14. 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]
  15. 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]
  16. 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]
  17. M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
    [CrossRef]
  18. 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]
  19. 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]
  20. S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial metamaterial cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29, 2462–2477 (2012).
    [CrossRef]
  21. 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]
  22. 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]
  23. 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]
  24. 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).
    [CrossRef]
  25. S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2011).
    [CrossRef]
  26. C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
    [CrossRef]
  27. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).
  28. J. Dong and J. Li, “Guided modes in the chiral negative refractive index fiber,” Chin. Opt. Lett. 8, 1032–1036 (2010).
    [CrossRef]
  29. N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mater. Express 2, 1254–1259 (2012).
    [CrossRef]

2012

2011

S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2011).
[CrossRef]

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[CrossRef]

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]

2010

J. Dong and J. Li, “Guided modes in the chiral negative refractive index fiber,” Chin. Opt. Lett. 8, 1032–1036 (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

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]

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]

2007

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

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

2005

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]

2004

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. Loschialpo, 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

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]

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

2001

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys. Condens. Matter 13, 1811–1819 (2001).
[CrossRef]

2000

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

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).
[CrossRef]

1998

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]

Abrahams, J.

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[CrossRef]

Anlage, S. M.

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[CrossRef]

S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2011).
[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.

Atakaramians, S.

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]

Bennett, C. L.

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[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]

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]

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]

Dong, J.

Fleming, S. C.

Forester, D. W.

J. Schelleng, C. Monzon, P. F. Loschialpo, 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]

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]

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]

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).
[CrossRef]

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]

Hu, L.

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

Kim, K. Y.

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]

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]

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.

Kurter, C.

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[CrossRef]

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.

Li, J.

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]

Loschialpo, P. F.

J. Schelleng, C. Monzon, P. F. Loschialpo, 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]

Love, J. D.

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

Lwin, R.

Medgyesi-Mitschang, L. N.

J. Schelleng, C. Monzon, P. F. Loschialpo, 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]

Monzon, C.

J. Schelleng, C. Monzon, P. F. Loschialpo, 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.

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]

Pendry, J. B.

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).
[CrossRef]

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.

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).
[CrossRef]

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, 1811–1819 (2001).
[CrossRef]

Schelleng, J.

J. Schelleng, C. Monzon, P. F. Loschialpo, 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]

Singh, N.

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]

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).
[CrossRef]

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]

Tae, H.-S.

Tuniz, A.

Ustinov, A. V.

C. Kurter, A. P. Zhuravel, J. Abrahams, C. L. Bennett, A. V. Ustinov, and S. M. Anlage, “Superconducting RF metamaterials made with magnetically active planar spirals,” IEEE Trans. Appl. Supercond. 21, 709–712 (2011).
[CrossRef]

Vier, D. C.

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Figures (17)

Fig. 1.
Fig. 1.

Dispersive relative permittivity (ϵ) and permeability (μ) functions. E1 and EP represent points where ϵ is negative unity and zero, respectively, while M1 and MP represent points where μ is negative unity and zero, respectively. These dispersion equations represent ϵz and μz in Section 3 and ϵr and μr in Section 4.

Fig. 2.
Fig. 2.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1 and (d) m=2, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 3.
Fig. 3.

SEH1 mode of a uniaxial anisotropic MTM-clad hollow-core CW as a function of diameter and frequency with material parameters μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f).

Fig. 4.
Fig. 4.

Normalized field and power distributions of a hollow-core CW with material parameters μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f). Normalized field distribution of (a) TE01 mode and (b) SEH0 mode for d=30mm. The transverse magnetic field is shown with white arrows over the normalized z component of magnetic field. The circular dashed line represents the core–clad interface. (c) Normalized Poynting vector versus radial distance for the modes in (a) (dashed curve) and in (b) (solid curve). The vertical dotted line represent the core–clad interface.

Fig. 5.
Fig. 5.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) SEH0 mode for several core diameters and (b) SEHm modes for an air-core diameter 10 mm. The material properties of the MTM clad are μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f).

Fig. 6.
Fig. 6.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE modes, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters. (b) TM modes, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 7.
Fig. 7.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1 and (d) m=2, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 8.
Fig. 8.

Normalized field and power distributions of a hollow-core CW with material parameters μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f). Normalized field distribution of (a) TM01 mode and (b), (c) SHE0 mode for d=20mm. The transverse electric field is shown with white arrows over the normalized z component of electric field. The circular dashed line represents the core–clad interface. (d) Normalized Poynting vector versus radial distance for the modes shown in (a)–(c) are shown with dashed, dotted, and solid curves, respectively. The vertical dotted line represents the core–clad interface.

Fig. 9.
Fig. 9.

Dispersion curves of TM modes of a uniaxial anisotropic MTM-clad hollow-core CW, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 10.
Fig. 10.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE and (b) TM modes, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 11.
Fig. 11.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1 and (d) m=2, with the material properties μr=1, μz=μ(f) and ϵr=2.25, ϵz=ϵ(f), for several core diameters.

Fig. 12.
Fig. 12.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1, and (d) m=2, with the material properties μz=1, μr=μ(f), and ϵz=2.25, ϵr=ϵ(f), for several core diameters. The insets are the enlargement of the curves to show the bifurcation point.

Fig. 13.
Fig. 13.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1, and (d) m=2, with the material properties μz=1, μr=μ(f), and ϵz=2.25, ϵr=ϵ(f), for several core diameters.

Fig. 14.
Fig. 14.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1, and (d) m=2, with the material properties μz=1, μr=μ(f), and ϵz=2.25, ϵr=ϵ(f), for several core diameters.

Fig. 15.
Fig. 15.

Normalized field and power distributions of a hollow-core CW with material parameters μz=1, μr=μ(f) and ϵz=2.25, ϵr=ϵ(f). Normalized (a), (c) electric and (b), (d) magnetic field distributions of the SHE1 for a 5 mm diameter air core. The transverse electric/magnetic fields are shown with white arrows over the normalized z component of electric/magnetic field. The circular dashed line represents the core–clad interface. (e) Normalized Poynting vector versus radial distance for β¯=3.096 and β¯=20.45 are shown with dashed and solid curves, respectively. The vertical dotted line represent the core–clad interface.

Fig. 16.
Fig. 16.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1, and (d) m=2, with the material properties μz=1, μr=μ(f), and ϵz=2.25, ϵr=ϵ(f), for several core diameters.

Fig. 17.
Fig. 17.

Dispersion curves of modes of a uniaxial anisotropic MTM-clad hollow-core CW: (a) TE, (b) TM, and hybrid modes with the azimuthal eigenvalues (c) m=1, and (d) m=2, with the material properties μz=1, μr=μ(f), and ϵz=2.25, ϵr=ϵ(f), for several core diameters.

Tables (1)

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Table 1. Summary of Mode Observation in a Hollow-Core Uniaxial MTM-Clad Waveguidea

Equations (6)

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ϵ(f)=1(fEP/f)2,
μ(f)=1Ff2/(f2fM02),
νg=cβ¯+fβ¯f,
β¯2(1ϵrεz)>ϵr(μrϵz)forSHE0,
β¯2(1μrμz)>μr(ϵzμz)forSEH0.
ηc=PcorePtotal=Pcore|Pcore|+|Pclad|=0a02πSzrdrdϕ|0a02πSzrdrdϕ|+|a02πSzrdrdϕ|,

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