Abstract

Infrared (IR) light is considered important for short-range wireless communication, thermal sensing, spectroscopy, material processing, medical surgery, astronomy etc. However, IR light is in general much harder to transport than optical light or microwave radiation. Existing hollow-core IR waveguides usually use a layer of metallic coating on the inner wall of the waveguide. Such a metallic layer, though reflective, still absorbs guided light significantly due to its finite Ohmic loss, especially for transverse-magnetic (TM) light. In this paper, we show that metal-wire based metamaterials may serve as an efficient TM reflector, reducing propagation loss of the TM mode by two orders of magnitude. By further imposing a conventional metal cladding layer, which reflects specifically transverse-electric (TE) light, we can potentially obtain a low-loss hollow-core fiber. Simulations confirm that loss values for several low-order modes are comparable to the best results reported so far.

© 2009 Optical Society of America

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References

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  1. J. A. Harrington, "A review of IR transmitting, hollow waveguides," Fiber Integr. Opt. 19, 211-217 (2000).
    [CrossRef]
  2. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
    [CrossRef] [PubMed]
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  4. B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
    [CrossRef]
  5. B. T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials," Appl. Phys. Lett. 85, 1 (2004).
    [CrossRef]
  6. E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, "Combined surface plasmon and classical waveguiding through metamaterial fiber design," Nano Lett., DOI:10.1021/nl900550j (2009).
    [PubMed]
  7. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
    [CrossRef]
  8. Y. Liu, G. Bartal, and X. Zhang, "All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region," Opt. Express 16, 15439-15448 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-20-15439.
    [CrossRef] [PubMed]
  9. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  10. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
    [CrossRef] [PubMed]
  11. D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef] [PubMed]
  12. E. Hecht, Optics, 4th ed. (Addison Wesley, San Francisco, 2002).
  13. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).
  14. M. Yan and P. Shum, "Analysis of perturbed Bragg fibers with an extended transfer matrix method," Opt. Express , 2596-2610 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-7-2596.
    [CrossRef] [PubMed]
  15. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
    [CrossRef]
  16. E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 34, 1783-1809 (1964).
  17. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-9-13-748.
    [CrossRef] [PubMed]

2009 (1)

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, "Combined surface plasmon and classical waveguiding through metamaterial fiber design," Nano Lett., DOI:10.1021/nl900550j (2009).
[PubMed]

2008 (2)

B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

2006 (1)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

2004 (1)

B. T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials," Appl. Phys. Lett. 85, 1 (2004).
[CrossRef]

2003 (1)

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef] [PubMed]

2002 (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

J. A. Harrington, "A review of IR transmitting, hollow waveguides," Fiber Integr. Opt. 19, 211-217 (2000).
[CrossRef]

1999 (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 34, 1783-1809 (1964).

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Bowden, B.

B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Elser, J.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Fink, Y.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Harrington, J. A.

B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
[CrossRef]

J. A. Harrington, "A review of IR transmitting, hollow waveguides," Fiber Integr. Opt. 19, 211-217 (2000).
[CrossRef]

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Joannopoulos, J. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

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., DOI:10.1021/nl900550j (2009).
[PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 34, 1783-1809 (1964).

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., DOI:10.1021/nl900550j (2009).
[PubMed]

Mitrofanov, O.

B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
[CrossRef]

Narimanov, E. E.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Piestun, R.

B. T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials," Appl. Phys. Lett. 85, 1 (2004).
[CrossRef]

Podolskiy, V. A.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Russell, P. S. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 34, 1783-1809 (1964).

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., DOI:10.1021/nl900550j (2009).
[PubMed]

Schurig, D.

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef] [PubMed]

Schwartz, B. T.

B. T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials," Appl. Phys. Lett. 85, 1 (2004).
[CrossRef]

Smith, D. R.

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef] [PubMed]

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., DOI:10.1021/nl900550j (2009).
[PubMed]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Wangberg, R.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

B. Bowden, J. A. Harrington, and O. Mitrofanov, "Low-loss modes in hollow metallic terahertz waveguides with dielectric coatings," Appl. Phys. Lett. 93, 181104 (2008).
[CrossRef]

B. T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials," Appl. Phys. Lett. 85, 1 (2004).
[CrossRef]

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, "Nanowire metamaterials with extreme optical anisotropy," Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 34, 1783-1809 (1964).

Fiber Integr. Opt. (1)

J. A. Harrington, "A review of IR transmitting, hollow waveguides," Fiber Integr. Opt. 19, 211-217 (2000).
[CrossRef]

Nano Lett. (1)

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, "Combined surface plasmon and classical waveguiding through metamaterial fiber design," Nano Lett., DOI:10.1021/nl900550j (2009).
[PubMed]

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Opt. Comm. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Comm. 179, 1-7 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Science (2)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, "Optical negative refraction in bulk metamaterials of nanowires," Science 321, 930 (2008).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other (5)

Y. Liu, G. Bartal, and X. Zhang, "All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region," Opt. Express 16, 15439-15448 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-20-15439.
[CrossRef] [PubMed]

E. Hecht, Optics, 4th ed. (Addison Wesley, San Francisco, 2002).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

M. Yan and P. Shum, "Analysis of perturbed Bragg fibers with an extended transfer matrix method," Opt. Express , 2596-2610 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-7-2596.
[CrossRef] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-9-13-748.
[CrossRef] [PubMed]

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Figures (9)

Fig. 1.
Fig. 1.

(a) Metal-wire medium as a TM reflector in planar geometry. (b) kx ~kz relations for TM light in both air (red curve) and an indefinite medium with εx =2,µy =1,εz =-10 (black curves), together with wavevectors illustrating reflection for TM light incidence. Axis unit: rad/m. λ=1µm.

Fig. 2.
Fig. 2.

Reflectance of TM-polarized incident light from two types of substrates, one silver and the other an indefinite medium derived from silver-wire-in-dielectric composite (inset). The wavelength is 10.6µm. (a) Reflectance spectrum for 0~90 degrees; (b) Zoom-in plot for 87~90 degrees.

Fig. 3.
Fig. 3.

Reflectance of TE-polarized incident light from two types of substrates, one plain silver and the other silver but with an indefinite medium layer on top (inset). The wavelength is 10.6µm.

Fig. 4.
Fig. 4.

Schematic diagrams for the proposed metal-wire metamaterial fiber structures. (a) A hollow-core fiber with a metal-wire based metamaterial cladding. Thin white lines in the inset indicate unit cells forming the metamaterial. (b) A hybrid-clad fiber: A hollow-core fiber with a thin layer of metamaterial as its inner cladding, and a bulk metal as its outer cladding. Dark grey regions are metal. Light grey region denotes dielectric material.

Fig. 5.
Fig. 5.

(a) Propagation loss, and (b) effective mode index of the TM01 mode as a function of metal filling fraction. The values for the mode when cladding is made of full metal are marked as ⋆.

Fig. 6.
Fig. 6.

Cross-sectional field distribution of the guided TM01 mode in a metamaterial-clad fiber with a 700µm core diameter. (a) Overall mode; (b) The zoom-in plot of the region outlined in (a) by the gray line (15×15µm2). Color shading is for the real part of the axial Poynting vector, while arrows are for transverse electric field. λ=10.6µm, Λ=2µm, fm =0.2.

Fig. 7.
Fig. 7.

Propagation losses of both TM01 and TE01 modes as a function of metal filling fraction. λ=10.6µm, Λ=2µm. The propagation loss values for the TM01 and TE01 modes at the fm =1 limit are marked as ⋆ and ✯, respectively.

Fig. 8.
Fig. 8.

Loss values for TE01 and TM01 modes guided by hybrid-clad fiber as a function of core diameter. The same curves for the full-metal fiber are also shown. λ=10.6µm, Λ=2µm, fm =0.2. The inner cladding has one layer of metal wires.

Fig. 9.
Fig. 9.

Propagation loss for the TM01 mode as a function of coating thickness, for a HMF with dielectric inner coating and a hybrid-clad fiber incorporating metamaterial.

Equations (15)

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εt=εd+fmεd(εmεd)εd+0.5fd(εmεd)
εz=fmεm+fdεd,
εx>0,μy>0 , εz<0 . (requirement1)
kz2εx+kx2εz=k02μy,
εxμy>1 , (requirement2)
εx>1,μy=1 , εz<0 .
εzεt(k02μtεtβ2)<0 .
μzμt(k02εtμtβ2)<0 .
εt>1,μt=1 , εz<0 .
ε̿=(εr000εθ000εz),μ̿=(μr000μθ000μz).
2Hzr2+1r22Hzθ2+1rHzr+μzμtkt2Hz=0 ,
2Ψr2+1rψr+1r2(μzμtkt2r2m2)ψ=0 .
μzμt(k02εtμtβ2)<0
ψ=𝓐 Im (k˜tr) +𝓑 Km (k˜tr) ,
εzεt(k02μtεtβ2)<0 .

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