Abstract

We present a mathematical model that allows interpreting the dispersion and attenuation of modes in hollow-core fibers (HCFs) on the basis of single interface reflection, giving rise to analytic and semi-analytic expressions for the complex effective indices in the case where the core diameter is large and the guiding is based on the reflection by a thin layer. Our model includes two core-size independent reflection parameters and shows the universal inverse-cubed core diameter dependence of the modal attenuation of HCFs. It substantially reduces simulation complexity and enables large scale parameter sweeps, which we demonstrate on the example of a HCF with a highly anisotropic metallic nanowire cladding, resembling an indefinite metamaterial at high metal filling fractions. We reveal design rules that allow engineering modal discrimination and show that metamaterial HCFs can principally have low losses at mid-IR wavelengths (< 1 dB/m at 10.6 µm). Our model can be applied to a great variety of HCFs with large core diameters and can be used for advanced HCF design and performance optimization, in particular with regard to dispersion engineering and modal discrimination.

© 2016 Optical Society of America

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2016 (1)

2015 (2)

A. Hartung, J. Kobelke, A. Schwuchow, J. Bierlich, J. Popp, M. A. Schmidt, and T. Frosch, “Low-loss single-mode guidance in large-core antiresonant hollow-core fibers,” Opt. Lett. 40, 3432–3435 (2015).
[Crossref] [PubMed]

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

2014 (4)

2013 (3)

2012 (4)

2011 (1)

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

2009 (2)

2006 (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

2005 (1)

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

2003 (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

2002 (2)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

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]

2001 (1)

2000 (2)

M. A. Kaliteevskii, V. V. Nikolaev, and R. A. Abram, “Calculation of the mode structure of multilayer optical fibers based on transfer matrices for cylindrical waves,” Opt. Spectrosc. 88, 792–795 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

1998 (2)

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

1996 (1)

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

1978 (1)

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” At&T Tech J 43, 1783 (1964).

Abdolvand, A.

P. S. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow -core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8, 278–286 (2014).
[Crossref]

Abram, R. A.

M. A. Kaliteevskii, V. V. Nikolaev, and R. A. Abram, “Calculation of the mode structure of multilayer optical fibers based on transfer matrices for cylindrical waves,” Opt. Spectrosc. 88, 792–795 (2000).
[Crossref]

Adikan, F. R. M.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

Adler, F.

Ahmad, R. U.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Anastassiou, C.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Argyros, A.

Atakaramians, S.

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]

Bierlich, J.

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Chang, W.

Cossel, K. C.

Coulombier, Q.

Devaiah, A. K.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Djurisic, A. B.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Ebendorff-Heidepriem, H.

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Elazar, J. M.

Engeness, T. D.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Fabian, H.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

Fermann, M. E.

Finger, M. A.

Fink, Y.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

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]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Fleming, S. C.

Frosch, T.

Frosz, M.

Gang, S. Y.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

Ghenuche, P.

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Granzow, N.

Grzesik, U.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

Haken, U.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[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]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

Hartl, I.

Hartung, A.

Hasan, D. N.

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

Hasan, M. M.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

Heitmann, W.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

Holzer, P.

P. S. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow -core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8, 278–286 (2014).
[Crossref]

Humbach, O.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

Ibanescu, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Gruyter, 2006).

Jacobs, S. A.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

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]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Joly, N. Y.

Kaliteevskii, M. A.

M. A. Kaliteevskii, V. V. Nikolaev, and R. A. Abram, “Calculation of the mode structure of multilayer optical fibers based on transfer matrices for cylindrical waves,” Opt. Spectrosc. 88, 792–795 (2000).
[Crossref]

Knight, J. C.

F. Yu and J. C. Knight, “Spectral attenuation limits of silica hollow core negative curvature fiber,” Opt. Express 21, 21466–21471 (2013).
[Crossref] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Kobelke, J.

Kolodny, U.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Koufman, J. A.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Kuhlmey, B. T.

Kumar, D. S.

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

Lee, H. W.

Lee, K. F.

Leindecker, N.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Love, J. D.

J. A. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Magnus, W.

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, 1966).
[Crossref]

Mahdiraji, G. A.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

Mahdy, M. R. C.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

Majewski, M. L.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” At&T Tech J 43, 1783 (1964).

Marom, E.

Maskaly, G. R.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

Matin, M. A.

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

Monro, T. M.

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

Mortensen, N. A.

Nikolaev, V. V.

M. A. Kaliteevskii, V. V. Nikolaev, and R. A. Abram, “Calculation of the mode structure of multilayer optical fibers based on transfer matrices for cylindrical waves,” Opt. Spectrosc. 88, 792–795 (2000).
[Crossref]

Oberhettinger, F.

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, 1966).
[Crossref]

Okoshi, T.

T. Okoshi, Optical Fibers (Academic, 1982).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

Popp, J.

Prideaux, P. H.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Rakic, A. D.

Rammler, S.

Rigneault, H.

Russell, P. S.

P. S. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow -core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8, 278–286 (2014).
[Crossref]

P. Ghenuche, S. Rammler, N. Y. Joly, M. Scharrer, M. Frosz, J. Wenger, P. S. Russell, and H. Rigneault, “Kagome hollow-core photonic crystal fiber probe for Raman spectroscopy,” Opt. Lett. 37, 4371–4373 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

Russell, P. S. J.

Scharrer, M.

P. Ghenuche, S. Rammler, N. Y. Joly, M. Scharrer, M. Frosz, J. Wenger, P. S. Russell, and H. Rigneault, “Kagome hollow-core photonic crystal fiber probe for Raman spectroscopy,” Opt. Lett. 37, 4371–4373 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” At&T Tech J 43, 1783 (1964).

Schmidt, M. A.

A. Tuniz, M. Zeisberger, and M. A. Schmidt, “Tailored loss discrimination in indefinite metamaterial-clad hollow-core fibers,” Opt. Express 24, 15702–15709 (2016)
[Crossref] [PubMed]

A. Hartung, J. Kobelke, A. Schwuchow, J. Bierlich, J. Popp, M. A. Schmidt, and T. Frosch, “Low-loss single-mode guidance in large-core antiresonant hollow-core fibers,” Opt. Lett. 40, 3432–3435 (2015).
[Crossref] [PubMed]

K. F. Lee, N. Granzow, M. A. Schmidt, W. Chang, L. Wang, Q. Coulombier, J. Troles, N. Leindecker, K. L. Vodopyanov, P. G. Schunemann, M. E. Fermann, P. S. J. Russell, and I. Hartl, “Midinfrared frequency combs from coherent supercontinuum in chalcogenide and optical parametric oscillation,” Opt. Lett. 39, 2056–2059 (2014).
[Crossref] [PubMed]

A. Hartung, J. Kobelke, A. Schwuchow, K. Wondraczek, J. Bierlich, J. Popp, T. Frosch, and M. A. Schmidt, “Double antiresonant hollow core fiber-guidance in the deep ultraviolet by modified tunneling leaky modes,” Opt. Express 22, 19131–19140 (2014).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, and P. S. J. Russell, “Excitation of a nanowire molecule in gold-filled photonic crystal fiber,” Opt. Lett. 37, 2946 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express 20, 28409–28417 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

Schunemann, P. G.

Schwuchow, A.

Shakibaei, B. H.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

Shapira, G.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Shapshay, S. M.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Shawon, M. J.

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

Shurgalin, M.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Skorobogatiy, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Snyder, J. A.

J. A. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Soljacic, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Soni, R. P.

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, 1966).
[Crossref]

Temelkuran, B.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

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]

Thorpe, M. J.

Torres, D.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Travers, J. C.

P. S. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow -core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8, 278–286 (2014).
[Crossref]

Troles, J.

Tuniz, A.

Uebel, P.

P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express 20, 28409–28417 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

Upadhyay, U. D.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Vodopyanov, K. L.

Wang, L.

Wang, T.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Wang, Z.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Weisberg, O.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001).
[Crossref] [PubMed]

Weiss, T.

Wenger, J.

Wondraczek, K.

Yan, M.

Yariv, A.

Ye, J.

Yeh, P.

Yu, F.

Zeisberger, M.

Ann. Rev. Mater. Res. (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

Appl. Opt. (1)

At&T Tech J (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” At&T Tech J 43, 1783 (1964).

IEEE Photonic Tech. L. (1)

M. M. Hasan, D. S. Kumar, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Robust optical fiber using single negative metamaterial cladding,” IEEE Photonic Tech. L. 25, 1043–1046 (2013).
[Crossref]

IEEE Photonics J. (1)

M. J. Shawon, G. A. Mahdiraji, M. M. Hasan, B. H. Shakibaei, S. Y. Gang, M. R. C. Mahdy, and F. R. M. Adikan, “Single negative metamaterial-based hollow-core bandgap fiber with multilayer cladding,” IEEE Photonics J. 7, 4600812 (2015).
[Crossref]

J. Non-Cryst. Solids (1)

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

P. S. Russell, P. Holzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow -core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8, 278–286 (2014).
[Crossref]

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]

New J. Phys. (1)

P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13063016 (2011).
[Crossref]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Opt. Express (6)

Opt. Lett. (6)

Opt. Spectrosc. (1)

M. A. Kaliteevskii, V. V. Nikolaev, and R. A. Abram, “Calculation of the mode structure of multilayer optical fibers based on transfer matrices for cylindrical waves,” Opt. Spectrosc. 88, 792–795 (2000).
[Crossref]

P. Soc. Photo-Opt Ins. (1)

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” P. Soc. Photo-Opt Ins. 5686, 310–321 (2005).

Phys. Rev. E (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608 (2003).
[Crossref]

Science (2)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[Crossref] [PubMed]

Other (5)

J. A. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

T. Okoshi, Optical Fibers (Academic, 1982).

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, 1966).
[Crossref]

J. D. Jackson, Classical Electrodynamics (Gruyter, 2006).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

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Figures (7)

Fig. 1
Fig. 1 Physical background of the single-interface reflection model for approximating the complex effective index dispersion of large core hollow-core fibers. (a) Schematic of hollow core fiber highlighting the microstructured cladding. (b) Reflection at the corresponding interface assuming gracing incidence.
Fig. 2
Fig. 2 (a) Schematic of the indefinite metamaterial hollow-core fiber analyzed by using the reflection model. (b) Details of the core-cladding boundary with the corresponding definitions of the relevant parameters.
Fig. 3
Fig. 3 Sketch of the unit cell and the associated boundaries used for the finite element simulations to obtain the reflection parameters. The blue and green arrows indicate the incident and the reflected light. The purple lines indicate the locations of the boundary conditions (PEC and PMC) that are used to define the two polarization states.
Fig. 4
Fig. 4 Comparison of the dependence of the relative complex effective indices on air core radius of the TE01, TM01, and HE11 modes calculated by our reflection model (lines) and full numerical simulations (symbols) at two wavelengths ((a): 3 µm, (b): 10.6 µm). The solid lines refer to the real parts of 1 − neff, the dashed lines to the imaginary parts of neff.
Fig. 5
Fig. 5 Comparison of the imaginary parts of the effective indices as function of the circumferential filling factor f for the TE01, TM01, and HE11 modes calculated by our reflection model (lines) and full numerical simulations (symbols) at two wavelengths ((a): 3 µm, (b): 10.6 µm). The arrows on the top of both plots indicate the different guidance regimes (cap.: capillary, diff.: diffraction, and indefinite metamaterial).
Fig. 6
Fig. 6 Reflection parameters νTE (a) and νTM (b) as function of the circumferential fill factor f and gap g at a wavelength of 3 µm. The scale bars (in logarithmic scale) on the top of the plots refer to the value of the individual reflection parameter. The different gray highlighted regions indicate the mode with the lowest loss for this particular combination of g and f.
Fig. 7
Fig. 7 Reflection parameters νTE (a) and νTM (b) as function of the circumferential fill factor f and gap g at a wavelength of 10.6 µm. The scale bars (in logarithmic scale) on the top of the plots refer to the value of the individual reflection parameter. The different gray highlighted regions indicate the mode with the lowest loss for this particular combination of g and f.

Tables (3)

Tables Icon

Table 1 Conditions for the critical discrimination parameter for the three lowest order HCF modes.

Tables Icon

Table 2 Numerical values of jmn (n-th zeros of the Bessel function Jm).

Tables Icon

Table 3 Numerical values of the coefficients in the equations for the effective index.

Equations (39)

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

E = E ( r ) e i ( β z + m ϕ ω t ) ,
H = H ( r ) e i ( β z + m ϕ ω t ) ,
E z = A 1 J m ( κ r ) ,
H z = A 2 J m ( κ r ) ,
E ϕ = β m κ 2 r A 1 J m ( κ r ) i Z 0 k 0 κ A 2 J m ( κ r ) ,
H ϕ = i k 0 Z 0 κ A 1 J m ( κ r ) β m κ 2 r A 2 J m ( κ r ) .
r T E = 1 + ν T E ψ ,
r T M = 1 + ν T M ψ .
H z E y = 2 Z 0 ν T E ,
E z H y = 2 Z 0 ν T M .
J 0 ( κ 0 R ) = J 1 ( κ 0 R ) = 0 ,
κ 0 = j 1 n R , J 1 ( j 1 n ) = 0 , n = 1 , 2 ,
ν T E J 0 ( κ R ) + 2 i k 0 κ J 0 ( κ R ) = 0 .
ν T E J 0 ( κ 0 R ) + 2 i k 0 κ 0 J 0 ( κ 0 R ) κ 1 R = 0 ,
κ 1 = i j 1 n ν T E 2 k 0 R 2 .
n e f f = 1 κ 0 2 2 κ 0 2 κ 0 κ 1 κ 0 2 ,
n e f f = 1 a n ( λ R ) 2 + i b n ν T E ( λ R ) 3 ,
a n = j 1 n 2 8 π 2 , b n = j 1 n 2 16 π 3 .
n e f f = 1 a n ( λ R ) 2 + i b n ν T M ( λ R ) 3 .
| β m κ 2 r J m ( κ r ) i Z 0 k 0 κ J m ( κ r ) i k 0 Z 0 κ J m ( κ r ) β m κ 2 r J m ( κ r ) | = 0
m 2 κ 0 2 R 2 J m ( κ 0 R ) 2 J m ( κ 0 R ) 2 = 0 .
J m 1 ( κ 0 R ) J m + 1 ( κ 0 R ) = 0 ,
κ 0 = j m + s , n R , J m + s ( j m + s , n ) = 0 , s = ± 1 , n = 1 , 2 ,
Δ = | 2 β m κ 2 R J m ( κ R ) ( Z 0 ν T E J m ( κ R ) + 2 i Z 0 k 0 κ J m ( κ R ) ) ( ν T M J m ( κ R ) + 2 i k 0 κ J m ( κ R ) ) 2 Z 0 β m κ 2 R J m ( κ R ) | = 0 .
κ 1 = i j m + s , n 4 k 0 R 2 ( ν T E + ν T M ) .
n e f f = 1 a m n s ( λ R ) 2 + i b m n s ( ν T E + ν T M ) ( λ R ) 3 ,
a m n s = j m + s , n 2 8 π 2 , b m n s = j m + s , n 2 32 π 3 .
H z = 1 i ω μ 0 E y x .
E y ( 0 , z ) = E ( i ) ( 1 + r T E ) e i β z ,
H z ( 0 , z ) = E ( i ) κ ω μ 0 ( 1 r T E ) e i β z .
H z E y = κ ω μ 0 1 r T E 1 + r T E .
r T E = E ( r ) E ( i ) = 1 + 2 ϵ 1 ψ .
H y ( 0 , z ) = H ( i ) ( 1 + r T M ) e i β z ,
r T M = H ( r ) H ( i ) = 1 + ν T M ψ ,
r T M = 1 + 2 ϵ ϵ 1 ψ .
J m ( x ) = s J m + s ( x ) + s m x J m ( x ) , s = ± 1 .
J m ( x ) = m 2 s m x 2 x 2 J m ( x ) + s x J m + s ( x ) .
J m ( j m + s , n ) = s m j m + s , n J m ( j m + s , n ) ,
J m ( j m + s , n ) = m 2 s m j m + s , n 2 j m + s , n 2 J m ( j m + s , n ) .

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