Abstract

Precise knowledge of modal behavior is of essential importance for understanding light guidance, particularly in hollow-core fibers. Here we present a semi-analytical model that allows determination of bands formed in revolver-type anti-resonant hollow-core fibers. The approach is independent of the actual arrangement of the anti-resonant elements, does not enforce artificial lattice arrangements and allows determination of the effective indices of modes of preselected order. The simulations show two classes of modes: (i) low-order modes exhibiting effective indices with moderate slopes and (ii) a high number of high-order modes with very strong effective index dispersion, forming a quasi-continuum of modes. It is shown that the mode density scales with the square of the normalized frequency, being to some extent similar to the behavior of multimode fibers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2019 (1)

2018 (8)

L. Cao, S.-F. Gao, Z.-G. Peng, X.-C. Wang, Y.-Y. Wang, and P. Wang, “High peak power 28 μm Raman laser in a methane-filled negative-curvature fiber,” Opt. Express 26(5), 5609–5615 (2018).
[Crossref] [PubMed]

F. Yu, M. Cann, A. Brunton, W. Wadsworth, and J. Knight, “Single-mode solarization-free hollow-core fiber for ultraviolet pulse delivery,” Opt. Express 26(8), 10879–10887 (2018).
[Crossref] [PubMed]

M. Bache, M. S. Habib, C. Markos, and J. Lægsgaard, “Poor-man’s model of hollow-core anti-resonant fibers,” J. Opt. Soc. Am. B 36(1), 69–80(2018).
[Crossref]

S. Fei Gao, Y. Ying Wang, W. Ding, D. Liang Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 2828 (2018).
[Crossref]

M. Xu, F. Yu, M. R. Hassan, and J. C. Knight, “Continuous-wave mid-infrared gas fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–8 (2018).

M. I. Hasan, N. Akhmediev, and W. Chang, “Empirical formulae for dispersion and effective mode area in hollow-core antiresonant fibers,” J. Light. Technol. 36(18), 4060–4065 (2018).
[Crossref]

M. Nissen, B. Doherty, J. Hamperl, J. Kobelke, K. Weber, T. Henkel, and M. A. Schmidt, “UV absorption spectroscopy in water-filled antiresonant hollow core fibers for pharmaceutical detection,” Sensors 18(2), 478 (2018).
[Crossref]

M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

2017 (11)

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
[Crossref]

M. Zeisberger and M. A. Schmidt, “Analytic model for the complex effective index of the leaky modes of tube-type anti-resonant hollow core fibers,” Sci. Rep. 7(1), 11761 (2017).
[Crossref] [PubMed]

M. H. Frosz, P. Roth, M. C. Günendi, and P. S. Russell, “Analytical formulation for the bend loss in single-ring hollow-core photonic crystal fibers,” Photonics Res. 5(2), 88–91 (2017).
[Crossref]

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
[Crossref]

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

M. A. Popenda, N. H. Stawska, L. M. Mazur, K. Jakubowski, A. Kosolapov, A. Kolyadin, and E. Bereś-Pawlik, “Application of negative curvature hollow-core fiber in an optical fiber sensor setup for multiphoton spectroscopy,” Sensors 17(10), 2278 (2017).
[Crossref]

M. I. Hasan, N. Akhmediev, and W. Chang, “Positive and negative curvatures nested in an antiresonant hollow-core fiber,” Opt. Lett. 42(4), 703–706 (2017).
[Crossref] [PubMed]

B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gérôme, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica 4(2), 209–217 (2017).
[Crossref]

D. Bird, “Attenuation of model hollow-core, anti-resonant fibres,” Opt. Express 25(19), 23215–23237 (2017).
[Crossref] [PubMed]

M. Xu, F. Yu, and J. Knight, “Mid-infrared 1W hollow-core fiber gas laser source,” Opt. Lett. 42(20), 4055–4058 (2017).
[Crossref] [PubMed]

Y. Wang and W. Ding, “Confinement loss in hollow-core negative curvature fiber: A multi-layered model,” Opt. Express 25(26), 33122–33133 (2017).
[Crossref]

2016 (1)

2015 (3)

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(14), 3432–3435 (2015).
[Crossref] [PubMed]

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6, 6767 (2015).
[Crossref] [PubMed]

W. Belardi, “Design and properties of hollow antiresonant fibers for the visible and near infrared spectral range,” J. Light. Technol. 33(21), 4497–4503 (2015).
[Crossref]

2014 (7)

2013 (4)

2012 (2)

2011 (3)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[Crossref] [PubMed]

2006 (2)

2004 (1)

2003 (1)

2002 (1)

1991 (1)

E. Yablonovitch, T. Gmitter, and K. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67(17), 2295–2298 (1991).
[Crossref] [PubMed]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO 2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

1971 (1)

1964 (1)

E. A. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
[Crossref]

Abdolvand, A.

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
[Crossref]

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8(4), 278–286 (2014).
[Crossref]

Abeeluck, A. K.

Addison, C. J.

Ahmed, G.

Akhmediev, N.

M. I. Hasan, N. Akhmediev, and W. Chang, “Empirical formulae for dispersion and effective mode area in hollow-core antiresonant fibers,” J. Light. Technol. 36(18), 4060–4065 (2018).
[Crossref]

M. I. Hasan, N. Akhmediev, and W. Chang, “Positive and negative curvatures nested in an antiresonant hollow-core fiber,” Opt. Lett. 42(4), 703–706 (2017).
[Crossref] [PubMed]

Alharbi, M.

Amezcua-Correa, R.

Amsanpally, A.

Antonio-Lopez, J. E.

Auguste, J.-L.

Bache, M.

Banu, M.

M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

Bartelt, H.

Baz, A.

Belardi, W.

Benabid, F.

Beres-Pawlik, E.

M. A. Popenda, N. H. Stawska, L. M. Mazur, K. Jakubowski, A. Kosolapov, A. Kolyadin, and E. Bereś-Pawlik, “Application of negative curvature hollow-core fiber in an optical fiber sensor setup for multiphoton spectroscopy,” Sensors 17(10), 2278 (2017).
[Crossref]

Bierlich, J.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

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(14), 3432–3435 (2015).
[Crossref] [PubMed]

Bird, D.

Bird, D. M.

Biriukov, A. S.

Birks, T.

Birks, T. A.

Blades, M. W.

Blondy, J. M.

Blondy, J.-M.

Bolwien, C.

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
[Crossref]

Bradley, T. D.

M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
[Crossref]

Brunton, A.

Cann, M.

Cao, L.

Cao, Y.

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R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
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M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
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M. A. Popenda, N. H. Stawska, L. M. Mazur, K. Jakubowski, A. Kosolapov, A. Kolyadin, and E. Bereś-Pawlik, “Application of negative curvature hollow-core fiber in an optical fiber sensor setup for multiphoton spectroscopy,” Sensors 17(10), 2278 (2017).
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M. Nissen, B. Doherty, J. Hamperl, J. Kobelke, K. Weber, T. Henkel, and M. A. Schmidt, “UV absorption spectroscopy in water-filled antiresonant hollow core fibers for pharmaceutical detection,” Sensors 18(2), 478 (2018).
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J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
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M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO 2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
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Poletti, F.

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
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J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
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Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core Kagome hollow-core photonic crystal fiber,” Opt. Lett. 36(5), 669–671 (2011).
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Russell, P. S.

M. H. Frosz, P. Roth, M. C. Günendi, and P. S. Russell, “Analytical formulation for the bend loss in single-ring hollow-core photonic crystal fibers,” Photonics Res. 5(2), 88–91 (2017).
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Sandfort, V.

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M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
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M. Nissen, B. Doherty, J. Hamperl, J. Kobelke, K. Weber, T. Henkel, and M. A. Schmidt, “UV absorption spectroscopy in water-filled antiresonant hollow core fibers for pharmaceutical detection,” Sensors 18(2), 478 (2018).
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M. Zeisberger and M. A. Schmidt, “Analytic model for the complex effective index of the leaky modes of tube-type anti-resonant hollow core fibers,” Sci. Rep. 7(1), 11761 (2017).
[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(14), 3432–3435 (2015).
[Crossref] [PubMed]

R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014).
[Crossref] [PubMed]

N. Granzow, P. Uebel, M. A. Schmidt, A. S. Tverjanovich, L. Wondraczek, and P. S. J. Russell, “Bandgap guidance in hybrid chalcogenide-silica photonic crystal fibers,” Opt. Lett. 36(13), 2432–2434 (2011).
[Crossref] [PubMed]

Schulze, H. G.

Schülzgen, A.

Schwuchow, A.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

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(14), 3432–3435 (2015).
[Crossref] [PubMed]

Scol, F.

Semjonov, S. L.

Shephard, J. D.

Slav, R.

M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

Slavik, R.

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
[Crossref]

Sollapur, R.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Spielmann, C.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Spittel, R.

Stawska, N. H.

M. A. Popenda, N. H. Stawska, L. M. Mazur, K. Jakubowski, A. Kosolapov, A. Kolyadin, and E. Bereś-Pawlik, “Application of negative curvature hollow-core fiber in an optical fiber sensor setup for multiphoton spectroscopy,” Sensors 17(10), 2278 (2017).
[Crossref]

Trabold, B. M.

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
[Crossref]

Travers, J. C.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8(4), 278–286 (2014).
[Crossref]

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Tverjanovich, A. S.

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Wadsworth, W. J.

Wang, P.

L. Cao, S.-F. Gao, Z.-G. Peng, X.-C. Wang, Y.-Y. Wang, and P. Wang, “High peak power 28 μm Raman laser in a methane-filled negative-curvature fiber,” Opt. Express 26(5), 5609–5615 (2018).
[Crossref] [PubMed]

S. Fei Gao, Y. Ying Wang, W. Ding, D. Liang Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 2828 (2018).
[Crossref]

Wang, X.-C.

Wang, Y.

Wang, Y. Y.

Wang, Y.-Y.

Weber, K.

M. Nissen, B. Doherty, J. Hamperl, J. Kobelke, K. Weber, T. Henkel, and M. A. Schmidt, “UV absorption spectroscopy in water-filled antiresonant hollow core fibers for pharmaceutical detection,” Sensors 18(2), 478 (2018).
[Crossref]

Wenger, J.

Wheeler, N. V.

M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
[Crossref]

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core Kagome hollow-core photonic crystal fiber,” Opt. Lett. 36(5), 669–671 (2011).
[Crossref] [PubMed]

Wöllenstein, J.

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
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Wondraczek, L.

Xu, M.

M. Xu, F. Yu, M. R. Hassan, and J. C. Knight, “Continuous-wave mid-infrared gas fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–8 (2018).

M. Xu, F. Yu, and J. Knight, “Mid-infrared 1W hollow-core fiber gas laser source,” Opt. Lett. 42(20), 4055–4058 (2017).
[Crossref] [PubMed]

Yablonovitch, E.

E. Yablonovitch, T. Gmitter, and K. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67(17), 2295–2298 (1991).
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Yang, F.

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6, 6767 (2015).
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Ying Wang, Y.

S. Fei Gao, Y. Ying Wang, W. Ding, D. Liang Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 2828 (2018).
[Crossref]

Yu, F.

Zeisberger, M.

M. Zeisberger and M. A. Schmidt, “Analytic model for the complex effective index of the leaky modes of tube-type anti-resonant hollow core fibers,” Sci. Rep. 7(1), 11761 (2017).
[Crossref] [PubMed]

Zhang, X.

S. Fei Gao, Y. Ying Wang, W. Ding, D. Liang Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 2828 (2018).
[Crossref]

Zheltikov, A. M.

Zürch, M.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Appl. Opt. (2)

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M. Xu, F. Yu, M. R. Hassan, and J. C. Knight, “Continuous-wave mid-infrared gas fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–8 (2018).

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M. Banu, S. Nawazuddin, N. V. Wheeler, J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, G. T. Jasion, and R. Slav, “Lotus-shaped negative curvature hollow core fiber with 10.5 dB/km at 1550 nm wavelength,” J. Light. Technol. 36(5), 1213–1219 (2018).
[Crossref]

J. R. Hayes, S. R. Sandoghchi, T. D. Bradley, Z. Liu, R. Slavik, M. A. Gouveia, N. V. Wheeler, G. Jasion, Y. Chen, E. N. Fokoua, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Antiresonant hollow core fiber with an octave spanning bandwidth for short haul data communications,” J. Light. Technol. 35(3), 437–442 (2017).
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R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Nat. Commun. (2)

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6, 6767 (2015).
[Crossref] [PubMed]

S. Fei Gao, Y. Ying Wang, W. Ding, D. Liang Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 2828 (2018).
[Crossref]

Nat. Photon. (1)

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8(4), 278–286 (2014).
[Crossref]

Opt. Express (17)

J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, and P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11(22), 2854–2861 (2003).
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A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, “Light transmission in negative curvature hollow core fiber in extremely high material loss region,” Opt. Express 21(8), 9514–9519 (2013).
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W. Belardi and J. C. Knight, “Effect of core boundary curvature on the confinement losses of hollow antiresonant fibers,” Opt. Express 21(19), 21912–21917 (2013).
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P. Jaworski, F. Yu, R. R. Maier, W. J. Wadsworth, J. C. Knight, J. D. Shephard, and D. P. Hand, “Picosecond and nanosecond pulse delivery through a hollow-core Negative Curvature Fiber for micro-machining applications,” Opt. Express 21(19), 22742–22753 (2013).
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A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow - core microstructured optical fiber with a negative curvature of the core boundary in the spectral region >3.5 μm,” Opt. Express 19(2), 1441–1448 (2011).
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F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3–4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012).
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M. S. Habib, J. E. Antonio-Lopez, C. Markos, A. Schülzgen, and R. Amezcua-Correa, “Single-mode, low loss hollow-core anti-resonant fiber designs,” Opt. Express 27(4), 3824–3836 (2019).
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T. A. Birks, G. J. Pearce, and D. M. Bird, “Approximate band structure calculation for photonic bandgap fibres,” Opt. Express 14(20), 9483–9490 (2006).
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D. Bird, “Attenuation of model hollow-core, anti-resonant fibres,” Opt. Express 25(19), 23215–23237 (2017).
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Y. Wang and W. Ding, “Confinement loss in hollow-core negative curvature fiber: A multi-layered model,” Opt. Express 25(26), 33122–33133 (2017).
[Crossref]

L. Cao, S.-F. Gao, Z.-G. Peng, X.-C. Wang, Y.-Y. Wang, and P. Wang, “High peak power 28 μm Raman laser in a methane-filled negative-curvature fiber,” Opt. Express 26(5), 5609–5615 (2018).
[Crossref] [PubMed]

F. Yu, M. Cann, A. Brunton, W. Wadsworth, and J. Knight, “Single-mode solarization-free hollow-core fiber for ultraviolet pulse delivery,” Opt. Express 26(8), 10879–10887 (2018).
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W. Belardi and J. C. Knight, “Hollow antiresonant fibers with low bending loss,” Opt. Express 22(8), 10091–10096 (2014).
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B. Debord, M. Alharbi, L. Vincetti, A. Husakou, C. Fourcade-Dutin, C. Hoenninger, E. Mottay, F. Gérôme, and F. Benabid, “Multi-meter fiber-delivery and pulse self-compression of milli-Joule femtosecond laser and fiber-aided laser-micromachining,” Opt. Express 22(9), 10735–10746 (2014).
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R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014).
[Crossref] [PubMed]

F. Poletti, “Nested antiresonant nodeless hollow core fiber,” Opt. Express 22(20), 23807–23828 (2014).
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W. Ding and Y. Wang, “Analytic model for light guidance in single-wall hollow-core anti-resonant fibers,” Opt. Express 22(22), 27242–27256 (2014).
[Crossref] [PubMed]

Opt. Lett. (12)

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(14), 3432–3435 (2015).
[Crossref] [PubMed]

P. Uebel, M. C. Günendi, M. H. Frosz, G. Ahmed, N. N. Edavalath, J.-M. Ménard, and P. S. Russell, “Broadband robustly single-mode hollow-core PCF by resonant filtering of higher-order modes,” Opt. Lett. 41(9), 1961–1964 (2016).
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M. I. Hasan, N. Akhmediev, and W. Chang, “Positive and negative curvatures nested in an antiresonant hollow-core fiber,” Opt. Lett. 42(4), 703–706 (2017).
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M. Xu, F. Yu, and J. Knight, “Mid-infrared 1W hollow-core fiber gas laser source,” Opt. Lett. 42(20), 4055–4058 (2017).
[Crossref] [PubMed]

P. Ghenuche, S. Rammler, N. Y. Joly, M. Scharrer, M. Frosz, J. Wenger, P. S. J. Russell, and H. Rigneault, “Kagome hollow-core photonic crystal fiber probe for Raman spectroscopy,” Opt. Lett. 37(21), 4371–4373 (2012).
[Crossref] [PubMed]

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core Kagome hollow-core photonic crystal fiber,” Opt. Lett. 36(5), 669–671 (2011).
[Crossref] [PubMed]

N. Granzow, P. Uebel, M. A. Schmidt, A. S. Tverjanovich, L. Wondraczek, and P. S. J. Russell, “Bandgap guidance in hybrid chalcogenide-silica photonic crystal fibers,” Opt. Lett. 36(13), 2432–2434 (2011).
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W. Belardi and J. C. Knight, “Hollow antiresonant fibers with reduced attenuation,” Opt. Lett. 39(7), 1853–1856 (2014).
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F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29(20), 2369–2371 (2004).
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S. O. Konorov, C. J. Addison, H. G. Schulze, R. F. B. Turner, and M. W. Blades, “Hollow-core photonic crystal fiber-optic probes for Raman spectroscopy,” Opt. Lett. 31(12), 1911–1913 (2006).
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N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27(18), 1592–1594 (2002).
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F. Gérôme, R. Jamier, J.-L. Auguste, G. Humbert, and J.-M. Blondy, “Simplified hollow-core photonic crystal fiber,” Opt. Lett. 35(8), 1157–1159 (2010).
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Optica (1)

Photonics Res. (1)

M. H. Frosz, P. Roth, M. C. Günendi, and P. S. Russell, “Analytical formulation for the bend loss in single-ring hollow-core photonic crystal fibers,” Photonics Res. 5(2), 88–91 (2017).
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[Crossref] [PubMed]

Sci. Rep. (1)

M. Zeisberger and M. A. Schmidt, “Analytic model for the complex effective index of the leaky modes of tube-type anti-resonant hollow core fibers,” Sci. Rep. 7(1), 11761 (2017).
[Crossref] [PubMed]

Science (1)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[Crossref] [PubMed]

Sensors (3)

M. A. Popenda, N. H. Stawska, L. M. Mazur, K. Jakubowski, A. Kosolapov, A. Kolyadin, and E. Bereś-Pawlik, “Application of negative curvature hollow-core fiber in an optical fiber sensor setup for multiphoton spectroscopy,” Sensors 17(10), 2278 (2017).
[Crossref]

M. Nissen, B. Doherty, J. Hamperl, J. Kobelke, K. Weber, T. Henkel, and M. A. Schmidt, “UV absorption spectroscopy in water-filled antiresonant hollow core fibers for pharmaceutical detection,” Sensors 18(2), 478 (2018).
[Crossref]

V. Sandfort, B. M. Trabold, A. Abdolvand, C. Bolwien, P. S. J. Russell, J. Wöllenstein, and S. Palzer, “Monitoring the wobbe index of natural gas using fiber-enhanced Raman spectroscopy,” Sensors 17(12), 2714 (2017).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Illustration of the cross section of a single-ring anti-resonant hollow-core fiber (i.e., revolver-type hollow-core fiber). The geometric parameters shown in the sketch are explained in the main text. A typical, numerically calculated intensity distribution of the fundamental core mode is shown (red). (b) Examples of intensity distributions of the top and bottom band edge mode using our model (grey background: ARE strand). The inset shows two anti-resonant elements and the scalar field distributions of top and bottom band edge modes with the corresponding boundary condition highlighted by the two black dots.
Fig. 2
Fig. 2 Band map (colored background) showing the formed ARE-bands between the LPl1 and LPl2 resonances (parameters given in the main text). Colors refer to different radial mode orders, while selected azimuthal mode orders l are labeled at the top of the graph. The red line refers to the fundamental core mode of the revolver-type HC-ARF obtained from FE-simulations while the black dashed lines correspond to the effective indices of the lowest-order ARE modes calculated using Eq. (25) of [28]. The black markers show the positions of the radial intensity distributions investigated in Fig. 3(a)-(d).
Fig. 3
Fig. 3 Normalized intensity distribution of the top and bottom band edge of the LP02 ARE mode (a) in the center of the transmission band (V = 0.5π), (b) slightly below the first resonance (V = 0.99π) and (c) after the first resonance (V = 1.04π). (d) A typical intensity distribution of a higher azimuthal order mode (l = 20) at the point of antiresonance (V = 0.50π). All four plots refer to the positions highlighted by the black dots in Fig. 2.
Fig. 4
Fig. 4 Band map over a large frequency range calculated using our mathematical model (simulation parameters are given in the main text). Different colors correspond to different radial mode orders m of the LPlm modes. The transparency of the bands scales inversely with the azimuthal mode order l in order to improve visibility and to prevent figure cluttering. The three insets show close-ups of the band map in the vicinity of the resonance points at V/π = 1, 2 and 3 (highlighted by the black dashed rectangles in the main figure).
Fig. 5
Fig. 5 Number M of ARE-modes as function of the planar waveguide parameter for various d/t ratios (20 ≤ d/t ≤ 80 in increments of 10). The example geometry considered for the band maps is defined by d/t = 40. Circles represent the sum of all modes using Eq. (2). Lines correspond to Eq. (3) which is a fit to the data points. The inset shows the number of modes as function of V2 in order to visualize the quadratic dependence.
Fig. 6
Fig. 6 Dependence of the band maps on the inter-ARE distance s while d and t were kept constant ((a) s = 2 µm, (b) s = 5 µm, (c) s = 10 µm).
Fig. 7
Fig. 7 Comparison between solutions from the vectorial (solid blue lines) and scalar (solid orange lines) wave equation for a single ARE. The dashed grey curves correspond to the solutions of Eq. (25) from [28].

Equations (19)

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D c = 2 c b sin  π / N sin  π / N
J l + 1 ( V a / t ) Y l 1 ( V b / t ) = Y l + 1 ( V a / t ) J l 1 ( V b / t ) .
M 0.512 ( 1 + d t ) V 2 .
ψ ( r ) = A 1 J l ( Q r / t ) 0 r < a A 2 J l ( U r / t ) + B 2 Y l ( U r / t ) a r b A 3 J l ( Q r / t ) + B 3 Y l ( Q r / t ) r > b
U 2 = k 0 2 t 2 ( n g 2 n eff 2 )
Q 2 = k 0 2 t 2 ( n a 2 n eff 2 )
A 2 = π 2 α [ Q Y l ( U α ) J l + 1 ( Q α ) U Y l + 1 ( U α ) J l ( Q α ) ] A 1
B 2 = π 2 α [ Q J l ( U α ) J l + 1 ( Q α ) U J l + 1 ( U α ) J l ( Q α ) ] A 1
A 3 = π 2 β [ Q J l ( U β ) Y l + 1 ( Q β ) U J l + 1 ( U β ) Y l ( Q β ) ] A 2 π 2 β [ Q Y l ( U β ) Y l + 1 ( Q β ) U Y l + 1 ( U β ) Y l ( Q β ) ] B 2
B 3 = π 2 β [ Q J l ( U β ) J l + 1 ( Q β ) U J l + 1 ( U β ) J l ( Q β ) ] A 2 + π 2 β [ Q Y l ( U β ) J l + 1 ( Q β ) U Y l + 1 ( U β ) J l ( Q β ) ] B 2
g top = { A 3 [ J l 1 ( Q γ ) J l + 1 ( Q γ ) ] + B 3 [ Y l 1 ( Q γ ) Y l + 1 ( Q γ ) ] } / Q l 1 = 0
g bot = [ A 3 J l ( Q γ ) + B 3 Y l ( Q γ ) ] / Q l = 0
ψ ( r ) = A 1 I l ( W r / t ) 0 r < a A 2 J l ( U r / t ) + B 2 Y l ( U r / t ) a r b A 3 I l ( W r / t ) + B 3 K l ( W r / t ) r > b
A 2 = π 2 α [ W Y l ( U α ) I l + 1 ( W α ) + U Y l + 1 ( U α ) I l ( Q α ) ] A 1
B 2 = π 2 α [ W J l ( U α ) I l + 1 ( W α ) + U J l + 1 ( U α ) I l ( W α ) ] A 1
A 3 = β [ W J l ( U β ) K l + 1 ( W β ) U J l + 1 ( U β ) K l ( W β ) ] A 2 + β [ W Y l ( U β ) K l + 1 ( W β ) U Y l + 1 ( U β ) K l ( W β ) ] B 2
B 3 = β [ W J l ( U β ) I l + 1 ( W β ) + U J l + 1 ( U β ) I l ( W β ) ] A 2 + β [ W Y l ( U β ) I l + 1 ( W β ) + U Y l + 1 ( U β ) I l ( W β ) ] B 2
g top = A 3 { [ I l 1 ( W γ ) + I l + 1 ( W γ ) ] + B 3 [ K l 1 ( W γ ) + K l + 1 ( W γ ) ] } / W l 1 = 0
g bot = [ A 3 J l ( Q γ ) + B 3 Y l ( Q γ ) ] / W l = 0

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