Abstract

Understanding bend loss in single-ring hollow-core photonic crystal fibers (PCFs) is becoming of increasing importance as the fibers enter practical applications. While purely numerical approaches are useful, there is a need for a simpler analytical formalism that provides physical insight and can be directly used in the design of PCFs with low bend loss. We show theoretically and experimentally that a wavelength-dependent critical bend radius exists below which the bend loss reaches a maximum, and that this can be calculated from the structural parameters of a fiber using a simple analytical formula. This allows straightforward design of single-ring PCFs that are bend-insensitive for specified ranges of bend radius and wavelength. It also can be used to derive an expression for the bend radius that yields optimal higher-order mode suppression for a given fiber structure.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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  13. C. L. Wei, C. R. Menyuk, and J. Hu, “Bending-induced mode non-degeneracy and coupling in chalcogenide negative curvature fibers,” Opt. Express 24, 2228–2239 (2016).
  14. S.-F. Gao, Y.-Y. Wang, X.-L. Liu, W. Ding, and P. Wang, “Bending loss characterization in nodeless hollow-core anti-resonant fiber,” Opt. Express 24, 14801–14811 (2016).
    [Crossref]
  15. M. Michieletto, J. K. Lyngsø, C. Jakobsen, J. Lægsgaard, O. Bang, and T. T. Alkeskjold, “Hollow-core fibers for high power pulse delivery,” Opt. Express 24, 7103–7119 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (5)

2015 (1)

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

2014 (1)

2013 (2)

2012 (1)

2011 (2)

2007 (2)

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” IEEE Photon. Technol. Lett. 19, 1257–1259 (2007).
[Crossref]

2006 (1)

2005 (1)

2002 (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref]

1997 (1)

1993 (1)

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11, 416–423 (1993).
[Crossref]

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[Crossref]

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. 43, 1783–1809 (1964).
[Crossref]

Ahmed, G.

Alagashev, G. K.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

Alkeskjold, T. T.

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref]

Archambault, J. L.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11, 416–423 (1993).
[Crossref]

Argyros, A.

Babic, F.

Bang, O.

Belardi, W.

Benabid, F.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87–124 (2011).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref]

Biriukov, A. S.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

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, 1441–1448 (2011).
[Crossref]

Birks, T. A.

Black, R. J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11, 416–423 (1993).
[Crossref]

Bradley, T. D.

Bures, J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11, 416–423 (1993).
[Crossref]

Burger, S.

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

Chen, Y.

Couny, F.

Dianov, E. M.

Ding, W.

Durniak, C.

J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” IEEE Photon. Technol. Lett. 19, 1257–1259 (2007).
[Crossref]

Edavalath, N. N.

Farr, L.

Fokoua, E. N.

Frosz, M. H.

Gao, S.-F.

Gray, D. R.

Gunendi, M. C.

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[Crossref]

Hayes, J. R.

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[Crossref]

Hu, J.

C. L. Wei, C. R. Menyuk, and J. Hu, “Bending-induced mode non-degeneracy and coupling in chalcogenide negative curvature fibers,” Opt. Express 24, 2228–2239 (2016).

Jakobsen, C.

Jasion, G. T.

Klose, R.

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

Knight, J. C.

Kolyadin, A. N.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

Kosolapov, A. F.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

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, 1441–1448 (2011).
[Crossref]

Lacroix, S.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11, 416–423 (1993).
[Crossref]

Lægsgaard, J.

Liu, X.-L.

Liu, Z. X.

Love, J. D.

J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” IEEE Photon. Technol. Lett. 19, 1257–1259 (2007).
[Crossref]

A. W. Snyder and J. D. Love, Optical Waveguide Theory, Science Paperbacks (Chapman and Hall, 1983), p. 734.

Lukovkin, A. Y.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

Lyngsø, J. K.

Mangan, B. J.

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. 43, 1783–1809 (1964).
[Crossref]

Mason, M. W.

Menard, J. M.

Menyuk, C. R.

C. L. Wei, C. R. Menyuk, and J. Hu, “Bending-induced mode non-degeneracy and coupling in chalcogenide negative curvature fibers,” Opt. Express 24, 2228–2239 (2016).

Michieletto, M.

Nold, J.

Petrovich, M. N.

Plotnichenko, V. G.

Poletti, F.

Pomplun, J.

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

Pryamikov, A. D.

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

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, 1441–1448 (2011).
[Crossref]

Rammler, S.

Richardson, D. J.

Roberts, P. J.

Russell, P. St.J.

Sabert, H.

Sandoghchi, S. R.

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. 43, 1783–1809 (1964).
[Crossref]

Schmidt, F.

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

Semjonov, S. L.

Setti, V.

Slavik, R.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, Science Paperbacks (Chapman and Hall, 1983), p. 734.

Stefani, A.

Tomlinson, A.

Uebel, P.

Vincetti, L.

Wadsworth, W. J.

Wang, P.

Wang, Y.-Y.

Wei, C. L.

C. L. Wei, C. R. Menyuk, and J. Hu, “Bending-induced mode non-degeneracy and coupling in chalcogenide negative curvature fibers,” Opt. Express 24, 2228–2239 (2016).

Weiss, T.

Wheeler, N. V.

Williams, D. P.

Yu, F.

Zschiedrich, L.

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[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. 43, 1783–1809 (1964).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” IEEE Photon. Technol. Lett. 19, 1257–1259 (2007).
[Crossref]

J. Lightwave Technol. (3)

J. Mod. Opt. (1)

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87–124 (2011).
[Crossref]

Laser Phys. (1)

G. K. Alagashev, A. D. Pryamikov, A. F. Kosolapov, A. N. Kolyadin, A. Y. Lukovkin, and A. S. Biriukov, “Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers,” Laser Phys. 25, 055101 (2015).

Opt. Express (8)

C. L. Wei, C. R. Menyuk, and J. Hu, “Bending-induced mode non-degeneracy and coupling in chalcogenide negative curvature fibers,” Opt. Express 24, 2228–2239 (2016).

S.-F. Gao, Y.-Y. Wang, X.-L. Liu, W. Ding, and P. Wang, “Bending loss characterization in nodeless hollow-core anti-resonant fiber,” Opt. Express 24, 14801–14811 (2016).
[Crossref]

M. Michieletto, J. K. Lyngsø, C. Jakobsen, J. Lægsgaard, O. Bang, and T. T. Alkeskjold, “Hollow-core fibers for high power pulse delivery,” Opt. Express 24, 7103–7119 (2016).
[Crossref]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005).
[Crossref]

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, 1441–1448 (2011).
[Crossref]

F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4  μm spectral region,” Opt. Express 20, 11153–11158 (2012).
[Crossref]

W. Belardi and J. C. Knight, “Hollow antiresonant fibers with low bending loss,” Opt. Express 22, 10091–10096 (2014).
[Crossref]

V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express 21, 3388–3399 (2013).
[Crossref]

Opt. Lett. (3)

Phys. Status Solidi A (1)

J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses in photonic crystal fibers,” Phys. Status Solidi A 204, 3822–3837 (2007).
[Crossref]

Science (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref]

Other (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory, Science Paperbacks (Chapman and Hall, 1983), p. 734.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Sketch of the geometry of a single-ring HC-PCF, showing the local coordinate system. The inner diameter of the six capillaries is d, and the core diameter (the minimum distance between two diametrically opposite capillaries) is D. (b) Index difference Δn0101 between LP01-like core and capillary modes, plotted against R/D for d/D=0.696 at four different values of λ/D.

Fig. 2.
Fig. 2.

Numerically calculated axial Poynting vector distributions and loss α of a single-ring PCF with d=55  μm, D=79  μm, λ=2.8  μm and capillary wall thickness t=1.15  μm, for (a) bend radius slightly greater than Rcr01=17.2  cm, (b) close to Rcr01, and (c) and (d) close to the radius of curvature that phase-matches the LP01 core mode to capillaries placed at θ=±60°. The arrows indicate the polarization of the electric field.

Fig. 3.
Fig. 3.

Numerically calculated bend loss for the fibers for θ=0°, plotted against normalized bend radius R/D. A:(d,D,λ)=(55,79,2.8)  μm, i.e., d/D=0.70 and λ/D=0.035. B:(d,D,λ)=(22,36,1.2)  μm, i.e., d/D=0.61, λ/D=0.033. The dashed vertical lines mark the corresponding analytical solutions for the critical bend radius using Eq. (4) with θ=0°. The dotted vertical line shows the bend radius for phase-matching to the capillaries at θ=±60°. In each case the loss is calculated for modes polarized normal to the bend, i.e., in the y direction in Fig. 1(a).

Fig. 4.
Fig. 4.

Experimentally measured bend loss in two fibers with the same shape parameters as in Fig. (3). (a) d/D=0.70 and (b) d/D=0.61. The bend radii were changed in steps of 1.25 cm, and between these steps the colors are interpolated. The measured loss versus wavelength in (b) was smoothed with a moving average filter. The gray rectangle in (a) marks the region where the core mode phase-matches to a resonance in the walls of the capillaries, causing high attenuation. In each case, the white solid and dashed lines are solutions of Eq. (4) for θ=0° and θ=30°, respectively.

Equations (5)

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

npq=1(upqπλdi)2,
(x,y)=(1+yR)n¯(x,y),
Δn01pq=1(upqπλD)21(u01πλd)2(1+d+D2Rcosθ).
Rcr01D=D2λ2·π2u012(d/D)21d/Dcosθ,
Rcr11D=D2λ2·π2(1+d/D)(u01D/d)2u112cosθ.

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