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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28609–28616
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Hypocycloid-shaped hollow-core photonic crystal fiber Part II: Cladding effect on confinement and bend loss

M. Alharbi, T. Bradley, B. Debord, C. Fourcade-Dutin, D. Ghosh, L. Vincetti, F. Gérôme, and F. Benabid  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28609-28616 (2013)
http://dx.doi.org/10.1364/OE.21.028609


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Abstract

We report on numerical and experimental studies on the influence of cladding ring-number on the confinement and bend loss in hypocycloid-shaped Kagome hollow core photonic crystal fiber. The results show that beyond the second ring, the ring number has a minor effect on confinement loss whereas the bend loss is strongly reduced with the ring-number increase. Finally, the results show that the increase in the cladding ring-number improves the modal content of the fiber.

© 2013 Optical Society of America

1. Introduction

Conversely, such a low attenuation-level with a hypocycloid-shaped core has been predicted and demonstrated to be achieved even with a single ring [12

12. A. V. V. Nampoothiri, A. M. Jones, C. Fourcade-Dutin, C. Mao, N. Dadashzadeh, B. Baumgart, Y. Y. Wang, M. Alharbi, T. Bradley, N. Campbell, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, “Hollow-core Optical Fiber Gas Lasers (HOFGLAS): a review [Invited],” Opt. Mater. Express 2(7), 948–961 (2012). [CrossRef]

15

15. L. Vincetti, “Numerical analysis of plastic hollow core microstructured fiber for Terahertz applications,” Opt. Fiber Technol. 15(4), 398–401 (2009). [CrossRef]

]. For example a 30-40 dB/km loss figure in the IR and Mid-IR domains was achieved in fibers with both 3-ring cladding [16

16. Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid, “Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and pulse compression,” Opt. Lett. 37(15), 3111–3113 (2012). [CrossRef] [PubMed]

] and in a single ring cladding fibers [12

12. A. V. V. Nampoothiri, A. M. Jones, C. Fourcade-Dutin, C. Mao, N. Dadashzadeh, B. Baumgart, Y. Y. Wang, M. Alharbi, T. Bradley, N. Campbell, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, “Hollow-core Optical Fiber Gas Lasers (HOFGLAS): a review [Invited],” Opt. Mater. Express 2(7), 948–961 (2012). [CrossRef]

,17

17. 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). [CrossRef] [PubMed]

]. However, the role of the cladding in light confinement is not fully understood. This is also illustrated in the prior numerical simulations that considered the cladding contribution to light confinement in circular or hexagonal core-shape Kagome HC-PCF, and which led to differences in conclusions [2

2. 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]

,6

6. 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]

,18

18. G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St J Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express 15(20), 12680–12685 (2007). [CrossRef] [PubMed]

,19

19. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010). [CrossRef] [PubMed]

]. For example in [19

19. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010). [CrossRef] [PubMed]

], the authors claim that the cladding has an adverse effect on light confinement, whilst in [2

2. 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]

,6

6. 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]

] the authors show that adding a cladding with three rings shows lower loss than a single anti-resonant ring hollow-fiber. The combination of the lack of a clear understanding in the cladding role in such fibers on one hand and of the recent ultra-low transmission loss reported in IC guiding HC-PCF with hypocycloid core-contour, which put this class of HC-PCF as an excellent waveguide candidate in spectral ranges where the PBG guiding HC-PCF failed to perform, call for a comprehensive investigation on how the cladding affects the optical performance of IC guiding HC-PCF.

2. Transmission loss evolution with cladding ring number

3. Bend loss and modal content evolution with cladding ring number

A further characterization of these different cladding ring-number fibers is made by measuring the macro bending behavior.
Fig. 2 Bending loss spectrum measured for four hypocycloid-core Kagome HC-PCF (with one, two, three and four cladding rings) at different bending radii (a) 5 cm, (b) 4 cm, (c) 3 cm and (d) 2 cm.
Figure 2 shows the bend-loss spectra for different bend radii (5 cm, 4 cm, 3 cm and 2 cm) measured with the four fiber designs. The bend was carried out by coiling the fiber four turns for each measurement run.

For a bend radius of 5 cm, the loss spectra in 1500nm-1750nm spectral range are comparable for the fibers with cladding ring number up to 3, all exhibiting a bend loss figure of ~2 dB/m. However, as the wavelength gets shorter towards the high-frequency transmission edge of the fundamental band, the loss in the single-ring fiber increases at a much higher rate than the rest of the fibers, indicating that the cladding layers act as a barrier to bend-induced mode-coupling between the core modes and radiation modes. This corroborated with the 4-ring fiber which bend loss figure reaches ~0.1 dB/m level in 1500nm-1750nm spectral range. Furthermore, for radii shorter than 5 cm, the spectra clearly show that the bending loss decreases with the cladding ring number. For example in the case with a bend radius of 3 cm, the spectra show that fibers with more than two layers exhibit a bend loss which is lower than the single ring design by more than one order of magnitude.
Fig. 3 (a) Zoom-in of measured bending loss evolution at the particular wavelength 1500 nm. (b) Critical radius versus number of cladding rings at 1310 nm and 1500 nm.
Figure 3(a) shows the evolution of the bend loss at a representative wavelength from the center of the transmission band (chosen to be 1500 nm) with the bend radius. The results show that when the fibers are bent with a bend radius of 5 cm, the bend loss is as low as 0.1 dB/m for a 4-ring HC-PCF, whilst it is ~50 dB/m for a single-ring fiber. Figure 3(b) shows the evolution of the deduced 3-dB radius (i.e. the bend radius at which the transmission is attenuated by 3dB upon a one full turn coil) at 1500 nm and at another wavelength from a spectral range that is closer to the short-wavelength transmission (chosen to be 1300 nm). For both wavelengths, the 3dB-radius is decreased by 1 cm per one ring addition to the cladding.

Furthermore, the evolution of the transmission loss with bend radius doesn’t show a uniform decrease but exhibits a resonant loss for a bend radius at 1.16 cm, and an oscillatory behavior shows a structured curve in the radial range of 2-8 cm. The loss resonant peaks are explained by the coupling between the fiber core HE11 mode and that of cladding hole (see Figs. 5(c)-5(f)) [9

9. T. D. Bradley, Y. Wang, M. Alharbi, B. Debord, C. Fourcade-Dutin, B. Beaudou, F. Gerome, and F. Benabid, “Optical Properties of Low Loss (70dB/km) Hypocycloid-Core Kagome Hollow Core Photonic Crystal Fiber for Rb and Cs Based Optical Applications,” J. Lightwave Technol. 31(16), 3052–3055 (2013). [CrossRef]

,26

26. V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express 21(3), 3388–3399 (2013). [CrossRef] [PubMed]

]. The origin of the oscillatory behaviour near 2-8 cm radial range is more complicated to trace back. We believe that it is due to a bending dependence of the Fano resonances [27

27. A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express 19(25), 25723–25728 (2011). [CrossRef] [PubMed]

].

Discussion and conclusion

The trend observed in the evolution of CL and bend loss with cladding ring-number increase, and the presence of several resonant peaks and dips in the CL spectra reveal a more intricate dynamics in the light confinement and call for further work to elucidate whether the CL is enhanced via coherent effect (i.e. Bragg interference) or whether the cladding acts as an index layer whose dimension and effective index are the physical parameters to control for further improving the CL. Furthermore, the resonant peaks and their coupling dynamics are also worthy of further exploration.

Acknowledgment

This research is funded by Agence Nationale de la Recherche through grants PHOTOSYNTH and ∑_LIM Labex Chaire. The authors thank the PLATINOM platform for technical assistance in the fiber fabrication.

References and links

1.

P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]

2.

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]

3.

F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006). [CrossRef] [PubMed]

4.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science 298(5592), 399–402 (2002). [CrossRef] [PubMed]

5.

Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core – shaped Kagome Hollow Core PCF,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Postdeadline Papers (Optical Society of America, 2010), CPDB4. [CrossRef]

6.

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]

7.

Y. Cheng, Y. Y. Wang, J. L. Auguste, F. Gerome, G. Humbert, J. M. Blondy, and F. Benabid, “Fabrication and Characterization of Ultra-large Core Size (> 100 μm) Kagome Fiber for Laser Power Handling,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (Optical Society of America, 2011), CTuE1.

8.

Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid, “Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and pulse compression,” Opt. Lett. 37(15), 3111–3113 (2012). [CrossRef] [PubMed]

9.

T. D. Bradley, Y. Wang, M. Alharbi, B. Debord, C. Fourcade-Dutin, B. Beaudou, F. Gerome, and F. Benabid, “Optical Properties of Low Loss (70dB/km) Hypocycloid-Core Kagome Hollow Core Photonic Crystal Fiber for Rb and Cs Based Optical Applications,” J. Lightwave Technol. 31(16), 3052–3055 (2013). [CrossRef]

10.

B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Cups curvature effect on confinement loss in hypocycloid-core Kagome HC-PCF,” in CLEO:2013 (Optical Society of America, 2013), CTu2K.4.

11.

B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber. Part I: Arc curvature effect on confinement loss,” Submitted for publication to Optics Express (2013).

12.

A. V. V. Nampoothiri, A. M. Jones, C. Fourcade-Dutin, C. Mao, N. Dadashzadeh, B. Baumgart, Y. Y. Wang, M. Alharbi, T. Bradley, N. Campbell, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, “Hollow-core Optical Fiber Gas Lasers (HOFGLAS): a review [Invited],” Opt. Mater. Express 2(7), 948–961 (2012). [CrossRef]

13.

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). [CrossRef] [PubMed]

14.

C. Wu, M. G. Raymer, Y. Y. Wang, and F. Benabid, “Quantum theory of phase correlations in optical frequency combs generated by stimulated Raman scattering,” Phys. Rev. B 82(5), 053834 (2010). [CrossRef]

15.

L. Vincetti, “Numerical analysis of plastic hollow core microstructured fiber for Terahertz applications,” Opt. Fiber Technol. 15(4), 398–401 (2009). [CrossRef]

16.

Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid, “Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and pulse compression,” Opt. Lett. 37(15), 3111–3113 (2012). [CrossRef] [PubMed]

17.

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). [CrossRef] [PubMed]

18.

G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St J Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express 15(20), 12680–12685 (2007). [CrossRef] [PubMed]

19.

S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010). [CrossRef] [PubMed]

20.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4/5), 359–371 (2001). [CrossRef]

21.

L. Vincetti and V. Setti, “Confinement Loss in Kagome and Tube Lattice Fibers: Comparison and Analysis,” J. Lightwave Technol. 30(10), 1470–1474 (2012). [CrossRef]

22.

L. Vincetti and V. Setti, “Extra loss due to Fano resonances in inhibited coupling fibers based on a lattice of tubes,” Opt. Express 20(13), 14350–14361 (2012). [CrossRef] [PubMed]

23.

M. Heiblum and J. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” J. Quantum Electron QE-11(2), 75–83 (1975). [CrossRef]

24.

L. Vincetti, M. Foroni, F. Poli, M. Maini, A. Cucinotta, S. Selleri, and M. Zoboli, “Numerical Modeling of S-Band EDFA Based on Distributed Fiber Loss,” J. Lightwave Technol. 26(14), 2168–2174 (2008). [CrossRef]

25.

Y. Tsuchida, K. Saitoh, and M. Koshiba, “Design of single-moded holey fibers with large-mode-area and low bending losses: the significance of the ring-core region,” Opt. Express 15(4), 1794–1803 (2007). [CrossRef] [PubMed]

26.

V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express 21(3), 3388–3399 (2013). [CrossRef] [PubMed]

27.

A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express 19(25), 25723–25728 (2011). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 16, 2013
Revised Manuscript: November 2, 2013
Manuscript Accepted: November 5, 2013
Published: November 13, 2013

Citation
M. Alharbi, T. Bradley, B. Debord, C. Fourcade-Dutin, D. Ghosh, L. Vincetti, F. Gérôme, and F. Benabid, "Hypocycloid-shaped hollow-core photonic crystal fiber Part II: Cladding effect on confinement and bend loss," Opt. Express 21, 28609-28616 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28609


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References

  1. P. Russell, “Photonic Crystal Fibers,” Science299(5605), 358–362 (2003). [CrossRef] [PubMed]
  2. F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and Photonic Guidance of Multi-Octave Optical-Frequency Combs,” Science318(5853), 1118–1121 (2007). [CrossRef] [PubMed]
  3. F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett.31(24), 3574–3576 (2006). [CrossRef] [PubMed]
  4. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,” Science298(5592), 399–402 (2002). [CrossRef] [PubMed]
  5. Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core – shaped Kagome Hollow Core PCF,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Postdeadline Papers (Optical Society of America, 2010), CPDB4. [CrossRef]
  6. 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]
  7. Y. Cheng, Y. Y. Wang, J. L. Auguste, F. Gerome, G. Humbert, J. M. Blondy, and F. Benabid, “Fabrication and Characterization of Ultra-large Core Size (> 100 μm) Kagome Fiber for Laser Power Handling,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (Optical Society of America, 2011), CTuE1.
  8. Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid, “Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and pulse compression,” Opt. Lett.37(15), 3111–3113 (2012). [CrossRef] [PubMed]
  9. T. D. Bradley, Y. Wang, M. Alharbi, B. Debord, C. Fourcade-Dutin, B. Beaudou, F. Gerome, and F. Benabid, “Optical Properties of Low Loss (70dB/km) Hypocycloid-Core Kagome Hollow Core Photonic Crystal Fiber for Rb and Cs Based Optical Applications,” J. Lightwave Technol.31(16), 3052–3055 (2013). [CrossRef]
  10. B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Cups curvature effect on confinement loss in hypocycloid-core Kagome HC-PCF,” in CLEO:2013 (Optical Society of America, 2013), CTu2K.4.
  11. B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber. Part I: Arc curvature effect on confinement loss,” Submitted for publication to Optics Express (2013).
  12. A. V. V. Nampoothiri, A. M. Jones, C. Fourcade-Dutin, C. Mao, N. Dadashzadeh, B. Baumgart, Y. Y. Wang, M. Alharbi, T. Bradley, N. Campbell, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, “Hollow-core Optical Fiber Gas Lasers (HOFGLAS): a review [Invited],” Opt. Mater. Express2(7), 948–961 (2012). [CrossRef]
  13. 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. Express19(2), 1441–1448 (2011). [CrossRef] [PubMed]
  14. C. Wu, M. G. Raymer, Y. Y. Wang, and F. Benabid, “Quantum theory of phase correlations in optical frequency combs generated by stimulated Raman scattering,” Phys. Rev. B82(5), 053834 (2010). [CrossRef]
  15. L. Vincetti, “Numerical analysis of plastic hollow core microstructured fiber for Terahertz applications,” Opt. Fiber Technol.15(4), 398–401 (2009). [CrossRef]
  16. Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid, “Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and pulse compression,” Opt. Lett.37(15), 3111–3113 (2012). [CrossRef] [PubMed]
  17. F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express20(10), 11153–11158 (2012). [CrossRef] [PubMed]
  18. G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St J Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express15(20), 12680–12685 (2007). [CrossRef] [PubMed]
  19. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express18(5), 5142–5150 (2010). [CrossRef] [PubMed]
  20. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron.33(4/5), 359–371 (2001). [CrossRef]
  21. L. Vincetti and V. Setti, “Confinement Loss in Kagome and Tube Lattice Fibers: Comparison and Analysis,” J. Lightwave Technol.30(10), 1470–1474 (2012). [CrossRef]
  22. L. Vincetti and V. Setti, “Extra loss due to Fano resonances in inhibited coupling fibers based on a lattice of tubes,” Opt. Express20(13), 14350–14361 (2012). [CrossRef] [PubMed]
  23. M. Heiblum and J. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” J. Quantum ElectronQE-11(2), 75–83 (1975). [CrossRef]
  24. L. Vincetti, M. Foroni, F. Poli, M. Maini, A. Cucinotta, S. Selleri, and M. Zoboli, “Numerical Modeling of S-Band EDFA Based on Distributed Fiber Loss,” J. Lightwave Technol.26(14), 2168–2174 (2008). [CrossRef]
  25. Y. Tsuchida, K. Saitoh, and M. Koshiba, “Design of single-moded holey fibers with large-mode-area and low bending losses: the significance of the ring-core region,” Opt. Express15(4), 1794–1803 (2007). [CrossRef] [PubMed]
  26. V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express21(3), 3388–3399 (2013). [CrossRef] [PubMed]
  27. A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express19(25), 25723–25728 (2011). [CrossRef] [PubMed]

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