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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25723–25728
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Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core

Alexey F. Kosolapov, Andrey D. Pryamikov, Alexander S. Biriukov, Vladimir S. Shiryaev, Maxim S. Astapovich, Gennady E. Snopatin, Victor G. Plotnichenko, Mikhail F. Churbanov, and Evgeny M. Dianov  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 25723-25728 (2011)
http://dx.doi.org/10.1364/OE.19.025723


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Abstract

A technologically simple optical fiber cross-section structure with a negative-curvature hollow-core has been proposed for the delivery of the CO2 laser radiation. The structure was optimized numerically and then realized using Te20As30Se50 (TAS) chalcogenide glass. Guidance of the 10.6 µm СО2-laser radiation through this TAS-glass hollow-core fiber has been demonstrated. The loss at λ=10.6 μm was amounted ~11 dB/m. A resonance behavior of the fiber bend loss as a function of the bend radius has been revealed.

© 2011 OSA

1. Introduction

At present, CO2-lasers remain the most required laser type for applications in the technology, medicine and certain special fields. In these applications, the CO2-laser radiation is, as a rule, transmitted through the air using a complicated system of mirrors. In recent years, however, more expensive high-power near-IR fiber and disk lasers began to expel CO2-lasers, because, among other things, they allow the use of optical fibers for the delivery and manipulation of the laser beam. Therefore, the development of fibers capable of transmitting powerful mid-IR radiation would regenerate interest in CO2-lasers.

By now, the optical loss in step-index chalcogenide glass fibers has been reduced to 1.5-2 dB/m at λ=10.6 µm owing to a reduction of the impurity As-O and Se-O bonds absorbing in this spectral region [1

1. J. Nishii, S. Morimoto, I. Inagawa, R. Iizuka, T. Yamashita, and T. Yamagishi, “Recent advances and trends in chalcogenide glass fiber technology: a review,” J. Non-Cryst. Solids 140, 199–208 (1992). [CrossRef]

3

3. V. S. Shiryaev, M. F. Churbanov, E. M. Dianov, V. G. Plotnichenko, J.-L. Adam, and J. Lucas, “Recent progress in preparation of chalcogenide As-Se-Te glasses with low impurity content,” J. Optoelectron. Adv. Mater. 7, 1773–1779 (2005).

]. The maximum power transmitted through a 1-m length of such a fiber amounted to 10.7 W, when an anti-reflection coating and water cooling were used [1

1. J. Nishii, S. Morimoto, I. Inagawa, R. Iizuka, T. Yamashita, and T. Yamagishi, “Recent advances and trends in chalcogenide glass fiber technology: a review,” J. Non-Cryst. Solids 140, 199–208 (1992). [CrossRef]

].

2. Fiber modeling and fabrication

The HC MOF with a negative curvature of the core boundary considered in this paper (Fig. 1
Fig. 1 A negative-core-curvature HC MOF with a cladding consisting of eight capillaries.
) belongs to the type of HC MOFs that do not support photonic band gaps [5

5. 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]

]. Such HC MOFs have a relatively high transmission loss in comparison with photonic band gap HC MOFs, but possess a larger bandwidth. The latter is due to the fact that the air-core localized modes are only weakly coupled with the cladding modes in the low loss wavelength regions. The high loss wavelengths in the transmission spectrum correspond to the avoided crossing of the air-core modes and the cladding modes. These wavelength regions are described by the ARROW model [10

10. 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). [CrossRef] [PubMed]

]. Authors of [7

7. F. Désévédavy, G. Renversez, J. Troles, P. Houizot, L. Brilland, I. Vasilief, Q. Coulombier, N. Traynor, F. Smektala, and J.-L. Adam, “Chalcogenide glass hollow core photonic crystal fibers,” Opt. Mater. 32(11), 1532–1539 (2010). [CrossRef]

] computed the core diameters for the chalcogenide HC MOF meeting the anti-resonant condition. In the case of the structure under consideration (Fig. 1) the ARROW model is also applicable because the capillary radius is much larger than the operating wavelength [11

11. L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010). [CrossRef] [PubMed]

]. Moreover, there exists an irregular spectral behavior of the leakage loss in the low loss regions. The latter effect is due to the weak coupling of the core modes with the dielectric modes having a high azimuthal dependence (modes with a high azimuthal index), the cut-off wavelengths of which fall in these spectral regions [11

11. L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010). [CrossRef] [PubMed]

]. The same HC MOF type with a positive curvature of the core boundary and a simplified cladding structure has been considered in [12

12. 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]

,13

13. 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). [CrossRef] [PubMed]

].

The chalcogenide glass refractive index at λ = 10.6 µm was taken to be 2.9064 [14

14. L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range of compositions,” J. of Non.-Crys Solids 27, 299–307 (1978).

] and the material loss, 50 dB/m (the latter is a typical and well-reproducible value). The geometry parameters dins and dout (Fig. 1) are much larger as compared to the source wavelength λ = 10.62 μm. This means that an individual capillary of the cladding possesses a high density of states of the leaky modes with a high azimuthal dependence and the loss spectrum must demonstrate an irregular behavior even in very narrow ranges of the low-loss spectral regions. To model the optimal design of the HC MOF, we used the FemLab 3.1 software. By means of the finite element method, we calculated the loss level of the fundamental HE11 air-core mode for the fiber with dins/dout = 0.8 and 0.85 for two values of Dcore = 260 and 380 μm (Fig. 2
Fig. 2 (a) The computed loss dependence of the HE11 air-core mode on the wavelength for a HC MOF with an air core diameter Dcore = 260 μm and with the value of ratio dins/dout = 0.8 (solid) and dins/dout = 0.85 (dashed) (b) the same dependencies for an HC MOF with an air core diameter Dcore = 380 μm.
).

The calculations were made in a narrow spectral region in the vicinity of the CO2-laser wavelength used in our experiments. As was expected, in the case of Dcore = 260 µm, the calculated loss spectrum is strongly inhomogeneous even in a spectral interval of ~8 nm and varies from 0.2 to ~1 dB/m (Fig. 2(a)). In the case of Dcore = 380 µm, the loss level is lower and the wavelength dependence is much smoother (Fig. 2(b)). In our opinion, in the case of a bigger value of Dcore one obtains a weaker coupling with the cladding modes with a high azimuthal dependence. Based on the results obtained, we produced several fibers with Dcore ~380 μm and dins/dout ~0.85.

The fiber preform was manufactured by the «stack and draw» technique from a substrate tube and eight capillaries. First, high-purity chalcogenide glass of As30Se50Te20 composition was produced by chemical-distillation melt purification [15

15. G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45(13), 1439–1460 (2009). [CrossRef]

, 16

16. V. S. Shiryaev, J.-L. Adam, X. H. Zhang, C. Boussard-Plédel, J. Lucas, and M. F. Churbanov, “Infrared fibers based on Te-As-Se glass system with low optical losses,” J. Non-Cryst. Solids 336(2), 113–119 (2004). [CrossRef]

]. The glass obtained had a low content of the limiting impurities: hydrogen - <2·10−6 mass%, oxygen - 2·10−5 mass%, carbon - 1·10−4 mass%, silicon - 5·10−5 mass% (as follows from laser mass spectroscopy and IR spectroscopy).

Next, we fabricated the substrate tube and the capillaries. The substrate tube with the outer diameter of 16 mm, the inner diameter of 11 mm, and the length of 120 mm was fabricated by centrifugal casting of the chalcogenide glass inside a vacuumized silica tube. The capillaries are usually drawn from a tube which is also fabricated by centrifugation. However, in this work, capillaries with the outer diameter of 3 mm and the inner diameter of 2.4 mm were prepared by the double crucible method from the chalcogenide glass melt [15

15. G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45(13), 1439–1460 (2009). [CrossRef]

]. For this, the TAS glass was placed in the cladding crucible, while the core crucible remained empty. The capillary wall thickness was determined by the geometrical dimensions of the double crucible die, the excess inert gas pressure over the melt, and the pressure inside the capillary. The elimination of centrifugation from the fabrication process of the capillaries allowed us to lower the probability of glass recrystallization and, thereby, to lower the fiber optical loss. The final preform was an assembly of the substrate tube and 8 capillaries forming a complete azimuthally symmetric layer of holes on the inner surface of the tube. The fiber was drawn at a conventional drawing tower at a temperature of 240°C. Some overpressure was maintained in the capillaries during fiber drawing to prevent their collapsing. The outer diameter of the obtained fiber was 750 µm, the core diameter of ~380 µm, and the capillary wall thickness of 13 µm (Fig. 3
Fig. 3 Fiber cross-section photograph obtained with the help of an electron microscope.
).

3. Results and discussion

The fiber loss spectrum was measured by the cut-back method on a Bruker IFS-113v Fourier Transform Infrared Spectrometer with a resolution of 0.1 cm−1 (Fig. 4
Fig. 4 Measured optical loss spectra of the chalcogenide microstructured hollow-core fiber in the region of the CO2-laser radiation (left) (the square dot was measured with help of the CO2 laser) and the CO2-laser radiation intensity (in a.u.) distribution over the fiber core (right).
(left)). In this experiment, light propagated not only through the air core but also through the substrate tube and the cladding capillaries. Therefore, the measured loss was the average of the loss in the air core and in the glass elements.

Fiber pieces, up to ~1 m in length, were found to be sufficiently transparent in the spectral range 2-10 µm, the loss at λ = 10.6 µm being ~13.5 dB/m, which makes the СО2-laser radiation transmission possible. Note that the TAS-glass microstructured hollow-core fibers first described in [7

7. F. Désévédavy, G. Renversez, J. Troles, P. Houizot, L. Brilland, I. Vasilief, Q. Coulombier, N. Traynor, F. Smektala, and J.-L. Adam, “Chalcogenide glass hollow core photonic crystal fibers,” Opt. Mater. 32(11), 1532–1539 (2010). [CrossRef]

] were nontransparent.

We also investigated the distribution of the CO2-laser radiation intensity over the fiber cross-section. In this experiment, a ZnSe lens was used to launch the radiation into the fiber, while the intensity distribution over the fiber output endface was observed with the help of an Electrophysics PV320 thermal imaging camera. We varied the fiber excitation conditions so as to excite preferentially either the hollow core, or the capillaries and the substrate tube. It was found that a much greater power can be transmitted through the core, which means that the light propagating through the glass owing to the total internal reflection experiences much stronger attenuation. The distribution in Fig. 4 (right) obtained under proper excitation conditions shows that the CO2-laser radiation is well confined in the hollow core. The additional maxima around the major maximum are due to light propagation through the glass on the places of contact of the capillaries. It was also established that the propagation regime in the core was multimode. The loss of the air-core modes measured with help of the CO2 laser was ~11 dB/m (Fig. 4 (left), square dot). The measured and calculated loss (Fig. 2(b)) in the vicinity of λ = 10.6 μm differ markedly. In our opinion, this difference is due to size and shape variations of the fiber cross section (Fig. 3) and also due to an increase in material loss after the drawing process [17

17. L. Brilland, J. Troles, P. Houizot, F. Désévédavy, Q. Coulombier, G. Renversez, T. Chartier, T. N. Nguyen, J.-L. Adam, and N. Traynor, “Interface impact on the transmission of chalcogenide photonic crystal fibres,” J. Ceram. Soc. Jpn. 116(1358), 1024–1027 (2008). [CrossRef]

].

Lastly, we measured the effect of fiber bending to a radius as small as 30 cm. We observed only a slight perturbation of the output near-field pattern under such bending (Fig. 5 inset), which means that the fiber continued to propagate light.

4. Conclusion

For the first time, guidance of the 10.6 µm СО2-laser radiation through a chalcogenide-glass microstructured hollow-core fiber has been demonstrated, the glass composition being As30Se50Te20. A further improvement of the technology and design of such fibers is expected to yield a reduction of the optical loss to below 1 dB/m. Because light proved to be well localized in the core, such fibers hold much promise for the delivery of the СО2-laser radiation.

References and links

1.

J. Nishii, S. Morimoto, I. Inagawa, R. Iizuka, T. Yamashita, and T. Yamagishi, “Recent advances and trends in chalcogenide glass fiber technology: a review,” J. Non-Cryst. Solids 140, 199–208 (1992). [CrossRef]

2.

T. Katsuyama and H. Matsumura, “Low loss Te-based chalcogenide glass optical fibers,” Appl. Phys. Lett. 49(1), 22–23 (1986). [CrossRef]

3.

V. S. Shiryaev, M. F. Churbanov, E. M. Dianov, V. G. Plotnichenko, J.-L. Adam, and J. Lucas, “Recent progress in preparation of chalcogenide As-Se-Te glasses with low impurity content,” J. Optoelectron. Adv. Mater. 7, 1773–1779 (2005).

4.

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(6916), 650–653 (2002). [CrossRef] [PubMed]

5.

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]

6.

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(1), 236–244 (2005). [CrossRef] [PubMed]

7.

F. Désévédavy, G. Renversez, J. Troles, P. Houizot, L. Brilland, I. Vasilief, Q. Coulombier, N. Traynor, F. Smektala, and J.-L. Adam, “Chalcogenide glass hollow core photonic crystal fibers,” Opt. Mater. 32(11), 1532–1539 (2010). [CrossRef]

8.

L. Brilland, F. Smektala, G. Renversez, T. Chartier, J. Troles, T. Nguyen, N. Traynor, and A. Monteville, “Fabrication of complex structures of Holey Fibers in Chalcogenide glass,” Opt. Express 14(3), 1280–1285 (2006). [CrossRef] [PubMed]

9.

F. Désévédavy, G. Renversez, J. Troles, L. Brilland, P. Houizot, Q. Coulombier, F. Smektala, N. Traynor, and J.-L. Adam, “Te-As-Se glass microstructured optical fiber for the middle infrared,” Appl. Opt. 48(19), 3860–3865 (2009). [CrossRef] [PubMed]

10.

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). [CrossRef] [PubMed]

11.

L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010). [CrossRef] [PubMed]

12.

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]

13.

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). [CrossRef] [PubMed]

14.

L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range of compositions,” J. of Non.-Crys Solids 27, 299–307 (1978).

15.

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45(13), 1439–1460 (2009). [CrossRef]

16.

V. S. Shiryaev, J.-L. Adam, X. H. Zhang, C. Boussard-Plédel, J. Lucas, and M. F. Churbanov, “Infrared fibers based on Te-As-Se glass system with low optical losses,” J. Non-Cryst. Solids 336(2), 113–119 (2004). [CrossRef]

17.

L. Brilland, J. Troles, P. Houizot, F. Désévédavy, Q. Coulombier, G. Renversez, T. Chartier, T. N. Nguyen, J.-L. Adam, and N. Traynor, “Interface impact on the transmission of chalcogenide photonic crystal fibres,” J. Ceram. Soc. Jpn. 116(1358), 1024–1027 (2008). [CrossRef]

18.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Curvature and microbending losses in single - mode optical fibres,” Opt. Quantum Electron. 11(1), 43–59 (1979). [CrossRef]

19.

G. Renversez, P. Boyer, and A. Sagrini, “Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling,” Opt. Express 14(12), 5682–5687 (2006). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2390) Fiber optics and optical communications : Fiber optics, infrared
(060.2400) Fiber optics and optical communications : Fiber properties
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 30, 2011
Revised Manuscript: November 17, 2011
Manuscript Accepted: November 21, 2011
Published: December 1, 2011

Citation
Alexey F. Kosolapov, Andrey D. Pryamikov, Alexander S. Biriukov, Vladimir S. Shiryaev, Maxim S. Astapovich, Gennady E. Snopatin, Victor G. Plotnichenko, Mikhail F. Churbanov, and Evgeny M. Dianov, "Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core," Opt. Express 19, 25723-25728 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25723


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References

  1. J. Nishii, S. Morimoto, I. Inagawa, R. Iizuka, T. Yamashita, and T. Yamagishi, “Recent advances and trends in chalcogenide glass fiber technology: a review,” J. Non-Cryst. Solids140, 199–208 (1992). [CrossRef]
  2. T. Katsuyama and H. Matsumura, “Low loss Te-based chalcogenide glass optical fibers,” Appl. Phys. Lett.49(1), 22–23 (1986). [CrossRef]
  3. V. S. Shiryaev, M. F. Churbanov, E. M. Dianov, V. G. Plotnichenko, J.-L. Adam, and J. Lucas, “Recent progress in preparation of chalcogenide As-Se-Te glasses with low impurity content,” J. Optoelectron. Adv. Mater.7, 1773–1779 (2005).
  4. 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,” Nature420(6916), 650–653 (2002). [CrossRef] [PubMed]
  5. 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]
  6. 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. Express13(1), 236–244 (2005). [CrossRef] [PubMed]
  7. F. Désévédavy, G. Renversez, J. Troles, P. Houizot, L. Brilland, I. Vasilief, Q. Coulombier, N. Traynor, F. Smektala, and J.-L. Adam, “Chalcogenide glass hollow core photonic crystal fibers,” Opt. Mater.32(11), 1532–1539 (2010). [CrossRef]
  8. L. Brilland, F. Smektala, G. Renversez, T. Chartier, J. Troles, T. Nguyen, N. Traynor, and A. Monteville, “Fabrication of complex structures of Holey Fibers in Chalcogenide glass,” Opt. Express14(3), 1280–1285 (2006). [CrossRef] [PubMed]
  9. F. Désévédavy, G. Renversez, J. Troles, L. Brilland, P. Houizot, Q. Coulombier, F. Smektala, N. Traynor, and J.-L. Adam, “Te-As-Se glass microstructured optical fiber for the middle infrared,” Appl. Opt.48(19), 3860–3865 (2009). [CrossRef] [PubMed]
  10. 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). [CrossRef] [PubMed]
  11. L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express18(22), 23133–23146 (2010). [CrossRef] [PubMed]
  12. 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]
  13. 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). [CrossRef] [PubMed]
  14. L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range of compositions,” J. of Non.-Crys Solids27, 299–307 (1978).
  15. G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater.45(13), 1439–1460 (2009). [CrossRef]
  16. V. S. Shiryaev, J.-L. Adam, X. H. Zhang, C. Boussard-Plédel, J. Lucas, and M. F. Churbanov, “Infrared fibers based on Te-As-Se glass system with low optical losses,” J. Non-Cryst. Solids336(2), 113–119 (2004). [CrossRef]
  17. L. Brilland, J. Troles, P. Houizot, F. Désévédavy, Q. Coulombier, G. Renversez, T. Chartier, T. N. Nguyen, J.-L. Adam, and N. Traynor, “Interface impact on the transmission of chalcogenide photonic crystal fibres,” J. Ceram. Soc. Jpn.116(1358), 1024–1027 (2008). [CrossRef]
  18. W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Curvature and microbending losses in single - mode optical fibres,” Opt. Quantum Electron.11(1), 43–59 (1979). [CrossRef]
  19. G. Renversez, P. Boyer, and A. Sagrini, “Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling,” Opt. Express14(12), 5682–5687 (2006). [CrossRef] [PubMed]

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