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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 1, Iss. 2 — Jun. 1, 2011
  • pp: 179–184
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Reducing spectral attenuation in small-core photonic crystal fibers

I. Gris-Sánchez, B.J. Mangan, and J.C. Knight  »View Author Affiliations


Optical Materials Express, Vol. 1, Issue 2, pp. 179-184 (2011)
http://dx.doi.org/10.1364/OME.1.000179


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Abstract

We describe a modified fabrication process to reduce spectral attenuation in highly nonlinear photonic crystal fibers (PCF) by reducing the effect of OH- content in the silica glass. In particular we show outstanding results for small core sizes of 2μm diameter including an attenuation of 10dB/km at the OH- peak wavelength of 1384nm, by annealing the preform prior to the fiber draw.

© 2011 OSA

1. Introduction

The spectra shown in Fig. 1 were obtained from PCF’s fabricated using the standard stack and draw process [20

20. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]

] and Suprasil F300 as the starting material. Although the exact concentration of OH- in the starting material is not known, the manufacturer’s specification is below 1ppm and is quoted to be typically 0.2ppm. This corresponds to an attenuation of 12.1dB/km at 1384nm [9

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

]. The fibers fabricated have different levels of attenuation at this wavelength, ranging from 8dB/km for large core diameters (e.g. 5μm and above) to as much as 200dB/km for untreated small-core fibers suggesting that additional OH- becomes significantly more of a problem for small core fibers.

2. Fabrication process

Each cane was placed inside a thick-walled F300 jacketing tube in order to ensure an acceptably large outer diameter of the final fiber. The jacketed cane (which formed the preform for the fiber draw) was continuously purged with nitrogen from one end whilst being passed through the fiber-drawing furnace at 20mm/min. The furnace temperature was set so that the pyrometer reading was at 1880°C. This process was repeated three times before the fiber was drawn in the usual way. The fibers were characterized within 7 days of their fabrication. The annealing conditions were chosen because they gave good results. Higher annealing temperatures and longer annealing times led to unacceptable distortion of the fiber structure, whilst shorter times were less effective at reducing attenuation.

3. Experiments

Subsequently, using a different annealed preform, a new set of fibers was fabricated to investigate the dependence of the attenuation on the fiber core diameter. Figure 2b shows the attenuation obtained from fibers of different core diameters (2.0, 1.5, 1.4 and 1.2μm) drawn, in that order, from the same cane during the same draw (draw speed and temperature settings were changed when reducing the fiber diameter). The tension (190g) and draw speed (32m/min) to obtain fibers with core diameters from 2μm and above were kept very similar. For fibers with core sizes below 2μm, the tension was lower (140g) to avoid fiber break, and the draw speed was slightly higher (up to 42m/min).

4. Discussion

The magnitude of the attenuation observed at 1384nm measured for a different set of fibers, as a function of the core diameter, is shown in Fig. 3
Fig. 3 The measured attenuation at the OH- peak wavelength of 1384nm increases dramatically for core sizes below 2um. The background loss component due to scattering also increase for small core sizes.
. The OH- absorption is almost constant at approximately 20dB/km for core diameters above 2 μm but then increases very rapidly to over 100dB/km for 1.2μm core diameter. An increase in the background scattering loss is also observed.

We have considered various explanations for the observed strong dependence of attenuation on core diameter. It is known that the losses due to surface scattering increase strongly for smaller core sizes [16

16. M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Mélin, M. Douay, and Y. Quiquempois, “Surface Roughness and Light Scattering in a Small Effective Area Microstructured Fiber,” J. Lightwave Technol. 27(11), 1597–1604 (2009). [CrossRef]

] but the wavelength dependence of such losses precludes this being directly responsible for the observed attenuation peaks. The “draw band” at 630nm is usually associated with damage to the silica network during the drawing process [18

18. P. Kaiser, “Drawing-induced coloration in vitreous silica fibers,” J. Opt. Soc. Am. 64(4), 475–481 (1974). [CrossRef]

], and might be expected to increase if the same size preform is drawn to a smaller final fiber, as in our experiments. The presence of a greater density of lattice defects might then facilitate the diffusion of hydrogen atoms or OH- ions into the core by vacancy hopping [33

33. H. Mehrer, Diffusion in Solids (Springer-Verlag Berlin Heidelberg, 2007), Chap 6.

]. A third possibility is that contaminants (hydrogen or OH-) introduced onto the silica surfaces diffuse only a short absolute distance into the core during subsequent fiber drawing. For large cores, this would result in contamination of only a small fraction of the total core area and therefore only a limited overlap with the guided mode profile. For smaller cores the same absolute distance of OH- ingress would make up much more of the core size and result in an increase of the overlap of the guided mode with the OH- contaminated glass.

In order to investigate this third possibility we have performed numerical simulations using the finite element method (FEM) to calculate the power of the fundamental mode as a function of distance from the core surface. The simulations were performed for a strand of silica surrounded by air which is a good approximation to the highly nonlinear PCF used in our experiments. The core is defined here as a pure uncontaminated silica rod surrounded by a ring of OH- doped silica of thickness given by the suggested diffusion length of OH- into silica. We calculated the ratio between the power of the fundamental mode that overlaps with the contaminated ring (Pring) and the total power of the mode (Ptotal), Pratio = Pring/Ptotal, and plotted it for different conjectured diffusion lengths for different core sizes as shown in Fig. 4
Fig. 4 The ratio (represented by Pratio) between the power of the fundamental mode contained within a diffusion ring starting at the core surface and the total power. Each line is calculated for diffusion lengths ranging from 0.1μm to 0.8μm and plotted for core diameters from 1μm to 6μm. Curves do not go to unity because some of the total power resides outside the core.
. The simulations were performed for diffusion lengths from 0.10μm to 0.80μm and for core diameters from 1μm to 6μm.

It is observed that although most of the simulated curves (Fig. 4) increase significantly for core diameters below 2µm, even the most rapid increase of these calculated curves is not nearly enough to explain the experimental observation shown in Fig. 3. When combined with the observation of a correlation between the appearance of the 630nm band and increased OH- absorption we conclude that this suggests that the appearance of a greatly increased number of lattice defect sites in the smaller-core fibers (as a result of their being drawn to a greater extent, and more rapidly) is a possible explanation for the stronger dependence of spectral attenuation on core diameter than anticipated in Fig. 4.

5. Conclusions

We have demonstrated an annealing process that reduces attenuation in small-core photonic crystal fibers to the lowest levels reported. The effect of the annealing is to reduce spectral absorption associated with OH- while eliminating the drawing-induced absorption band at 630nm wavelength and also reducing the overall background attenuation generally attributed to scattering. There remains a strong residual dependence of the OH- absorption features and the background scattering losses on core diameter for core diameters below 2μm. Using numerical simulations we have shown that this strong dependence cannot be explained by the diffusion depth of OH- ions from the surfaces alone. Instead, we tentatively attribute it to the rapid increase in the number and density of drawing-induced defect sites in the silica lattice when the preform is drawn to smaller diameters. To understand the contribution of each OH- source in the final fiber (extrinsic or intrinsic) a deeper study of the material would be necessary.

Acknowledgments

We would like to acknowledge Dr. James Stone for useful discussions. This work has been part funded by the EU FP7 programme “CARS EXPLORER” and the UK Engineering and Physical Sciences Research Council. IGS acknowledges the Mexican Council for Science and Technology (CONACyT) for financial support.

References and links

1.

A. Kudlinski, G. Bouwmans, O. Vanvincq, Y. Quiquempois, A. Le Rouge, L. Bigot, G. Mélin, and A. Mussot, “White-light cw-pumped supercontinuum generation in highly GeO(2)-doped-core photonic crystal fibers,” Opt. Lett. 34(23), 3631–3633 (2009). [CrossRef] [PubMed]

2.

B. A. Cumberland, J. C. Travers, S. V. Popov, and J. R. Taylor, “Toward visible cw-pumped supercontinua,” Opt. Lett. 33(18), 2122–2124 (2008). [CrossRef] [PubMed]

3.

J. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, “Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber,” Opt. Lett. 30(15), 1938–1940 (2005). [CrossRef] [PubMed]

4.

C. Guo, S. Ruan, P. Yan, E. Pan, and H. Wei, “Flat supercontinuum generation in cascaded fibers pumped by a continuous wave laser,” Opt. Express 18(11), 11046–11051 (2010). [CrossRef] [PubMed]

5.

W. Wadsworth, N. Joly, J. Knight, T. Birks, F. Biancalana, and P. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12(2), 299–309 (2004). [CrossRef] [PubMed]

6.

J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008). [CrossRef] [PubMed]

7.

S. A. Dekker, R. Pant, A. C. Judge, C. Martijn de Sterke, B. J. Eggleton, I. Gris-Sánchez, and J. C. Knight, “Highly-Efficient, Octave Spanning Soliton Self Frequency Shift Using a Photonic Crystal Fiber with Low OH Loss,” in Frontiers in Optics, OSA Technical Digest (CD)(Optical Society of America, 2010), PDPB6. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-PDPB6

8.

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225–2227 (2003). [CrossRef] [PubMed]

9.

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

10.

J. Stone and G. E. Walrafen, “Overtone vibrations of OH groups in fused silica optical fibers,” J. Chem. Phys. 76(4), 1712–1722 (1982). [CrossRef]

11.

M. Nielsen, C. Jacobsen, N. Mortensen, J. Folkenberg, and H. Simonsen, “Low-loss photonic crystal fibers for transmission systems and their dispersion properties,” Opt. Express 12(7), 1372–1376 (2004). [CrossRef] [PubMed]

12.

M. Nielsen, N. Mortensen, M. Albertsen, J. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12(8), 1775–1779 (2004). [CrossRef] [PubMed]

13.

K. Tajima, “Low loss PCF by reduction of hole surface imperfection,” Eur. Conf. Optical Commun. (ECOC) (2007) Paper PD2.1.

14.

R. T. Bise and D. J. Trevor, “Surface absorption in microstructured optical fibers,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper WI4, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2004-WI4

15.

K. Kurokawa, K. Nakajima, K. Tsujikawa, T. Yamamoto, and K. Tajima, “Ultra-wideband transmission over low loss pcf,” J. Lightwave Technol. 27(11), 1653–1662 (2009). [CrossRef]

16.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Mélin, M. Douay, and Y. Quiquempois, “Surface Roughness and Light Scattering in a Small Effective Area Microstructured Fiber,” J. Lightwave Technol. 27(11), 1597–1604 (2009). [CrossRef]

17.

P. Roberts, F. Couny, H. Sabert, B. Mangan, T. Birks, J. Knight, and P. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express 13(20), 7779–7793 (2005). [CrossRef] [PubMed]

18.

P. Kaiser, “Drawing-induced coloration in vitreous silica fibers,” J. Opt. Soc. Am. 64(4), 475–481 (1974). [CrossRef]

19.

Y. Hayashi, Y. Okuda, H. Mitera, and K. Kato, “Formation of Drawing or Radiation-Induced Defects in Germanium Doped Silica Core Optical Fiber,” Jpn. J. Appl. Phys. 33(Part 2, No. 2B), L233–L234 (1994). [CrossRef]

20.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]

21.

A. Monteville, D. Landais, O. Le Goffic, D. Tregoat, N. J. Traynor, T. Nguyen, S. Lobo, T. Chartier, and J. Simon, “Low Loss, Low OH, Highly Non-linear Holey Fiber for Raman Amplification,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMC1, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2006-CMC1

22.

K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow Loss and Long Length Photonic Crystal Fiber,” J. Lightwave Technol. 22(1), 7–10 (2004). [CrossRef]

23.

K. Tajima, J. Zhou, K. Kurokawa, and K. Nakajima, “Low water peak photonic crystal fibers,” 29th European conference on optical communication ECOC'03 (Rimini, Italy), pp. 42–43 (2003).

24.

I. Gris-Sánchez, B. J. Mangan, and J. C. Knight, “Reducing Spectral Attenuation in Solid-Core Photonic Crystal Fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWK1. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OWK1

25.

Heraeus, “High purity rods”. http://heraeus-quarzglas.com/media/webmedia_local/downloads/broschren_sf/2009_sf/PCF.pdf

26.

Heraeus, “Quartz glass for optics data and properties” http://www.heraeus-quarzglas.com/media/webmedia_local/downloads/broschren_mo/SO_Data_and_properties_ EN.pdf.

27.

L. Nuccio, S. Agnello, and R. Boscaino, “Intrinsic generation of OH groups in dry silicon dioxide upon thermal treatments,” Appl. Phys. Lett. 93(15), 151906 (2008). [CrossRef]

28.

L. Nuccio, S. Agnello, and R. Boscaino, “Annealing of radiation induced oxygen deficient point defects in amorphous silicon dioxide: evidence for a distribution of the reaction activation energies,” J. Phys. Condens. Matter 20(38), 385215 (2008). [CrossRef]

29.

R. K. Iler, The Chemistry of Silica (John Wiley and Sons, New York, 1979), Chap 6.

30.

R. H. Doremus, Glass Science, (John Wiley and Sons, New York, 1973), Chap 7.

31.

E. J. Friebele, G. H. Sigel, and D. L. Griscom, “Drawing-induced defect centers in a fused silica core fiber,” Appl. Phys. Lett. 28(9), 516–518 (1976). [CrossRef]

32.

Y. Hibino and H. Hanafusa, “Defect structure and formation mechanisms of drawing-induced absorption at 630nm in silica optical fibers,” J. Appl. Phys. 60(5), 1797–1801 (1986). [CrossRef]

33.

H. Mehrer, Diffusion in Solids (Springer-Verlag Berlin Heidelberg, 2007), Chap 6.

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Materials for Fiber Optics

History
Original Manuscript: February 24, 2011
Revised Manuscript: April 11, 2011
Manuscript Accepted: April 21, 2011
Published: May 2, 2011

Citation
I. Gris-Sánchez, B.J. Mangan, and J.C. Knight, "Reducing spectral attenuation in small-core photonic crystal fibers," Opt. Mater. Express 1, 179-184 (2011)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-2-179


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References

  1. A. Kudlinski, G. Bouwmans, O. Vanvincq, Y. Quiquempois, A. Le Rouge, L. Bigot, G. Mélin, and A. Mussot, “White-light cw-pumped supercontinuum generation in highly GeO(2)-doped-core photonic crystal fibers,” Opt. Lett. 34(23), 3631–3633 (2009). [CrossRef] [PubMed]
  2. B. A. Cumberland, J. C. Travers, S. V. Popov, and J. R. Taylor, “Toward visible cw-pumped supercontinua,” Opt. Lett. 33(18), 2122–2124 (2008). [CrossRef] [PubMed]
  3. J. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, “Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber,” Opt. Lett. 30(15), 1938–1940 (2005). [CrossRef] [PubMed]
  4. C. Guo, S. Ruan, P. Yan, E. Pan, and H. Wei, “Flat supercontinuum generation in cascaded fibers pumped by a continuous wave laser,” Opt. Express 18(11), 11046–11051 (2010). [CrossRef] [PubMed]
  5. W. Wadsworth, N. Joly, J. Knight, T. Birks, F. Biancalana, and P. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12(2), 299–309 (2004). [CrossRef] [PubMed]
  6. J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008). [CrossRef] [PubMed]
  7. S. A. Dekker, R. Pant, A. C. Judge, C. Martijn de Sterke, B. J. Eggleton, I. Gris-Sánchez, and J. C. Knight, “Highly-Efficient, Octave Spanning Soliton Self Frequency Shift Using a Photonic Crystal Fiber with Low OH Loss,” in Frontiers in Optics, OSA Technical Digest (CD)(Optical Society of America, 2010), PDPB6. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2010-PDPB6
  8. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225–2227 (2003). [CrossRef] [PubMed]
  9. O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996). [CrossRef]
  10. J. Stone and G. E. Walrafen, “Overtone vibrations of OH groups in fused silica optical fibers,” J. Chem. Phys. 76(4), 1712–1722 (1982). [CrossRef]
  11. M. Nielsen, C. Jacobsen, N. Mortensen, J. Folkenberg, and H. Simonsen, “Low-loss photonic crystal fibers for transmission systems and their dispersion properties,” Opt. Express 12(7), 1372–1376 (2004). [CrossRef] [PubMed]
  12. M. Nielsen, N. Mortensen, M. Albertsen, J. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12(8), 1775–1779 (2004). [CrossRef] [PubMed]
  13. K. Tajima, “Low loss PCF by reduction of hole surface imperfection,” Eur. Conf. Optical Commun. (ECOC) (2007) Paper PD2.1.
  14. R. T. Bise and D. J. Trevor, “Surface absorption in microstructured optical fibers,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper WI4, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2004-WI4
  15. K. Kurokawa, K. Nakajima, K. Tsujikawa, T. Yamamoto, and K. Tajima, “Ultra-wideband transmission over low loss pcf,” J. Lightwave Technol. 27(11), 1653–1662 (2009). [CrossRef]
  16. M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Mélin, M. Douay, and Y. Quiquempois, “Surface Roughness and Light Scattering in a Small Effective Area Microstructured Fiber,” J. Lightwave Technol. 27(11), 1597–1604 (2009). [CrossRef]
  17. P. Roberts, F. Couny, H. Sabert, B. Mangan, T. Birks, J. Knight, and P. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express 13(20), 7779–7793 (2005). [CrossRef] [PubMed]
  18. P. Kaiser, “Drawing-induced coloration in vitreous silica fibers,” J. Opt. Soc. Am. 64(4), 475–481 (1974). [CrossRef]
  19. Y. Hayashi, Y. Okuda, H. Mitera, and K. Kato, “Formation of Drawing or Radiation-Induced Defects in Germanium Doped Silica Core Optical Fiber,” Jpn. J. Appl. Phys. 33(Part 2, No. 2B), L233–L234 (1994). [CrossRef]
  20. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]
  21. A. Monteville, D. Landais, O. Le Goffic, D. Tregoat, N. J. Traynor, T. Nguyen, S. Lobo, T. Chartier, and J. Simon, “Low Loss, Low OH, Highly Non-linear Holey Fiber for Raman Amplification,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMC1, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2006-CMC1
  22. K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow Loss and Long Length Photonic Crystal Fiber,” J. Lightwave Technol. 22(1), 7–10 (2004). [CrossRef]
  23. K. Tajima, J. Zhou, K. Kurokawa, and K. Nakajima, “Low water peak photonic crystal fibers,” 29th European conference on optical communication ECOC'03 (Rimini, Italy), pp. 42–43 (2003).
  24. I. Gris-Sánchez, B. J. Mangan, and J. C. Knight, “Reducing Spectral Attenuation in Solid-Core Photonic Crystal Fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWK1. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OWK1
  25. Heraeus, “High purity rods”. http://heraeus-quarzglas.com/media/webmedia_local/downloads/broschren_sf/2009_sf/PCF.pdf
  26. Heraeus, “Quartz glass for optics data and properties” http://www.heraeus-quarzglas.com/media/webmedia_local/downloads/broschren_mo/SO_Data_and_properties_ EN.pdf.
  27. L. Nuccio, S. Agnello, and R. Boscaino, “Intrinsic generation of OH groups in dry silicon dioxide upon thermal treatments,” Appl. Phys. Lett. 93(15), 151906 (2008). [CrossRef]
  28. L. Nuccio, S. Agnello, and R. Boscaino, “Annealing of radiation induced oxygen deficient point defects in amorphous silicon dioxide: evidence for a distribution of the reaction activation energies,” J. Phys. Condens. Matter 20(38), 385215 (2008). [CrossRef]
  29. R. K. Iler, The Chemistry of Silica (John Wiley and Sons, New York, 1979), Chap 6.
  30. R. H. Doremus, Glass Science, (John Wiley and Sons, New York, 1973), Chap 7.
  31. E. J. Friebele, G. H. Sigel, and D. L. Griscom, “Drawing-induced defect centers in a fused silica core fiber,” Appl. Phys. Lett. 28(9), 516–518 (1976). [CrossRef]
  32. Y. Hibino and H. Hanafusa, “Defect structure and formation mechanisms of drawing-induced absorption at 630nm in silica optical fibers,” J. Appl. Phys. 60(5), 1797–1801 (1986). [CrossRef]
  33. H. Mehrer, Diffusion in Solids (Springer-Verlag Berlin Heidelberg, 2007), Chap 6.

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