Abstract

We have studied the generation mechanisms of two different radiation-induced point defects, the Ge(1) and Ge(2) centers, in a germanosilicate fiber and in its original preform. The samples have been investigated before and after X-ray irradiation using the confocal microscopy luminescence and the electron paramagnetic resonance techniques. Our experimental results show the higher radiation sensitivity of the fiber as compared to the perform and suggest a relation between Ge(1) and Ge(2) generation. To explain our data we have used different models, finding that the destruction probability of the Ge(1) and Ge(2) defects is larger in fiber than in preform, whereas the generation one is similar. Finally we found that the higher radiation sensitivity of the fiber at low doses is essentially related to the presence of germanium lone pair center generated by the drawing.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
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  23. 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]
  24. G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
    [CrossRef] [PubMed]
  25. S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
    [CrossRef]
  26. A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
    [CrossRef]
  27. S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
    [CrossRef]
  28. A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.
  29. The difference in positioning the bulk samples (preform and reference sample) and the fiber inside the microwave cavity is the main error source.
  30. G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
    [CrossRef]
  31. M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
    [CrossRef]

2011 (1)

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

2009 (3)

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

2008 (2)

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

2007 (1)

2005 (1)

2001 (1)

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

1999 (4)

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

1996 (2)

H. G. Limberger, P.-Y. Fonjallaz, R. P. Salathé, and F. Cochet, “Compaction- and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68(22), 3069–3071 (1996).
[CrossRef]

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

1995 (1)

1994 (1)

V. B. Neustruev, “Colour centres in germanosilicate glass and optical fibres,” J. Phys. Condens. Matter 6(35), 6901–6936 (1994).
[CrossRef]

1992 (1)

L. Skuja, “Isoelectronic series of twofold coordinated Si, Ge, and Sn atoms in glassy SiO2: a luminescence study,” J. Non-Cryst. Solids 149(1-2), 77–95 (1992).
[CrossRef]

1990 (1)

K. Awazu, H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands 5.14 and 0.452 eV in 9 SiO2:GeO2 glasses heated under H2 atmosphere,” J. Appl. Phys. 68(6), 2713–2718 (1990).
[CrossRef]

1989 (1)

1986 (2)

U. Österberg and W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11(8), 516–518 (1986).
[CrossRef] [PubMed]

E. J. Friebele and D. L. Griscom, “Color center in glass optical fiber waveguides,” Mat. Res. Soc. Symp. Proc. 61, 319–331 (1986).
[CrossRef]

1984 (1)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

1976 (1)

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]

1974 (1)

E. J. Friebele, D. L. Griscom, and G. H. Sigel., “Defect centers in a germanium-doped silica-core optical fiber,” J. Appl. Phys. 45(8), 3424–3428 (1974).
[CrossRef]

Agnello, S.

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

Albert, J.

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

Alessi, A.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

Archambault, J. L.

Awazu, K.

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

K. Awazu, H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands 5.14 and 0.452 eV in 9 SiO2:GeO2 glasses heated under H2 atmosphere,” J. Appl. Phys. 68(6), 2713–2718 (1990).
[CrossRef]

Baggio, J.

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Ban, C.

Bayon, J. F.

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

Bisutti, J.

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Boscaino, R.

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

Boukenter, A.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Brebner, J. L.

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

Cannas, M.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

Carpanese, M.

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

Champagnon, B.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Chiodini, N.

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

Cochet, F.

H. G. Limberger, P.-Y. Fonjallaz, R. P. Salathé, and F. Cochet, “Compaction- and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68(22), 3069–3071 (1996).
[CrossRef]

David, L.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Dong, L.

Douay, M.

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

Essid, M.

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

Faivre, A.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Flammer, I.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Fleming, J. W.

Fonjallaz, P.-Y.

H. G. Limberger, P.-Y. Fonjallaz, R. P. Salathé, and F. Cochet, “Compaction- and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68(22), 3069–3071 (1996).
[CrossRef]

Friebele, E. J.

T. E. Tsai, M. A. Saifi, E. J. Friebele, D. L. Griscom, and U. Osterberg, “Correlation of defect centers with second-harmonic generation in Ge-doped and Ge-P-doped silica-core single-mode fibers,” Opt. Lett. 14(18), 1023–1025 (1989).
[CrossRef] [PubMed]

E. J. Friebele and D. L. Griscom, “Color center in glass optical fiber waveguides,” Mat. Res. Soc. Symp. Proc. 61, 319–331 (1986).
[CrossRef]

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]

E. J. Friebele, D. L. Griscom, and G. H. Sigel., “Defect centers in a germanium-doped silica-core optical fiber,” J. Appl. Phys. 45(8), 3424–3428 (1974).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Fujimaki, M.

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

Gelardi, F. M.

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

Girard, S.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Grandi, S.

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

Griscom, D. L.

T. E. Tsai, M. A. Saifi, E. J. Friebele, D. L. Griscom, and U. Osterberg, “Correlation of defect centers with second-harmonic generation in Ge-doped and Ge-P-doped silica-core single-mode fibers,” Opt. Lett. 14(18), 1023–1025 (1989).
[CrossRef] [PubMed]

E. J. Friebele and D. L. Griscom, “Color center in glass optical fiber waveguides,” Mat. Res. Soc. Symp. Proc. 61, 319–331 (1986).
[CrossRef]

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]

E. J. Friebele, D. L. Griscom, and G. H. Sigel., “Defect centers in a germanium-doped silica-core optical fiber,” J. Appl. Phys. 45(8), 3424–3428 (1974).
[CrossRef]

D. L. Griscom, “Trapped-electron centers in pure and doped glassy silica: A review and synthesis,” J. Non-Cryst. Solids (to be published), doi:.

Hazemann, J. L.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Ho, C. K. F.

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Kam, C. H.

Kasahara, T.

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

Katoh, T.

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Kawazoe, H.

K. Awazu, H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands 5.14 and 0.452 eV in 9 SiO2:GeO2 glasses heated under H2 atmosphere,” J. Appl. Phys. 68(6), 2713–2718 (1990).
[CrossRef]

Le Parc, R.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Levelut, C.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Limberger, H. G.

Marcandella, C.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Margulis, W.

Martinez, V.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Meinardi, F.

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

Messina, G.

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

Meunier, J.-P.

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Miyazaki, N.

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

Morazzoni, F.

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

Neustruev, V. B.

V. B. Neustruev, “Colour centres in germanosilicate glass and optical fibres,” J. Phys. Condens. Matter 6(35), 6901–6936 (1994).
[CrossRef]

Ngo, N. Q.

Niay, P.

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

Nikogosyan, D. N.

Ohki, Y.

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

Origlio, G.

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Osterberg, U.

Österberg, U.

Ouerdane, Y.

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

G. Origlio, M. Cannas, S. Girard, R. Boscaino, A. Boukenter, and Y. Ouerdane, “Influence of the drawing process on the defect generation in multistep-index germanium-doped optical fibers,” Opt. Lett. 34(15), 2282–2284 (2009).
[CrossRef] [PubMed]

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Paillet, P.

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Paleari, A.

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

Parlato, A.

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

Payne, D. N.

Pita, K.

Poumellec, B.

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

Reekie, L.

Richard, N.

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

Russell, P. S.

Saifi, M. A.

Salathé, R. P.

Scotti, R.

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

Seol, K. S.

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

Shimoto, S.

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

Sigel, G. H.

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]

E. J. Friebele, D. L. Griscom, and G. H. Sigel., “Defect centers in a germanium-doped silica-core optical fiber,” J. Appl. Phys. 45(8), 3424–3428 (1974).
[CrossRef]

Simon, J. P.

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

Skuja, L.

L. Skuja, “Isoelectronic series of twofold coordinated Si, Ge, and Sn atoms in glassy SiO2: a luminescence study,” J. Non-Cryst. Solids 149(1-2), 77–95 (1992).
[CrossRef]

Slattery, S. A.

Tokuhiro, S.

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

Tsai, T. E.

Yamane, M.

K. Awazu, H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands 5.14 and 0.452 eV in 9 SiO2:GeO2 glasses heated under H2 atmosphere,” J. Appl. Phys. 68(6), 2713–2718 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

H. G. Limberger, P.-Y. Fonjallaz, R. P. Salathé, and F. Cochet, “Compaction- and photoelastic-induced index changes in fiber Bragg gratings,” Appl. Phys. Lett. 68(22), 3069–3071 (1996).
[CrossRef]

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]

IEEE Trans. Nucl. Sci. (1)

S. Girard, Y. Ouerdane, G. Origlio, C. Marcandella, A. Boukenter, N. Richard, J. Baggio, P. Paillet, M. Cannas, J. Bisutti, J.-P. Meunier, and R. Boscaino, “Radiation effects on Silica-Based preforms and optical fibers—I: Experimental study with canonical samples,” IEEE Trans. Nucl. Sci. 55(6), 3473–3482 (2008).
[CrossRef]

J. Appl. Phys. (3)

E. J. Friebele, D. L. Griscom, and G. H. Sigel., “Defect centers in a germanium-doped silica-core optical fiber,” J. Appl. Phys. 45(8), 3424–3428 (1974).
[CrossRef]

K. Awazu, H. Kawazoe, and M. Yamane, “Simultaneous generation of optical absorption bands 5.14 and 0.452 eV in 9 SiO2:GeO2 glasses heated under H2 atmosphere,” J. Appl. Phys. 68(6), 2713–2718 (1990).
[CrossRef]

R. Le Parc, B. Champagnon, C. Levelut, V. Martinez, L. David, A. Faivre, I. Flammer, J. L. Hazemann, and J. P. Simon, “Density and concentration fluctuations in SiO2–GeO2 optical fiber glass investigated by small angle x-ray scattering,” J. Appl. Phys. 103(9), 094917 (2008).
[CrossRef]

J. Non-Cryst. Solids (6)

L. Skuja, “Isoelectronic series of twofold coordinated Si, Ge, and Sn atoms in glassy SiO2: a luminescence study,” J. Non-Cryst. Solids 149(1-2), 77–95 (1992).
[CrossRef]

A. Alessi, S. Girard, C. Marcandella, M. Cannas, A. Boukenter, and Y. Ouerdane, “Raman investigation of the drawing effects on Ge-doped fibers,” J. Non-Cryst. Solids 357(1), 24–27 (2011).
[CrossRef]

D. L. Griscom, “Trapped-electron centers in pure and doped glassy silica: A review and synthesis,” J. Non-Cryst. Solids (to be published), doi:.

A. Alessi, S. Agnello, F. M. Gelardi, G. Messina, and M. Carpanese, “Influence of Ge doping level on the EPR signal of Ge(1), Ge(2) and E'Ge defects in Ge-doped silica,” J. Non-Cryst. Solids (to be published), doi:.

G. Origlio, S. Girard, M. Cannas, Y. Ouerdane, R. Boscaino, and A. Boukenter, “Paramagnetic germanium-related centers induced by energetic radiation in optical fibers and preforms,” J. Non-Cryst. Solids 355(18-21), 1054–1056 (2009).
[CrossRef]

M. Essid, J. Albert, J. L. Brebner, and K. Awazu, “Correlation between oxygen-deficient center concentration and KrF excimer laser induced defects in thermally annealed Ge-doped optical fiber preforms,” J. Non-Cryst. Solids 246(1-2), 39–45 (1999).
[CrossRef]

J. Phys. Condens. Matter (2)

V. B. Neustruev, “Colour centres in germanosilicate glass and optical fibres,” J. Phys. Condens. Matter 6(35), 6901–6936 (1994).
[CrossRef]

M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, and Y. Ohki, “Paramagnetic centres induced in Ge-doped SiO2 glass with UV irradiation,” J. Phys. Condens. Matter 11(12), 2589–2594 (1999).
[CrossRef]

J. Phys. D Appl. Phys. (1)

B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UV-induced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D Appl. Phys. 29(7), 1842–1856 (1996).
[CrossRef]

Mat. Res. Soc. Symp. Proc. (1)

E. J. Friebele and D. L. Griscom, “Color center in glass optical fiber waveguides,” Mat. Res. Soc. Symp. Proc. 61, 319–331 (1986).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (4)

M. Fujimaki, T. Kasahara, S. Shimoto, N. Miyazaki, S. Tokuhiro, K. S. Seol, and Y. Ohki, “Structural changes induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass,” Phys. Rev. B 60(7), 4682–4687 (1999).
[CrossRef]

N. Chiodini, F. Meinardi, F. Morazzoni, A. Paleari, and R. Scotti, “Optical transitions of paramagnetic Ge sites created by x-ray irradiation of oxygen-defect-free Ge-doped SiO2 by the sol-gel method,” Phys. Rev. B 60(4), 2429–2435 (1999).
[CrossRef]

A. Alessi, S. Agnello, S. Grandi, A. Parlato, and F. M. Gelardi, “Refractive index change dependence on Ge(1) defects in γ-irradiated Ge-doped silica,” Phys. Rev. B 80(1), 014103 (2009).
[CrossRef]

S. Agnello, R. Boscaino, M. Cannas, and F. M. Gelardi, “Instantaneous diffusion effect on spin-echo decay: Experimental investigation by spectral selective excitation,” Phys. Rev. B 64(17), 174423 (2001).
[CrossRef]

Other (3)

A. B. Devine, J. P. Duraud, and E. Dooryhée, Structure and Imperfections in Amorphous and Crystalline Silicon Dioxide (Wiley, New York, 2000).

The difference in positioning the bulk samples (preform and reference sample) and the fiber inside the microwave cavity is the main error source.

G. Pacchioni, L. Skuja, and D. L. Griscom, Defects in SiO2 and related dielectrics: Science and Technology, (Kluwer Academic Publishers, Dordrecht, 2000).

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Figures (6)

Fig. 1
Fig. 1

Ge-doping profile both in FGe fiber (○) and PGe preform (▬). The diameter ratio between the preform and the fiber is ~80.4, the values reported on the x-axis have been rescaled by this ratio for the preform.

Fig. 2
Fig. 2

a) Optical absorption spectra recorded in the ~11% (▬) and ~4.5% wt (▬) Ge doped zones of the non-irradiated preform; b) optical absorption spectrum of the 4.5% Ge doped zone of the non-irradiated preform after the subtraction of a tangent to the minima of the band (▬); c) zoom around 3.8 eV of the optical absorption spectrum recorded in the ~11% Ge doped zone of the non-irradiated preform, the grey curve is a Gaussian tail describing the other OA activities.

Fig. 3
Fig. 3

GLPC profile obtained through CML measurements on the non-irradiated preform (-○-) and fiber (-●-) samples as a function of the distance from the core center; in the inset we report the zoom of the CML signal from the core center recorded between −10 and 10 µm. For the preform data, the distance from the center is rescaled by the ratio between fiber and preform diameters.

Fig. 4
Fig. 4

GLPC related PL amplitude recorded at the center of the fiber core as a function of the irradiation dose expressed in kGray (kGy), the point at 10−2 kGy stays for the measurements recorded on the non-irradiated fiber.

Fig. 5
Fig. 5

a) EPR spectra recorded in the fiber (▬) and in the preform (▬) at the dose of 20 kGy; b) Ge(2) concentration as a function of the Ge(1) concentration in fiber FGe (●) and in preform PGe (○), (▬) fit law see the text.

Fig. 6
Fig. 6

a) Ge(1) concentration as a function of the dose; b) Ge(2) concentration as a function of the dose. Data of fiber (○) and preform (●), fit of fiber data (--), fit of the preform data (▬).

Equations (11)

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

G e + G L P C G e ( 1 ) + G e ( 2 )
d G e ( 1 , 2 ) d x = c G L P C ( x ) G e ( x ) b G e ( 2 ) G e ( 1 )
d G e ( 1 ) d x = c G L P C G e b ( G e ( 1 ) ) 2
G e ( 1 ) = G L P C G e c b tanh [ x G L P C G e c b ]
s a t f s a t p = G L P C f G L P C p b p c f b f c p
D s a t f D s a t p = G L P C f G L P C p b f c f b p c p
1 b = s a t D s a t
c = s a t D s a t 1 G e G L P C
d G e ( 1 ) d x = q G e r G e ( 1 ) d G e ( 2 ) d x = s G L P C g G e ( 2 )
G e ( 1 ) = q G e r ( 1 e r x ) G e ( 2 ) = s G L P C g ( 1 e g x )
s a t f [ G e ( 1 ) ] s a t p [ G e ( 1 ) ] = q f r p q p r f s a t f [ G e ( 2 ) ] s a t p [ G e ( 2 ) ] = s f g p s p g f G L P C f G L P C p

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