Abstract

The formation and bleaching of color centers during annealing of pre-darkened ytterbium-doped silica fibers is modeled by three-electron bond (TEB) = Si<O2:∙Yb absorption centers. The nature of a center and underlying mechanism for its annealing in formation, shift and dissociation of chemical bonds is described in terms of a Markov statistical model with state change set by Bose-Einstein phonon statistics. The center hold one terminal and four active states with activation energies for transitions among these found to match bond energies of molecular oxygen in ionic character bonds of 1 and 1½ bond order. Experimentally observed in- and decrease in absorption during ramp and isothermal annealing of pre-darkened ytterbium co-doped silica fibers are hereby matched by a set of = Si<O2:∙Yb centers.

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2013 (1)

2012 (1)

2011 (1)

2010 (2)

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

M. J. Söderlund, J. J. Montiel i Ponsoda, J. P. Koplow, and S. Honkanen, “Thermal bleaching of photodarkening in ytterbium-doped fibers,” Proc. SPIE7580, 75800B, 75800B-8 (2010).
[CrossRef]

2009 (5)

2008 (1)

2007 (2)

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488 nm irradiation,” Opt. Lett.32(12), 1626–1628 (2007).
[CrossRef] [PubMed]

A. V. Kimmel, P. V. Sushko, and A. L. Shluger, “Structure and spectroscopic properties of trapped holes in silica,” J. Non-Cryst. Solids353(5-7), 599–604 (2007).
[CrossRef]

1998 (1)

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids239(1–3), 16–48 (1998).
[CrossRef]

1997 (1)

V. O. Sokolov and V. B. Sulimov, “Threefold coordinated oxygen atom in silica glass,” J. Non-Cryst. Solids217(2–3), 167–172 (1997).
[CrossRef]

1986 (1)

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

1983 (1)

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

1980 (1)

L. Pauling, “The nature of silicon-oxygen bonds,” Am. Mineral.65, 321 (1980).

1972 (1)

P. H. Krupenie, “The spectrum of molecular oxygen,” J. Phys. Chem. Ref. Data1(2), 423–534 (1972).
[CrossRef]

1970 (2)

C. C. Robinson and J. T. Fournier, “Co-ordination of Yb3+ in phosphate, silicate, and germinate glasses,” J. Phys. Chem. Solids31(5), 895–904 (1970).
[CrossRef]

R. Schnadt and J. Schneider, “The Electronic Structure of the Trapped-Hole Center in Smoky Quartz,” Phys. Kondens. Materie11, 19–42 (1970).

Arai, K.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Baggio, J.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Ballato, J.

Basu, C.

Blackmore, E. W.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Boukenter, A.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Boyland, A. J.

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488 nm irradiation,” Opt. Lett.32(12), 1626–1628 (2007).
[CrossRef] [PubMed]

Dadier, B.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Deschamps, T.

Dodd, P. E.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Dong, L.

Dragic, P. D.

Eden, J. G.

Engholm, M.

Ferlet-Cavrois, V.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Fleming, J. W.

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

Fournier, J. T.

C. C. Robinson and J. T. Fournier, “Co-ordination of Yb3+ in phosphate, silicate, and germinate glasses,” J. Phys. Chem. Solids31(5), 895–904 (1970).
[CrossRef]

Foy, P. R.

Friebele, E. J.

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

Galvin, T. C.

Girard, S.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Gonnet, C.

Griscom, D. L.

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

Handa, T.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Hawkins, T.

Honda, T.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Honkanen, S.

Ishii, Y.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Jetschke, S.

Kimmel, A. V.

A. V. Kimmel, P. V. Sushko, and A. L. Shluger, “Structure and spectroscopic properties of trapped holes in silica,” J. Non-Cryst. Solids353(5-7), 599–604 (2007).
[CrossRef]

Kirchhof, J.

Koplow, J. P.

Krupenie, P. H.

P. H. Krupenie, “The spectrum of molecular oxygen,” J. Phys. Chem. Ref. Data1(2), 423–534 (1972).
[CrossRef]

Kumata, K.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Leich, M.

Liu, Y.-S.

Long, K. J.

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

Marcandella, C.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Mattsson, K. E.

Meunier, J.-P.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Montiel i Ponsoda, J. J.

Namikawa, H.

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

Nilsson, J.

Norin, L.

Ollier, N.

Ouerdane, Y.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Paillet, P.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Pauling, L.

L. Pauling, “The nature of silicon-oxygen bonds,” Am. Mineral.65, 321 (1980).

Payne, D.

Reichel, V.

Robin, T.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Robinson, C. C.

C. C. Robinson and J. T. Fournier, “Co-ordination of Yb3+ in phosphate, silicate, and germinate glasses,” J. Phys. Chem. Solids31(5), 895–904 (1970).
[CrossRef]

Röpke, U.

Sahu, J. K.

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488 nm irradiation,” Opt. Lett.32(12), 1626–1628 (2007).
[CrossRef] [PubMed]

Schnadt, R.

R. Schnadt and J. Schneider, “The Electronic Structure of the Trapped-Hole Center in Smoky Quartz,” Phys. Kondens. Materie11, 19–42 (1970).

Schneider, J.

R. Schnadt and J. Schneider, “The Electronic Structure of the Trapped-Hole Center in Smoky Quartz,” Phys. Kondens. Materie11, 19–42 (1970).

Schwank, J. R.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Shaneyfelt, M. R.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Shluger, A. L.

A. V. Kimmel, P. V. Sushko, and A. L. Shluger, “Structure and spectroscopic properties of trapped holes in silica,” J. Non-Cryst. Solids353(5-7), 599–604 (2007).
[CrossRef]

Skuja, L.

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids239(1–3), 16–48 (1998).
[CrossRef]

Söderlund, M. J.

Sokolov, V. O.

V. O. Sokolov and V. B. Sulimov, “Threefold coordinated oxygen atom in silica glass,” J. Non-Cryst. Solids217(2–3), 167–172 (1997).
[CrossRef]

Sones, C.

Standish, R. J.

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

Sulimov, V. B.

V. O. Sokolov and V. B. Sulimov, “Threefold coordinated oxygen atom in silica glass,” J. Non-Cryst. Solids217(2–3), 167–172 (1997).
[CrossRef]

Sushko, P. V.

A. V. Kimmel, P. V. Sushko, and A. L. Shluger, “Structure and spectroscopic properties of trapped holes in silica,” J. Non-Cryst. Solids353(5-7), 599–604 (2007).
[CrossRef]

Tortech, B.

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

Unger, S.

Vezin, H.

Yoo, S.

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488 nm irradiation,” Opt. Lett.32(12), 1626–1628 (2007).
[CrossRef] [PubMed]

Am. Mineral. (1)

L. Pauling, “The nature of silicon-oxygen bonds,” Am. Mineral.65, 321 (1980).

Electron. Lett. (1)

S. Yoo, A. J. Boyland, R. J. Standish, and J. K. Sahu, “Measurement of photodarkening in Yb-doped aluminosilicate fibres at elevated temperature,” Electron. Lett.46(3), 233–244 (2010).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

S. Girard, Y. Ouerdane, B. Tortech, C. Marcandella, T. Robin, B. Dadier, J. Baggio, P. Paillet, V. Ferlet-Cavrois, A. Boukenter, J.-P. Meunier, J. R. Schwank, M. R. Shaneyfelt, P. E. Dodd, and E. W. Blackmore, “Radiation Effects on ytterbium- and Ytterbium/erbium-Doped Double-Clad Optical Fibers,” IEEE Trans. Nucl. Sci.56(6), 3293–3299 (2009).
[CrossRef]

J. Appl. Phys. (2)

D. L. Griscom, E. J. Friebele, K. J. Long, and J. W. Fleming, “Fundamental defect centers in glass: Electron spin resonance and optical absorption studies of irradiated phosphorous-doped silica glass and optical fibers,” J. Appl. Phys.54(7), 3743–3762 (1983).
[CrossRef]

K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Handa, “Aluminum or phosphorous co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys.59(10), 3430 (1986).
[CrossRef]

J. Non-Cryst. Solids (3)

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Figures (11)

Fig. 1
Fig. 1

(a) CC state II with two 0.5 bond order Si-O interactions (∙∙∙) and oxygen in σ-bond parallel to a TEB link (“1+TEB”), (b) CC state iii with one 1.55 and one 0.5 bond order Si-O interaction and oxygen in “½” bond parallel to a TEB link (“½+TEB”), (c) terminal state ii TEB link, (d) terminal state 0 with two separate oxygen anti-bond against the valence electron of Yb in a TEB link, (e) fully bridged SiO4 with two resonant bonds indicated by ellipses leading to four resonant 1.55 bond order Si-O interactions.

Fig. 2
Fig. 2

(a) Six-fold coordinated Yb3+ with three (AlO4, PO6 and = Si<O2 center) edge matches, (b) four-fold coordinated Yb3+ with one edge match = Si<O2 center, (c) AlO4 tetrahedron with four shared corners internally linked by two σ- and one TEB bond, (d) PO4 tetrahedron with three shared corners and one double bond oxygen internally linked by four σ- and one π-bond, (e) PO4 tetrahedron with two shared and two non-shared corners internally linked by four σ-bonds and the 5th electron in TEB (as in POHC of [17]).

Fig. 3
Fig. 3

(a) Potential bond energy as function of inter nuclei distance for single O-O sigma bond in parallel to (0 – 100% polarized) “½” (TEB↓ and TEB↑) bond, (b) Potential bond energy as function of inter nuclei distance for “½” bond in parallel to (0 – 100% polarized) “½” bond (TEB↓ and TEB↑).

Fig. 4
Fig. 4

State diagram for annealing of PD material with activation energies for transitions, note EB1 is II↑ and EB2 is II↓ covalent bond energy of Table 3 for the respective CC site ionic character.

Fig. 5
Fig. 5

Experimental temperature cycles (dots) from [11] with model (solid lines) anneal of pre-darkened fiber at 60-180 K/min rates for CC type/ state distribution as given in Table 5.

Fig. 6
Fig. 6

Experimental absorption spectra (dots) from [11] with (solid curves) model anneal of pre-darkened fiber F1. The measures are after PD at 296 K and after a 296K→ 598K→ 296K thermal cycle and further →419 K and →577 K.

Fig. 7
Fig. 7

Experimental temperature ramps (dots) from [12] with model anneal of pre-darkened fiber F2 at 5 – 20 K/min rates for CC type/ state distribution of Table 6.

Fig. 8
Fig. 8

Experimental absorption spectra (dots) from [12] with (solid curves) model anneal of pre-darkened fiber F2. The measures are for pre-darkened fiber at 296 K and after ramp to 453 K, 518 K, 547 K and 583 K for 5 K/min ramps.

Fig. 9
Fig. 9

Absorption as function of time for isothermal anneals at 510 K, 556 K and 676 K with dots from [13] with solid curve model calculations for F3 by CC type and state distribution as given in Table 7.

Fig. 10
Fig. 10

Absorption as function of time for 296 K→ 556 K ramp, 556 K anneal and 556K→ 920 K ramp given by open dots from [23], solid dots from [13] and with model solid curve for F3 by CC type and state distribution as given in Table 7.

Fig. 11
Fig. 11

(a) Probability frequency as function of demarcation energy ED for pre-darkened fibers F1, F2 and F3 by 2 K/min anneal ramps by induced loss at 1000 nm, and hereto corresponding (b) characteristic frequency νD as function of demarcation energy ED

Tables (7)

Tables Icon

Table 1 The Pauling ionic character of single bond interactions [19] and corresponding resonant TEB ionic character κ found as the geometric average of bonds where YO2 (AO2) are edge connections between Yb (Al) and = Si<O2 in tetrahedral units (Al is to share one corner with Yb). The |Y|/|A| in octahedral units hold one edge connection to = Si<O2 and two TEB linked edges to Y, A, |Y|, |A| or P|.

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Table 2 The potential energy for O-O bond, with spectroscopic term for molecular oxygen of [18] by: DE dissociation energy, r0 relaxed bond length and potential well shape parameters (a and a+).

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Table 3 The = Si<O2 (σ + TEB and ½ + TEB) covalent bond energy VC (eV) for bond length (pm) in XO2 or |X| CC types for TEB ionic character κ gives the phonon transition energy. State II↑ (EII↑ (eV) by σII↑ (eV) spread) and phonon assisted iii↑ (Eiii↑ by σiii↑) gives the bond to anti-bond photon excitation energy.

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Table 4 Transition activation energies

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Table 5 The fiber F1 distribution on XO2 and |X| CCs of ionic character κ, number of active sites relative to number of Yb (NAS/NYb) and initial distribution of tetrahedral and octahedral CCs on states (II and iii).

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Table 6 The fiber F2 distribution on XO2 and |X| CCs of ionic character κ, number of active CC sites relative to number of Yb (NS/NYb) and initial distribution on states (II and iii) for octahedral CCs.

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Table 7 Fiber F3 distribution on XO2 and |X| CCs of ionic character κ, number of active CC sites relative to number of sites in F1 and initial distribution on states (II and iii) for tetrahedral and octahedral CCs.

Equations (14)

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E B = V c (r,κ)+κEA(O) E IP (κ),
V b (r)= D E [ exp(2 a ± (r r 0 )2exp( a ± (r r 0 ) ],
V c (r,κ)= V σ (r)+κ E SZ (r), E SZ (r)= V σ+SZ (r) V σ (r),
V(t)=μEexp(iωt),
E II = V b* ( r II ) V b ( r II )κ E SZ ( r II ),
V b* ( r II )=(1+ R * (κ,T)) D E [ exp(2 a ± ( r II r 0 ) ],
R * (κ,T)=[ 1κ R * ]( R * δ R * T),
E (κ)=2.980.6κ
α(ν)= z κ z ρ(z)( σ a, g (ν, κ z )( N iii +2 N II )+ σ a, g II (ν, κ z ) N II ) ,
g X (ν, κ z )=exp(½ [ hν E X ( κ z ) σ X ( κ z ) ] 2 ),
k U,z (T,t)= N U,z (t) N T ν 0 [ exp( E U,z k B T )1 ] 1
d N U,z (t) dt = k U,z (T,t) N U,z (t)Δ N U,z (t)=(1exp( k U,z (T,t)Δt)) N U,z (t),
M ¯ ¯ Z =( A 1 k DT (T,t)/ k Σ1 0 0 0 0 1 A 1 0 A 3 k R (T,t)/ k Σ3 0 0 A 1 k 3 (T,t)/ k Σ1 1 A 2 A 3 k S1 (T,t)/ k Σ3 A 4 0 A 1 k 1 (T,t)/ k Σ1 A 2 k S2 (T,t)/ k Σ2 1 A 3 0 A 5 0 A 2 k 4 (T,t)/ k Σ2 0 1 A 4 0 0 0 A 3 k 2 (T,t)/ k Σ3 0 1 A 5 ),
p z,2 = M ¯ ¯ Z p z,1

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