Abstract

The description of the photodarkening (PD) kinetics of Yb-doped silica fibers with a stretched exponential function is analyzed in more detail, revealing a dependence of the determined PD parameter values on the measurement time. Thereby, serious uncertainties may occur in advanced interpretations of the results, e.g., the discussion of the rate constant as a function of the Yb inversion, if the measurement time is too short. A method to circumvent the problems of the fitting procedure is suggested, taking advantage of the self-similarity of the PD curves for different inversions. An exponent of 4.3±0.5 in the power-law dependence of the PD rate constant τ1 on the Yb inversion was found for a typical aluminium-codoped fiber.

© 2008 Optical Society of America

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References

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  1. J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, Proc. SPIE 6453, 64531E (2007).
    [CrossRef]
  2. A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.
  3. S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, Opt. Express 15, 14838 (2007).
    [CrossRef] [PubMed]
  4. J. Koponen, M. Söderlund, H. J. Hoffman, D. A. V. Kliner, J. P. Koplow, and M. Hotoleanu, Appl. Opt. 47, 1247 (2008).
    [CrossRef] [PubMed]
  5. J. Koponen, M. Laurila, and M. Hotoleanu, Appl. Opt. 47, 4522 (2008).
    [CrossRef] [PubMed]
  6. S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, Opt. Express 16, 15540 (2008).
    [CrossRef] [PubMed]
  7. P. D. Dragic, C. G. Carlson, and A. Croteau, Opt. Express 16, 4688 (2008).
    [CrossRef] [PubMed]
  8. M. Engholm and L. Norin, Opt. Express 16, 1260 (2008).
    [CrossRef] [PubMed]
  9. S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, Opt. Lett. 32, 1626 (2007).
    [CrossRef] [PubMed]

2008 (5)

2007 (3)

Basu, C.

Boyland, A. J.

Bufetov, I. A.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Carlson, C. G.

Croteau, A.

Dianov, E. M.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Dragic, P. D.

Engholm, M.

Hoffman, H. J.

J. Koponen, M. Söderlund, H. J. Hoffman, D. A. V. Kliner, J. P. Koplow, and M. Hotoleanu, Appl. Opt. 47, 1247 (2008).
[CrossRef] [PubMed]

J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, Proc. SPIE 6453, 64531E (2007).
[CrossRef]

Hotoleanu, M.

Jetschke, S.

Kirchhof, J.

Kliner, D.

J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, Proc. SPIE 6453, 64531E (2007).
[CrossRef]

Kliner, D. A. V.

Koplow, J.

J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, Proc. SPIE 6453, 64531E (2007).
[CrossRef]

Koplow, J. P.

Koponen, J.

Laurila, M.

Leich, M.

Melkumov, M. A.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Nilsson, J.

Norin, L.

Payne, D.

Röpke, U.

Sahu, J. K.

Schwuchow, A.

Shubin, A. V.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Smirnow, S. A.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Söderlund, M.

J. Koponen, M. Söderlund, H. J. Hoffman, D. A. V. Kliner, J. P. Koplow, and M. Hotoleanu, Appl. Opt. 47, 1247 (2008).
[CrossRef] [PubMed]

J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, Proc. SPIE 6453, 64531E (2007).
[CrossRef]

Sones, C.

Unger, S.

Yashkov, M. V.

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, in Conference on Lasers and Electro-Optics Europe-EQEC (Optical Society of America, 2007), paper CJ3-1-THU.

Yoo, S.

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Figures (4)

Fig. 1
Fig. 1

Time dependence of the PD excess loss α for two different Yb inversions (thin bright curves, stretched exponential functions obtained by the fitting procedure). Inset, systematic and statistical deviation of the PD curves α ( t ) from the stretched exponential function α Fit ( t ) .

Fig. 2
Fig. 2

Fit values of the PD parameters obtained by fitting with a stretched exponential function in dependence on the measurement time (Yb inversion 0.36 and 0.69, respectively). (a) Equilibrium loss α eq , (b) rate constant τ 1 (inset, stretching parameter β).

Fig. 3
Fig. 3

Determination of the slope of the PD rate constant versus the Yb inversion (log–log plot) from fit values of τ 1 for similar evolution states of PD (almost parallel dashed lines for equal α ( t m ) α eq ) and for incommensurable states (bold lines).

Fig. 4
Fig. 4

Self-similarity of the PD curves from Fig. 1. The measurement curve of I Yb 1 = 0.36 was transformed using τ 1 τ 2 = 16.4 (x axis) and α eq 2 α eq 1 = 1.78 (y axis).

Equations (6)

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α ( t ) = α eq [ 1 exp ( ( t τ ) β ) ] ,
τ 1 ( I Yb ) s ,
I Yb = σ abs σ abs + σ em 1 1 + P sat P p ,
σ abs A h ν p P p ( 1 I Yb ) = ( σ em A h ν p P p + 1 τ Yb ) I Yb .
α 2 ( t ) = α eq 2 α eq 1 α 1 ( τ 1 τ 2 t ) .
s = log ( τ 1 τ 2 ) log ( I Yb 2 I Yb 1 ) ,

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