[1] [1] D. E. McCumber, Phys. Rev. A 136, 954 (1964).

[2] [2] P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, San Diego, 1999).

[3] [3] D. Kouznetsov, J.-F. Bisson, K. Takaichi, and K. Ueda, J. Opt. Soc. Am. B 22, 1605 (2005).

[4] [4] R. S. Quimby, J. Appl. Phys. 92, 180 (2002).

[5] [5] R. M. Martin and R. S. Quimby, J. Opt. Soc. Am. B 23, 1770 (2006).

[6] [6] W. Li, H. Pan, L. Ding, H. Zeng, W. Lu, G. Zhao, C. Yan, L. Su, and J. Xu, Appl. Phys. Lett. 88, 221117 (2006).

[7] [7] W. Li, H. Pan, L. Ding, H. Zeng, G. Zhao, C. Yan, L. Su, and J. Xu, Opt. Express 14, 686 (2006).

[8] [8] C. Yan, G. Zhao, L. Zhang, J. Xu, X. Liang, D. Juan, W. Li, H. Pan, L. Ding, and H. Zeng, Solid State Commun. 137, 451 (2006).

[9] [9] D. Kouznetsov, "Broadband laser materials and the McCumber relation" http://www.ils.uec.ac.jp/~dima/2006CHINA/perpetual.pdf.

[10] [10] D. Kouznetsov, Comment on "Efficient diode-pumped Yb:Gd2SiO5 laser" Appl. Phys. Lett. 90, 066101 (2006).

[11] [11] G. Zhao, L. Su, J. Xua, and H. Zeng, Response to "Comment on 'Efficient diode-pumped Yb:Gd2SiO5 laser'" [Appl. Phys. Lett. 90, 066101 (2007)] Appl. Phys. Lett. 90, 066103 (2007).

[12] [12] R. C. Hilborn, Am. J. Phys. 50, 982 (1982).

[13] [13] A. Thorne, U. Litzen, and S. Johansson, Spectrophysics: Principles and Applications (Springer-Verlag, Berlin, 1999).

[14] [14] H. Haken, Laser Theory (Springer-Verlag, Berlin, 1984).

[15] [15] P. W. Milonni and J. H. Eberly, Lasers (John Wiley and Sons, New York, 1988).

[16] [16] J.-F. Bisson and D. Kouznetsov, "Saturation broadening and Kramers-Kronig relations in quasi-three-level lasers" J. Lightwave Technol. (under consideration).

[17] [17] E. Desurvire, J. Lightwave Technol. 8, 1517 (1990).

[18] [18] Until now, there is no evidence that the concept of the effective cross-sections does not apply to Yb:Gd2SiO5. The strong violation of the McCumber relation in graphics presented by Refs. [6-8] can be attributed also to the errors at the measurement of 'sigma'e('omega') caused by the reabsorption in vicinity of the zero-line[11].

[19] [19] M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, IEEE J. Quantum Electron. 38, 1629 (2002).