Complex Susceptibility of Saturated Erbium-Doped Fiber Lasers and Amplifiers

It is shown that the real part of the complex susceptibility of saturated erbium-doped fibers is fully characterized by the gain and a pair of readily determined material parameters. This result highlights an inconsistency in the standard theory, which is readily resolved. Explicit values for the linewidth broadening coefficient, which determines the rate of change of refractive index with gain, are presented for an erbium-doped fiber for the first time, based on theoretical inference from measured gain characteristics