Comments on “Study of the Complex Atomic Susceptibility of Erbium-Doped Fiber Amplifiers”

This comment aims to report and correct a mistake in the paper by Desurvire (J. Lightw. Technol., vol. 8, no. 10, pp. 1517-1527, Oct. 1990) with regard to the expression of the complex susceptibility of quasi-three-level laser systems. The derived susceptibility formula contradicts the assumption of thermal equilibrium between sublevels within each manifold and leads to the wrong conclusion that the real and imaginary parts of the susceptibility of saturated materials do not verify the Kramers-Kronig relations (KKR). The corrected formula for the susceptibility is hereby proposed. The poles of the susceptibility obtained with the new formula are all located in the upper half plane of the complex plane, in accordance with the principle of causality. Hence, the KKR should be valid in the saturated regime.