Study of the complex atomic susceptibility of erbium-doped fiber amplifiers

A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.<
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