Amplified spontaneous emission (ASE) and Rayleigh backscattering (RBS) in strongly pumped fiber amplifiers are studied, employing a rate equation model. Approximate expressions for the ASE and RBS, as well as for the amplifier noise figure are derived, based on approximate analytical expressions for the amplified signal, which are valid for both three-level and four-level systems. Numerical examples for rare-earth-doped fibers, show good agreement between these approximate expressions and the exact numerical solutions for strong pumping and for injected signals which are not too weak.
Amos A. Hardy and Ram Oron, "Amplified Spontaneous Emission and Rayleigh Backscattering in Strongly Pumped Fiber Amplifiers," J. Lightwave Technol. 16, 1865- (1998)