A simple dynamic model of laser-gain-clamped erbium-doped fiber amplifiers (EDFA's) using ordinary differential equations is presented. The model not only provides a fast means of calculating EDFA gain dynamics, but also shows explicitly how the laser relaxation oscillation frequency and damping constant are affected by design parameters through analytical expressions. It is shown that the dynamic power excursion caused by relaxation oscillations can be reduced by increasing the oscillation frequency. The simplified model has two limitations: first, the amplified spontaneous emission (ASE) spectrum is not fully resolved and the noise figure can not be studied; second, the effect of spectral hole burning, which also causes gain excursion, can not be modeled. The first limitation can be removed by ASE-resolved modeling, where the concept of average inversion is also utilized to save computing time.
Qian Yu and Chongcheng Fan, "Simple Dynamic Model of All-Optical Gain-Clamped Erbium-Doped Fiber Amplifiers," J. Lightwave Technol. 17, 1166- (1999)