We derive a theoretical description of the transient response for erbium fiber ring lasers, which includes the effects of amplified spontaneous emission and the large number of longitudinal modes that are present in large cavities. Based on these modified rate equations, the full transient period is simulated and compared with experimental measurements performed at 1560 nm, showing reasonable agreement with theory. Approximate analytical relations are also derived for the key characteristics of the laser response, including steady-state and transient parameters such as build-up time, frequency, and the decay constant of relaxation oscillations. The results are useful in the measurement of fiber laser parameters and in the design of novel fiber laser sensors, such as intracavity laser absorption sensors based on spectral narrowing during the transient period of power build-up in a laser cavity.
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