Three-level passively Q-switched fiber laser

We present a minimal yet predictive model for passively Q-switched erbium-doped fiber lasers (EDFLs) that incorporates a three-level gain system, pump modulation, and a saturable absorber (SA). The formulation explicitly includes a fast pump reservoir coupled algebraically to the metastable manifold via the scale-parameter ratio of the erbium lifetimes, enabling direct diagnosis of micro-timescale exchanges that shape pulse widths. Using averaged-power balances, amplified spontaneous emission (ASE)-seeded startup dynamics, and compact dimensionless equations, we analyze pulse generation, recovery times, and duty cycles as functions of pump power and output-coupler reflectivity. Numerical simulations calibrated to absolute power scaling yield sub-microsecond pulse widths and peak powers. Gaussian fits provide closed-form characterizations of the simulated pulses, while analytic recovery-time formulas agree with numerics within a few percent; verification against the quantum-defect inequality confirms physical consistency. We also show that the absorbed pump power is pulse-synchronously modulated in the SA regime, providing a simple, directly measurable diagnostic of the fast reservoir. Another novelty is that the proposed model is quasi-distributed: it accounts for the powers of the counter-propagating laser and spontaneous-emission waves, as well as a one-side-propagating pump wave, all averaged along the active fiber. This approximation is used for simulating the populations of the active ions corresponding to these powers, which, in turn, permits modeling the temporal laser processes. Importantly, in simulating the energy-level populations, the time-dependent absorbed pump power is fully accounted for.