We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature of the governing equations. Pulse-train uniformity is achieved in three parameter regimes in which the amplitude and the chirp decouple from the polarization and the phase. Alignment of the polarizer either near the slow or the fast axis of the fiber is sufficient to establish this stable mode locking.

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