Quantitative modeling of nonlinear phase asymmetry for enhanced self-starting in all-PM NALM fiber oscillators

We report a quantitative framework for predicting and optimizing the self-starting performance of ultrafast all-polarization-maintaining (PM) nonlinear amplifying loop mirror (NALM) fiber oscillators, where reliable startup remains a key challenge. By introducing a nonlinear phase-asymmetry factor into an analytically defined figure of merit (FoM), the coupled effects of power splitting ratio, nonreciprocal phase bias, and structural asymmetry on small-signal transmission are unified into a single predictive model. The FoM accurately identifies the optimal startup condition and its evolution with increased loop asymmetry. To experimentally validate the theory, short segments of PM highly nonlinear fiber (HNLF) were inserted asymmetrically inside the loop to controllably enhance the nonlinear phase imbalance. As the HNLF length increases from 0 to 0.97 m, the pump threshold is reduced from 920 mW to 273 mW, in excellent agreement with the FoM-predicted trend. Numerical simulations further reproduce the measured spectral and temporal characteristics and enable quantitative extraction of the asymmetry factor, completing the model validation. This FoM-based approach thus provides the first experimentally verified quantitative guideline for designing robust, low-threshold, and environmentally stable PM-NALM fiber oscillators.