Generalized method of moments for investigation of ultra-fast fiber amplifiers with gain-managed nonlinearity

Fiber-based ultrafast laser sources are rapidly expanding in both scientific and industrial domains, making them highly desirable for a variety of applications. The recently demonstrated gain-managed nonlinear (GMN) regime is particularly appealing because it enables the generation of high-energy, clean sub-50-fs pulses in a straightforward setup. However, the complex interaction between nonlinear pulse evolution and the longitudinally evolving gain shaping presents a scientific challenge in understanding how the parameters of GMN laser systems influence the characteristics of the output pulses. In this work, we introduce a computationally efficient approach using the generalized Method of Moments to analyze the dynamically evolving pulse characteristics. This method considers pulse asymmetry in GMN systems and assesses position- and frequency-dependent gain by solving population inversion rate equations. We apply our approach to demonstrate an effective multidimensional parameter optimization of a GMN amplifier.