Operating regimes and performance optimization in mode-locked fiber lasers

We derive a theoretical model to characterize the mode-locking dynamics in a single-mode fiber laser cavity with a combination of waveplates and a passive polarizer. The averaging process results in the cubic-quintic Ginzburg-Landau equation (CQGLE) where all the coefficients depend explicitly on the setting of the waveplates as well as the fiber birefringence. A comparison between full numerical simulations and the CQGLE shows a good agreement that allows for characterizing the stability and operating regimes of the laser cavity. A low-dimensional model is developed via the method of proper orthogonal decomposition (POD) to study the multi-pulsing transition of the CQGLE, and the results agree qulitatively with the CQGLE model. The theory allows one to develop guidelines for engineering and optimizing high-energy, high peak-power pulses in the laser cavity.