Operating regime analysis of mode-locking fiber laser with difference equation model

We proposed a difference equation model for fiber lasers mode-locked with nonlinear polarization evolution. It can be used to characterize intra-cavity nonlinear dynamics, such as steady one-pulse, period multiplication, multi-pulsing and chaos. The influence of adjusting wave-plate is also studied. By shifting linear phase bias, overdriving of saturable absorber is solved, and pulses of higher energy could be achieved. The modulation depth is found to affect the transition of intra-cavity dynamics.