Theoretical study on the actively mode-locked fiber laser with the q-parameter and the ABCD law

The q-parameter and the ABCD law are useful tools for analyzing the propaga tion or oscillation behavior of the spatial Gaussian laser beam. In this le tter, we apply these tools to the theory of the actively mode-locked Er3+-d oped fiber laser (AML-EDFL). Based on the q-parameter definition, we derive the ABCD matrices for the four primary elements which influence the pulse forming in the AML-EDFL, including the amplitude modulator, the optical fil ter, the fiber with dispersion, and the fiber with nonlinearity. With the a id of the split-step q-parameter processing algorithm, the laser characteri stics versus some typical laser parameters are investigated in detail.