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 propagation or oscillation behavior of the spatial Gaussian laser beam. In this letter, we apply these tools to the theory of the actively mode-locked Er/sup 3+/-doped 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 filter, the fiber with dispersion, and the fiber with nonlinearity. With the aid of the split-step q-parameter processing algorithm, the laser characteristics versus some typical laser parameters are investigated in detail.