Novel analytic theory for actively mode-locked fiber laser

The time-domain ABCD matrix formalism is based on the propagation of a Gaussian pulse which is characterized by the pulsewidth and chirp. In this paper, the time-domain ABCD matrix of the SPM (self phase modulation) is perfected so as to acquire more information. With the time-domain ABCD matrices of amplitude modulation, filtration from the optical bandpass, group velocity dispersion and SPM, the detailed characteristics of actively mode-locked fiber laser are described and the steady-state solutions are derived for two simple cases. The application of the formalism is also helpful to understand the mechanism of mode-locking in an actively mode-locked fiber laser.