Novel Analytic Theory for Laser Mode-Locking

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, we will perfect this method and derive time-domain ABCD matrices for more optical devices. Especially, we extend this perfected theory to analyze the principle of passive mode-locking by reasonable approximation though, as we know, the output pulse generated from passive mode-locking fiber laser is of sech-shape. It is attractive because it can present a fairly apparent view to understand the mechanism of fiber lasers as well as analytic results to understand the pulse characteristics.