Extended matrix method for Gaussian pulse propagation and generalized mode-locking master equation

An extended matrix method to study pulse propagation in temporal Gaussian s ystems in presence of time and frequency detuning effects is developed and shown to be fully analogous to that used in the paraxial ray (or wave) theo ry of misaligned optical systems. A generalized Huygens integral with the k ernel expressed in terms of the temporal matrix elements is derived to desc ribe propagation of an arbitrary pulse through the system. In case of perio dic pulse propagation, such as pulse propagation in actively mode-locked la sers, a generalized time-domain master equation equivalent to the Huygens i ntegral propagator is rigorously derived. (C) 2001 Published by Elsevier Sc ience B.V.