Simple analysis of Gaussian pulses and beams in mode-locked lasers

An ABCD matrix representation in space and time of a mode-locked laser is presented. The conventional stability concept of Gaussian beams in laser cavities implies, instead of stability, an equilibrium condition, which can be indifferent, stable, or unstable. It is further shown that when beam and pulse evolution in the laser are intertwined, stable mode locking can be the result of evolution of a noise spike in an otherwise unstable (in the conventional sense) cavity.