Laser mode-locking with saturable absorbers

In this paper we describe a mode-locked laser in terms of traveling pulses of light. We show that the energy absorbed by a saturable absorber is a minimum if the pulselength is a minimum, and that two pulses are essentially as favorable as one if they meet at the position of the dye cell. Under steady-state pulsing conditions, however, we show that the pulses will have a width which depends on their energy. We find that for parameters appropriate to present Nd: glass experiments, the expected length is about 10
^-11
seconds, in agreement with observations. Finally, we demonstrate the rather surprising result that a linearly dispersive medium does not broaden the mode-locked laser pulses to first order.