Mode-locking theory for ultra-short few-femtosecond laser pulses

We propose a new model which is valid for ultra-fast pulse propagation in a mode-locked laser cavity in the few femtosecond to hundreds of attoseconds pulse regime, thus deriving the equivalent of the master mode-locking equation for ultra-short pulses that has dominated mode-locking theory for two decades. The short pulse equation with dissipative gain and loss terms allows for the generation of stable ultra-short optical pulses from initial white-noise, thus providing the first theoretical framework for quantifying the pulse dynamics and stability as pulseswidths approach the attosecond regime.