Gain balance of pulses and noise in passive mode locking with slow saturable absorber

We employ a recently developed gain balance principle to study the problem of passive mode locking with a slow saturable absorber in the presence of noise and solitonic pulse compression. We calculate the compression of the chirped pulse under general conditions and show that there is a minimal achievable pulse width owing to stability requirements. We derive the slow-absorber mode locking parameter, which must exceed a pulse-width-dependent minimal value to sustain mode locking, and calculate the fraction of the total intracavity power that resides in the pulse. We show that choosing the system parameters in an attempt to achieve shorter pulses reduces the pulse power, which, in contrast to fast-absorber passive mode locking, can attain arbitrary small values. Finally, we discuss the modification of the continuum stability condition needed to account for the effect of noise.