  In this work, we identify and characterize intra-pulse intensity noise
shaping by saturable absorbers applied in mode-locked lasers and ultra-low
noise nonlinear fiber amplifiers. Reshaped intra-pulse intensity noise
distributions are shown to be inevitably interconnected with self-amplitude
modulation, the fundamental physical mechanism for initiation and stabilization
of ultra-short pulses in the steady-state of a mode-locked laser. A theoretical
model is used to describe the ultrafast saturation dynamics by an intra-pulse
noise transfer function for widely-applied slow and fast saturable absorbers.
For experimental verification of the theoretical results, spectrally-resolved
relative intensity noise measurements are applied on chirped input pulses to
enable the direct measurement of intra-pulse noise transfer functions using a
versatile experimental platform. It is further demonstrated, how the
characterized intra-pulse intensity noise distribution of ultrafast laser
systems can be utilized for quantum-limited intensity noise suppression via
tailored optical bandpass filtering.
