  Spatiotemporal mode-locking (STML) has become an emerging approach to realize
organized wavepackets in high-dimensional nonlinear photonic systems.
Mode-locking in one dimensional systems employs a saturable absorber to resist
fluctuations in the temporal domain. Analogous suppression of fluctuations in
the space-time domains to retain a consistent output should also exist for
STML. However, experimental evidence of such a resistance remains elusive, to
our knowledge. Here, we report experimental observation of such a
spatiotemporal stabilizer in STML, by embedding a spatial light modulator (SLM)
into a multi-mode fibre (MMF) laser. Mode decomposition reveals the mode
content remains steady for an STML state when applying phase perturbations on
the SLM. Conversely, the mode content changes significantly for a non-STML
lasing state. Numerical simulations confirm our observation and show that
spatial filtering and saturable absorber mainly contribute to the observed
stability. The capability to resist the spatial phase fluctuations is observed
to depend on the intracavity pulse energy as well as the modal pulse energy
condensed in the low-order modes. Our work constitutes another building block
for the concept of STML in multi-mode photonic systems.
