  Mode-locked lasers play a key role in modern science and technology. Not only
do they lay the foundation for ultrafast optics and play a central role in
nonlinear optics, but also they have important applications in imaging,
telecommunications, sensing, and computing. While substantial efforts have
focused on mode-locking the spectral modes of lasers, relatively little
attention has been paid to mode-locking their temporal modes. However, temporal
mode-locking presents ample opportunities to develop new technologies and to
study the intersection of nonlinear, non-Hermitian, and topological phenomena,
which, in recent years, has been a priority for the field of topological
physics. Here, we theoretically predict and experimentally realize topological
temporal mode-locking in a laser cavity with time-delayed intracavity
couplings. These couplings introduce non-Hermitian point-gap topology into the
temporal modes of our laser and conspire with an effective nonlocal
nonlinearity to generate mode-locked temporal structures in our laser cavity,
whose form can be tailored by suitably engineering the underlying couplings. We
harness this approach to realize a nonlinearity-driven non-Hermitian skin
effect, and we show that the topological temporal modes of our laser are robust
against disorder-induced localization. The flexibility and programmability of
our topological temporal mode-locking scheme reveals new opportunities to study
nonlinear and non-Hermitian topological phenomena in mode-locked photonic
resonators and could enable new applications of mode-locked lasers to sensing
and optical computing.
