  Transition metal dichalcogenides are known to possess large optical
nonlinearities and driving these materials at high intensities is desirable for
many applications. Understanding their optical responses under repetitive
intense excitation is essential to improve the performance limit of these
strong-field devices and to achieve efficient laser patterning. Here, we report
the incubation study of monolayer MoS${}_{2}$ and WS${}_{2}$ induced by 160 fs,
800 nm pulses in air to examine how their ablation threshold scales with the
number of admitted laser pulses. Both materials were shown to outperform
graphene and most bulk materials; specifically, MoS${}_{2}$ is as resistant to
radiation degradation as the best of the bulk thin films with a record fast
saturation. Our modeling provides convincing evidence that the small reduction
in threshold and fast saturation of MoS${}_{2}$ originates in its excellent
bonding integrity against radiation-induced softening. Sub-ablation damages, in
the forms of vacancies, lattice disorder, and nano-voids, were revealed by
transmission electron microscopy, photoluminescence, Raman, and second harmonic
generation studies, which were attributed to the observed incubation. For the
first time, a sub-ablation damage threshold is identified for monolayer
MoS${}_{2}$ to be 78% of single-shot ablation threshold, below which
MoS${}_{2}$ remains intact for many laser pulses. Our results firmly establish
MoS${}_{2}$ as a robust material for strong-field devices and for
high-throughput laser patterning.
