  Strong two-photon absorption (TPA) in monolayer MoS2 is demonstrated in
contrast to saturable absorption (SA) in multilayer MoS2 under the excitation
of femtosecond laser pulses in the near infrared region. MoS2 in the forms of
monolayer single crystal and multilayer triangular islands are grown on either
quartz or SiO2/Si by employing the seeding method through chemistry vapor
deposition. The nonlinear transmission measurements reveal that monolayer MoS2
possesses a giant nonsaturation TPA coefficient, larger than that of
conventional semiconductors. As a result of TPA, two-photon pumped frequency
up-converted luminescence is observed directly in the monolayer MoS2. For the
multilayer MoS2, the SA response is demonstrated with the ratio of the
excited-state absorption cross section to ground-state cross section of 0.18.
In addition, the laser damage threshold of the monolayer MoS2 is 97 GW/cm2,
larger than that of the multilayer MoS2 of 78 GW/cm2.
