Saturable absorption is a nonlinear optical phenomenon that is characterized by the reduced optical loss at high light intensity. At low light intensity, the saturable absorber (SA) absorbs light and results in an optical loss. When the light intensity is increased, the available energy states become depleted, leading to a reduction in absorption. For semiconductors, the saturated optical absorption under strong excitation is in conjunction with the Pauli expulsion of occupying carriers at the edge of the filled conduction band thus allowing photons to penetrate through the material without further absorption. [1] When incorporated into a mode-locked laser cavity, the saturable absorption process begins from the inherent noise fluctuations of a laser cavity. A dominant noise spike with the highest intensity will saturate the absorber and decreases the absorbance loss such as the pedestal peaks. [2] Next, this noise spike is amplified in subsequent round trips until a stable pulse train is eventually formed. This favors the generation of ultrafast laser pulses over continuous-wave laser operation. During the formation of ultrafast laser pulses, the SA is operated either as slow or fast SA. The main difference between these two SA configurations is their relaxation time. The relaxation time of a slow SA is longer than its pulse duration measured from the mode-locked laser. The long time constant results in reduced saturation intensity due to slow recovery of absorption. [3] Therefore, the slow SA self-starts the modelocked laser at a lower power threshold. In contrast, the relaxation time of fast SA is shorter than its pulse duration measured from the mode-locked laser. Owing to the fast relaxation time, the electrons in the conduction band will return to the valence band at a period shorter than the pulse duration. This constitutes the higher power threshold to self-start the mode-locked laser.Despite the difficulty to self-start the mode-locking, the fast SA is responsible for the stabilization of the laser. The fast SA has ultrafast carrier relaxation time for the SA to recover from bleaching with minimal time. [4] Besides stabilization, ultrafast relaxation time is also crucial to shortening the pulse duration of the mode-locked laser. [5] Before the advent of ultrashort pulse with relaxation time ranging from a few ps to a few hundred fs, semiconductor saturable absorber mirror (SESAM) was demonstrated with a complex post-fabrication process. For instance, ion implantation is needed to reduce its relaxation time to ps time scale. This encourages the discovery of a material with sub-picosecond recovery time, such as carbon nanotube (CNT) [6] and graphene. [7] Both CNT and graphene have ultrafast and slow recovery from saturation. In a femtosecond laser, the CNT will typically act as a slow SA due to its recovery time of few ps, whereas the graphene will typically act as a fast SA due to its