The ability to tune the optical response of a material via electrostatic gating is crucial for optoelectronic applications, such as electro-optic modulators, saturable absorbers, optical limiters, photodetectors and transparent electrodes. The band structure of single layer graphene (SLG), with zero-gap, linearly dispersive conduction and valence bands, enables an easy control of the Fermi energy E$_F$ and of the threshold for interband optical absorption. Here, we report the tunability of the SLG non-equilibrium optical response in the near-infrared (1000-1700nm/0.729-1.240eV), exploring a range of E$_F$ from -650 to 250 meV by ionic liquid gating. As E$_F$ increases from the Dirac point to the threshold for Pauli blocking of interband absorption, we observe a slow-down of the photobleaching relaxation dynamics, which we attribute to the quenching of optical phonon emission from photoexcited charge carriers. For E$_F$ exceeding the Pauli blocking threshold, photobleaching eventually turns into photoinduced absorption, due to hot electrons excitation increasing SLG absorption. The ability to control both recovery time and sign of nonequilibrium optical response by electrostatic gating makes SLG ideal for tunable saturable absorbers with controlled dynamics.
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