We report a 2µm ultrafast solid-state Tm:Lu 2 O 3 laser, mode-locked by single-layer graphene, generating transform-limited∼410fs pulses, with a spectral width∼11.1nm at 2067nm. The maximum average output power is 270mW, at a pulse repetition frequency of 110MHz. This is a convenient high-power transformlimited laser at 2µm for various applications, such as laser surgery and material processing.Ultrafast lasers operating at∼2µm are of great interest due to their potential in various applications, e.g. telecoms 1 , medicine 2,3 , material processing 3,4 and environment monitoring 5 . They can be used for light detection and ranging measurements 5 and free-space optical communications 5 , due to the 2-2.5µm atmospheric transparency window 5 . Because water (main constituent of human tissue) absorbs more strongly at∼2µm (∼100/cm) 3 than at other conventional laser wavelengths (e.g.∼10/cm at∼1.5µm, and∼1/cm at∼1µm) 3 , sources working at∼2µm are promising for medical diagnostic 3 and laser surgery 3 . Currently, the dominant technique for ultrafast pulse generation at 2µm relies on semiconductor saturable absorber mirrors (SESAMs) 6,7 . In-GaAsSb quantum-well-based SESAMs have been used to mode-lock Tm,Ho:NaY(WO 4 ) 2 8 and Tm:Sc 2 O 3 9 lasers, generating 258fs pulses with 155mW output power at 2µm 8 , and 246fs pulses with 325mW output at 2.1µm 9 . However, SESAMs require complex growth techniques (e.g. molecular beam epitaxy 6 ), often combined with ion implantation 8,9 to reduce recovery time 6,7 .Nanotubes and graphene have emerged as promising saturable absorbers (SA), due to their low saturation intensity 10-14 , low-cost 10 and easy fabrication 12,14,15 . With nanotubes, broadband operation can be achieved by using a distribution of tube diameters 10,16 . With graphene, this is intrinsic, due to the gapless linear dispersion of Dirac electrons 12,14 . Ultrafast pulse generation at 0.8 17 , 1 18 , 1.3 19 and 1.5µm [10][11][12]14,[20][21][22][23] was demonstrated with graphene-based SAs (GSAs). Ref.25 reported a 1.94µm Tm-doped fiber laser mode-locked by a polymer composite with graphene produced by liquid phase exfoliation of graphite 14,24 . Compared to solidstate lasers, fiber lasers have some advantages, such as compact geometry and alignment-free operation. However, their output power is typically very low (∼mW 26 ) and their output spectrum generally has side-bands 26 . Solid-state lasers have the advantage, compared to fibre lasers, of sustaining ultrafast pulses with higher output power (typically≥100mW) 6,7 and better pulse quality (e.g. transform-limited with sideband-free profile in