# Passively Q-Switched Operation of a Tm,Ho:LuVO\({}_{4}\) Laser with a Graphene Saturable Absorber
## 1 Introduction  
Solid-state lasers emitting at 2 \(\upmu\)m with ultra-short pulses are used in many fields, such as remote sensing, medicine, and gas detection, as well as frequency conversion of mid-IR wavelengths, due to their high peak power and pulse energy [1; 2; 3; 4]. A passively Q-switched (PQS) with a saturable absorber (SA) is a compact way, in which microsecond (\(\upmu\)s) pulsed Q-switching operation in the mid-Mid-infrared wavelength range can be achieved. Recently, many SAs, such as carbon nanotubes, two-dimensional (2D) materials and ion-doped crystals, with broadband saturable absorption at 1-3 \(\upmu\)m, have been used for passive Q-switching operations [5; 6; 7; 8]. The carbon nanotubes are typically a one-dimensional (1D) SA material, which has been widely applied in fiber lasers emitting at wavelengths of 1-2 \(\upmu\)m [5; 9], but its performance is poor when used in solid-state lasers emitting at 2 \(\upmu\)m, because its bandwidth is limited by the diameter of single-walled carbon nanotubes, and its broadband saturable absorption characteristics rely on mixing single-walled carbon nanotubes with different diameters [9]. 2D materials are low-cost materials offering excellent performance and are used as the SA for PQS and mode-locked mode operations, due to their ultrafast recovery time, moderate modulation depth, high nonlinear effects and broadband saturable absorption [10; 11]. Compared withthe 1D and 2D SAs, ion-doped crystals, such as the Cr:ZnS crystal, have inherent defects which affect the stability, electronic structures and optical properties of ion-doped crystals [8; 12]. Among the 2D materials, graphene is a 2D sheet of sp2-bonded carbon atoms with a honeycomb lattice [13]: this has attracted attention from workers in many disciplines, especially as it has special capabilities with regard to nonlinear saturable absorption. Graphene has very good thermal conductivity and optical properties, due to its zero-bandgap structure, and pure non-defective single-layer graphene with a thermal conductivity of up to 5300 W/m\(\cdot\)K and its optical absorption is decided, independent of optical frequencies and optical conductivity constants [14]. Therefore, graphene is used as an SA in fiber and solid-state laser devices at a 1-2 \(\upmu\)m wavelength range to achieve stable PQS and mode-locked laser emissions, owning to its ultrafast recovery time and moderate modulation depths [14; 15; 16; 17; 18]. [PERSON] et al. have demonstrated that a PQS mode of Ytterbium lasers with a graphene SA possessing a 1.9-\(\upmu\)J pulse energy and a 190-ns pulse duration were achieved from Yb-doped calcium niobium gallium garnet disordered garnet crystal [15]. [PERSON] et al. demonstrated a PQS mode operation of Nd:LiF\({}_{4}\) laser with an SA of graphene in 2016. The output wavelengths of 1.31 and 1.32 \(\upmu\)m and an average output power of 1.33 W were acquired with the largest pulse energy of 17.3 \(\upmu\)J [16]. [PERSON] et al. demonstrated a Tm:KLu(WO\({}_{4}\))\({}_{2}\) laser with an SA in 2015, and a 310-mW average output power was achieved [17]. [PERSON] et al. demonstrated a PQS mode Ho:YVO\({}_{4}\) laser at 2052.1 nm with a graphene SA in 2016, and a 265.2-ns pulse width at 131.6 kHz was acquired [14]. [PERSON] et al. demonstrated a fiber laser operating at 1.94 \(\upmu\)m with a graphene SA in 2012, and a 3.6-ps pulse width and a 0.4-nJ energy at 6.46 MHz were obtained in a thulium-doped fiber laser [18]. Vanadate crystals are of particular interest as a potential laser host material, because they are suitable for rare-earth ions doped or co-doped lasers, such as Nd:GdVO\({}_{4}\), Nd:GdVO\({}_{4}\), Tm,Ho:YVO\({}_{4}\), Tm,Ho:GdVO\({}_{4}\), Ho:LVO\({}_{4}\) and Tm,Ho:LuVO\({}_{4}\)[8; 19; 20; 21; 22; 23; 24; 25]. Nd:GdVO\({}_{4}\) and Nd:YVO\({}_{4}\) lasers have been demonstrated at 1 \(\upmu\)m wavelength range [26; 27].