## 1 Introduction  
Diode-pumped ytterbium-doped lasers have received continuous attention in past years due to their high conversion efficiency, high average power, and ultrashort pulse duration [1; 2]. The ytterbium ion has a very simple electronic energy level structure composed of only two manifolds, \({}^{2}\)F\({}_{5/2}\) and \({}^{2}\)F\({}_{7/2}\). The absorption peaks are located in the 900-980 nm range, which matches well with the emission bands of commercial high-power and high-brightness InGaAs diode lasers. Therefore, it is advantageous to realize high-power, highly efficient, and cost-effective ytterbium-doped solid-state lasers with diode pumping. Owing to the simple electronic energy level structure, Yb\({}^{3+}\) possesses unique laser properties so that many undesired effects, such as upconversion, excited-state absorption, cross-relaxation, and concentration quenching, may be reduced or eliminated, resulting in low quantum defect and low thermal load. In addition, the large lower-level splitting results in a broad emission bandwidth, which is beneficial to generate ultrashort pulses by various mode-locking techniques. Until now, a number of Yb\({}^{3+}\)-doped laser materials have been developed to generate femtosecond pulses [3; 4; 5; 6; 7]. The shortest pulse duration reported thus far was 32 fs in a Yb:CaGdAlO\({}_{4}\) oscillator optically pumped by a fiber laser [8]. Such femtosecond lasers in the 1 \(\upmu\)m wavelength range may be a valuable alternative to Ti:sapphire lasers in many applications. With the thin-disk scheme, diode-pumped ytterbium lasers with hundreds of watts of average power [9; 10; 11], tens of micro joules of pulse energy [12; 13; 14], and sub-100 fs pulse duration [15; 16] have been realized.  
Among the numerous Yb\({}^{3+}\)-doped materials, Yb\({}^{3+}\)-doped oxyorthosilicate exhibits outstanding laser performance in both continuous wave (CW) and mode-locking operation. Yb\({}^{3+}\) in oxyorthosilicate has a large ground state splitting to form a quasi-four-level band. As a result, the laser threshold is greatly reduced and the laser emission cross-section has a broad band, which is essential for producing ultrashort pulses down to sub-100 fs duration. The Yb\({}^{3+}\)-doped oxyorthosilicate family has several members, such as Yb:Y\({}_{2}\)SiO\({}_{5}\) (Yb:YSO), Yb:Lu\({}_{2}\)SiO\({}_{5}\) (Yb:LSO), Yb:SczSiO\({}_{5}\) (Yb:SSO), Yb:GdzSiO\({}_{5}\) (Yb:GSO) and their allowed compounds Yb:LYSO and Yb:GYSO. Extensive experiments on CW and mode-locking operations have been carried out with these laser crystals [17; 18; 19; 20; 21; 22; 23]. Among them, Yb:GSO has the largest ground state splitting of up to 1067 cm\({}^{-1}\) for any ytterbium-doped crystals and offers better thermal conductivity than Yb:YSO. However, a strong tendency to cleave along the (100) plane caused by the P2\({}_{1}\)/c monoclinic structure of GSO makes it difficult for practical laser applications. A feasible way to overcome the cleavage difficulty is to make an alloyed Yb:(Gd\({}_{1-x}\)Y\({}_{x}\))SiO\({}_{5}\) crystal which incorporates the large ground state splitting of Yb:GSO and good mechanical properties of Yb:YSO. The 50/50 alloyed Yb:GYSO crystal (\(x=0.5\)) has a ground state splitting of 995 cm\({}^{-1}\) and a fluorescence life time of 1.92 ms, indicating it as a promising candidate for the efficient generation of high-power femtosecond lasers.  
In this paper, we report the first diode-pumped Kerr-lens mode-locking (KLM) of a Yb:GYSO oscillator. Stable 141 fs pulses were produced at a central wavelength of 1094 nm with 10.1 nm bandwidth. With the pump power of 5 W, an average output power of 237 mW was obtained. The shortest pulse duration of only 55 fs was achieved by adjusting the position of the concave mirror and the angles of the end mirrors where the central wavelength was shifted to 1054 nm with a bandwidth of 23.5 nm. The output power was 27 mW.