## 3 Results and Discussion  
Through changing the transmittance of the output coupler, which were transmission of 50% (\(T\) = 50%) and transmission of 30% (\(T\) = 30%), influence on output characteristics of Ho:YVO\({}_{4}\) laser has been analyzed. The output couplers were selected because in a preliminary experiment we investigated with transmission of 10%, 20%, 30% and 50%. Stable PQS were achieved for \(T\) = 30% and 50%, as well as provided better stability and repeatability of the pulse train. With lower transmittances, damage was shown on the surface of graphene and instable pulse trains were observed on the oscilloscope. The following figures show the performance of the Ho Q-switched _versus_ the pump power. The pulsed wave operation started at 4.1 W absorbed pump power. Figure 2 shows the average output powers _versus_ the absorbed pump power. From Figure 2, we can see the average output powers increases as the increase of absorbed pump power. In PQS mode, the maximum average output power of 2.2 W can be obtained by using an output coupler with \(T\) = 30% at the absorbed pump power of 9.3 W. The slope efficiency is 12%. For the transmission of 50%, the slope efficiency is 9% with the maximum average output power of 1.5 W. In the continuous wave (CW) mode, the maximum output powers change to 3.35 W and 3.72 W, with the output couplers of \(T\) = 30% and \(T\) = 50%, respectively. The slope efficiencies are 17% and 20%. This is because the increase of pumping power will result in the increase of the ratio of the initial and threshold inversed population. The average output power and the efficiency of the Q-switched laser were lower than that in the CW mode, which could be attributed to the intra-cavity loss caused by inserting graphene for the Q-switched laser. The measured slope efficiency is well below the quantum efficiency. We attribute this to the low absorptivity of Ho crystal. Other factors that should be considered are difficulties with accurate mode matching between the pumping beam and oscillation beam. Figure 1: Schematic of the experimental setup. Figure 2: Variation of average output power _versus_ absorbed pump power. The variation of the pulse width and the repetition frequency _versus_ the absorbed pump power under different transmissions of output coupler are shown in Figures 3 and 4 respectively. From Figure 3, we can see that all the pulse width decreases with the increase of the pumping power. For the two different output couplers of \(T\) = 30% and \(T\) = 50%, the pulse widths decrease from 709.1 to 295.2 ns, from 810.5 to 421.5 ns, respectively. We attribute this pulse shortening to the larger gain of the resonator when the transmission of the output coupler is low. Low output coupler transmission is usually beneficial to the energy storage and to realize the pulsed laser easily, further improving the pulse energy and reducing the pulse duration of Q-switched laser. The population stored in the upper-level manifold became large under the low Q value of the resonator. When the graphene became bleached, the resonator was under a high Q value, the photon in the resonator appeared to increase rapidly at a shorter time that produced a narrower pulse duration with a slight change of the pump power. As for the repetition frequency, we can see from Figure 4 that they all increase with the augment of the pump power. For the \(T\) = 30% and \(T\) = 50%, the pulse repetition frequency (PRF) grows with the pump power from 31.8 to 131.6 kHz, from 44.6 to 122.7 kHz, respectively. Moreover, we can find that the pulse width and pulse repetition frequency of Ho:YVO\({}_{4}\) laser can be controlled by choosing an output coupler and changing the pump power through the analysis. According to the data of average output power and pulse repetition, we can calculate the pulse energy, which is shown in Figure 5. As we can see, the maximum output pulse energy is 16.8 \(\upmu\)J for 117.6 kHz repetition rate with T = 30%. The highest single-pulse energy shows at 9 W, which is not the highest absorbed power.