# Beam Control in an Intracavity Frequency-Doubling Semiconductor Disk Laser
## 3 Experimental Results and Discussion
Figure 7 illustrates the beam quality of the fundamental frequency laser under various input powers from 6 W to 25 W. It can be seen that the value of M\({}^{2}_{\rm x}\) (the black) is in the range from 2.70 to 3.65. By contrast, the M\({}^{2}_{\rm y}\) (the red) is much better, which varies from 1.35 to 1.62. The measured spot shows that the fundamental laser beam is not perfectly circular but elliptical as shown in the inset of Figure 7. At higher input power, fluctuation appears in the M\({}^{2}\) curve, which may be resulted from the completion of high-order modes. The beam quality of the green laser is represented in Figure 8. At the input power lower than 18 W, M\({}^{2}_{\rm x}\) is slightly better than M\({}^{2}_{\rm y}\), which is below 4.0 in this range. The lowest value of M\({}^{2}_{\rm x}\) is nearly 2. The values of M\({}^{2}_{\rm y}\) are around 3.4, and they are not sensitive to the input power. At higher input power, the beam quality becomes unstable especially for M\({}^{2}_{\rm x}\). So we measured the M\({}^{2}\) value multiple times for each input power, and the error bar is shown in Figure 8. For M\({}^{2}_{\rm x}\), the average value increases dramatically from 2.20 to 7.61 with the input power variating from 16 W to 25 W. The error enlarges with increasing input power, which is more likely due to more high-order mode generation and a correspondingly more unstable cavity. It is related to the beam quality fluctuations of the fundamental frequency laser as mentioned in Figure 1:0 In contrast, it is quite different for M\({}^{2}_{\rm y}\) at higher input power. Even though the error of M\({}^{2}_{\rm y}\) is larger than that at lower input power, but the error range is much lower  
Figure 1:1 Spectrum of the fundamental and green SDL. Figure 1:2 Output powers of the green SDL. than that of M\({}_{\rm x}^{2}\). The M\({}_{\rm y}^{2}\) is in the range from 2.0 to 3.6. It seems that the y-axis is much more stable than the x-axis, which is insensitive to input power. In order to improve the beam quality of the green laser under a high power operation, we introduce a simple aperture into the V-shaped cavity which is shown in Figure 1:3 The aperture is located between the SDL chip and M1, and the distance from the SDL is about 150 mm. Figure 9 shows the measured beam quality at input power of 25 W with different diameter sizes D of the aperture. The insets in Figure 9 are the beam profiles and the aperture used in this experiment. For this given power, the beam quality measurement starts from the diameter size of 1.5 mm. When reducing the aperture size, the values of the M\({}_{\rm x}^{2}\) and M\({}_{\rm y}^{2}\) slightly decline. However, when the aperture narrows to D \(<\) 1.0 mm, the M\({}_{\rm x}^{2}\) and M\({}_{\rm y}^{2}\) drop dramatically to approximate 1.5 at D = 0.8 mm (the smallest size of this aperture). The beam quality gets better both in x and y axis, and especially M\({}_{\rm x}^{2}\) exhibits a three- to four-fold improvement. Furthermore, the beam profile changes from ellipse to near circular shape shown in the inset of Figure 1:4 In such a V-shape laser cavity, the distances between the SDL chip and the mirrors should be carefully chosen for effective transverse mode selection. However, the optimal conditions can only be valid for a certain pump power range, increasing the difficulty in the design. In this paper, we utilize an aperture to control the beam size of the fundamental laser without changing the cavity configuration. Through this experiment, some important parameters like the optical pump  
Figure 1:5 Beam quality M\({}^{2}\) factors of the green laser in x and y directions. Figure 1:6 Beam quality M\({}^{2}\) factors of the fundamental laser in x and y directions. The inset is the beam profile at input power of 25 W.  
size can be determined to ensure fundamental mode operation, which could ensure mode matching and appropriate focusing into the non-linear crystal. We also investigate the dependences of output power and beam brightness on the aperture size.