## 3 Results  
The power curves of the array under free running (red), SBC at an OC with reflectivity of 33% (blue), VSBC with maximum output power (yellow), and VBSPC (green) are shown in Figure 3. With the coolant temperature of 25 \({}^{\circ}\)C, the power of the four devices was measured by Ophir FL500A. Too small power feedback leads to an unstable combining, and large overlapping reduces the combined power for VSBC. The output power of the laser bar is 30.2 W when it is under free running at 40 A, and the electro-optic conversion efficiency is 51.2%. The power of VSBC is 17.4 W at the same driven current and the combining efficiency is 57.6%. With the same current, the power of SBC at an OC with a reflectivity of 33% is 16.7 W and the beam combining efficiency is about 55%. The power of the VBSPC is 16.2 W, 7% lower than that of VSBC and the beam combining efficiency is 53.6%. The power loss of VBSPC compared with VSBC is caused by additional optical elements. The combining efficiency of VBSPC is 1.3% lower than that of SBC at an OC with a reflectivity of 33%. The reasons for the combining efficiency of the four devices lower than 71% [33] are (1) the laser array we used in this paper was coated with a reflectivity about 5% higher than 0.5%, (2) more optical components that bring energy loss were employed in VBSPC. From the measured result, we found that the grating brings a significant fraction of the loss, about 10%. VBSPC shows a combining efficiency close to that of SBC. The M\({}^{2}\) factors in the fast axis (M\({}^{2}\)\({}_{Y}\)) and slow axis (M\({}^{2}\)\({}_{X}\)) of a single emitter constituting the laser bar (blue), the SBC at an OC with reflectivity of 33% (green), VBSPC (red), and VSBC (yellow) are shown in Figure 4a,b from 15 A to 40 A. The M\({}^{2}\) measurement system is from Thorlabs (M2 MS). The M\({}^{2}\)\({}_{Y}\) of the four devices are very close in the range from 1.4 to 1.88 and increase slowly. At 40 A, the M\({}^{2}\)\({}_{Y}\) of SBC, VSBC, and VBSPC are higher  
Figure 3: The power–current characteristics of free running (red), SBC at an OC with reflectivity of 33% (blue), VSBC with maximum output power (yellow), and VBSPC (green). Figure 2: Schematic diagram of BSPC setup. than that of a single emitter. Maybe the reason is the imperfect overlapping of beams on the grating caused by spherical aberration of the transform leans. With the increase in driving current, the M\({}^{2}\)x values of the four devices increased very fast. The high driving current leads to the increase of high-order mode operation [25] and the effect of lateral carrier accumulation also brings the rise of M\({}^{2}\)x [37]. At 40A, the M\({}^{2}\)x of the single emitter, SBC, VSBC, and VBSPC increased to 8.97, 9.33, 7.4, and 3.92. M\({}^{2}\)x of VBSPC shows an improvement of 56%, 52%, and 57% better than that of the single emitter, VSBC, and SBC, respectively. The noticeable improvement of M\({}^{2}\)x is attributed to the mode selection of VSBC and the narrowed waist by BSPC. VBSPC improves beam quality significantly with an efficiency close to that of SBC. Another important parameter for laser is brightness, which is defined as follows:  
\[B=\frac{P}{\lambda^{2}M_{x}^{2}M_{y}^{2}} \tag{1}\]  
In Equation (1), the \(P\) and the \(\lambda\) are the output power and the center wavelength of the laser (940 nm), respectively. The brightness of SBC (green), SBC with BSPC (yellow), and VBSPC (red) with the increase in the driving current are shown in Figure 5. The brightness of SBC and VBSPC initially increases and reaches 110 MW\(\cdot\)cm\({}^{-2}\cdot\)sr\({}^{-1}\), 204.1 MW\(\cdot\)cm\({}^{-2}\cdot\)sr\({}^{-1}\), and 262 MW\(\cdot\)cm\({}^{-2}\cdot\)sr\({}^{-1}\) from 15 A to 40 A. The brightness of VBSPC is about 2.36 times and 1.28 times higher than that of SBC and VSBC. The attainment brightness of VBSPC is owing to the excellent M\({}^{2}\) factors and high combining efficiency.