# High-Power, High-Beam-Quality, Long-Pulse-Width 532 nm Laser Based on a 4f Optical System
## 4 Results and Discussion  
Figure 4 shows the relationship between the average power of the 532 nm laser and the pump current when the repetition rate is 10 kHz. The red curve represents the output  
Figure 3: Schematic diagram of a long-pulse-width 532 nm acousto-optic Q-switched laser. Figure 2: Schematic diagram of a 532 nm acousto-optic Q-switched laser with a cavity length of 600 mm. power of the 532 nm laser with the 4f optical system, i.e., the extended cavity, while the black curve represents the output power of the 532 nm laser with the short cavity. From Figure 4, it can be observed that as the pump current increases, the average power of the 532 nm laser also increases. However, when the pump current reaches between 16 and 19 A, the rate of increase in average power significantly slows down. This change is due to the thermal effects of the Nd:YAG crystal impacting the stability of the resonator, causing the laser to enter an unstable operating region. As the pump current continues to increase, the laser returns to a stable operating region, allowing the average power of the 532 nm laser to continue growing. Ultimately, at a pump current of 28 A, the output power of the 532 nm laser with the short cavity reaches a maximum of 127 W, while the output power of the 532 nm laser with the 4f optical system reaches a maximum of 112 W. Additionally, it can be observed that with the addition of the 4f optical system, the doubling of the laser cavity length leads to a decrease in laser power. The primary reason for the decrease in power is that the coating on the convex lens is not a 100% anti-reflective coating, which results in losses due to partial reflections from the two convex lens surfaces and absorption by the lens. The experiment used a photodetector (THORLABS, DET10A2) (Newton, NJ, USA) and an oscilloscope (Tektronix, TDS3054B) (Beaverton, OR, USA) to measure the pulse width. Figure 5 shows the relationship between the pulse width of the 532 nm laser and the pump current. The red curve represents the pulse width variation of the 532 nm laser with the 4f optical system, i.e., the extended cavity, while the black curve represents the pulse width variation of the 532 nm laser with the short cavity. From the figure, it is clear that the pulse width decreases as the pump current increases. When the pump current is 28 A, the pulse width of the short-cavity laser reaches 58 ns, while the pulse width of the 4f optical system extended-cavity laser reaches 85 ns. The pulse width broadening ratio is 46.5%, indicating a significant increase in pulse width. From Figure 5, it can be seen that the pulse width gradually decreases because, with increasing current, the gain gradually increases, leading to more particles reversing per unit time and thus a narrower pulse width for Q-switching. Additionally, losses within the laser cavity contribute to a reduced rate of pulse width broadening. The time series of the short-cavity 532 nm laser and 4f extended-cavity laser reveal the dynamic behavior of the laser under different pump currents, including periodicity, quasi periodicity, and possible chaotic roaming phenomena. The evolution path of the laser state in phase space indicates that the system may evolve into a chaotic attractor under specific pump currents [19]. This evolutionary process is consistent with known chaotic scenarios, such as period doubling and quasi periodic paths, indicating that pump current is a key parameter controlling the chaotic behavior of lasers. As the pump current increases,  
Figure 4: The output power of the short-cavity 532 nm laser and the 4f extended-cavity laser under different pump currents. the laser transitions from a stable laser output to a chaotic state. This transition can be observed through time series analysis, where periodic patterns are gradually replaced by more complex dynamics [20].