# Compact 15 mJ Fiber-Solid Hybrid Hundred-Picosecond Laser Source for Laser Ablation on Copper
## 3 Experimental Results and Discussion
### Compensation for Self-Focusing and Thermally Induced Brefringence Effect  
First, it is worth noting that, for a millijoule-level laser amplifier, the nonuniformity of the input beam intensity will deteriorate the beam quality and even damage the optical components [32; 33]. To avoid the self-focusing effect caused by the phase distortion of the laser beam during the transmission process, we performed beam shaping on the laser beam from the regenerative amplifier. The beam-shaping device consists of a SA and a  
Figure 3: Temporal pulse profile of (**a**) before and (**b**) after broadening. SF1. The design of the SA adopts the grayscale coding mask method. The principle is to realize the modulation of the light transmission energy by adjusting the size and position of the microstructure of the light transmission unit at the edge of the SA, thereby achieving the purpose of beam shaping [34]. Subsequently, it is fabricated by photolithography and coating film. An enlarged view of the grayscale effect of the light-transmitting unit is shown in Figure 4, which shows the partial energy transmittance distribution. The result of the theoretical simulation is shown in Figure 5a, which depicts the intensity distribution of one-dimensional (1D) and two-dimensional (2D) views of the transverse field when the laser beam propagates 1 m via SA. The experimental measurement result is shown in Figure 5b, which is consistent with the theoretical result. The laser beam intensity of Nd:YAG regenerative amplifier is an ideal Gaussian distribution, which features high central intensity and relatively weak edge intensity. It is obvious from Figure 5 that the intensity distribution of the central part becomes relatively flat by using a soft-edge aperture. Therefore, SA can effectively reduce the central intensity of the laser beam and suppress the Fresnel diffraction. Then, we use the SF1 to relay-image the laser beam at SA to the image plane. Figure 4: The design layout of grayscale coding mask (enlarged view). The Nd:YAG rod crystal has extremely high energy storage under high pump power, which will cause quite obvious thermal effects. The Nd:YAG gain medium is heated and cooled simultaneously during operation, thus forming a nonuniform radial temperature distribution. As a result, the temperature gradient and thermal strain photo-elastic effect generated inside the Nd:YAG crystal rod will cause the nonuniformity of the refractive index distribution, resulting in a thermally induced birefringence effect and thermal lens effect. The thermally induced birefringence will lead to severe thermal depolarization and limit the output energy of picosecond laser source when the linearly polarized laser beam passes through the Nd:YAG crystal. Therefore, the compensation of the thermally induced birefringence is a significant issue that needs to be solved for the 10 mJ-level hundred-picosecond laser source, especially in a double-pass laser amplifier [35; 36; 37]. This is because, in the double-pass amplifier, the generated thermal depolarization power will be reflected back to the pre-stage regenerative amplifier, thereby damaging the optical components. In our double-pass amplifier, a 45\({}^{\circ}\) Faraday rotator (FR4) is arranged between the Nd:YAG 2 and the HR3 to compensate for thermal depolarization. When a linearly polarized laser beam is transmitted through the same Nd:YAG 2 with a 90\({}^{\circ}\) polarization rotation, since the phases of the tangential and radial components of the polarization are exchanged, each point in the cross-section of the Nd:YAG 2 gain crystal has the same phase delay. In other words, when the laser beam passes through Nd:YAG 2 for the second time, each point in the propagation direction should have exactly the same beam distribution as the first time to ensure that the thermally induced depolarization effect is perfectly compensated.