Ultra-short ultra-intense lasers can provide unprecedented extreme physical conditions and new experimental methods, leading to significant applications in laser acceleration, plasma physics, strong field physics, and high-energy density physics. OPCPA technology is an important method for realizing ultrashort laser amplification. Currently, the highest output peak power based on OPCPA technology is up to 4.9 PW. To further increase the peak power, larger-size crystals are required, and the gain spectrum width can be compressed to tens of femtoseconds. The extreme light physical line station (SEL), an integral part of the hard X-ray free electron laser (SHINE) project, a significant national science and technology infrastructure in China, is undertaking the construction of an ultra-short and ultra-intense laser (SEL-100 PW), aiming for a remarkable peak power of 100 PW. The interaction between the ultra-high focused intensity produced by a 100 PW laser and hard X-ray free electron laser is used to explore the strong field quantum electrodynamics (QED) and other frontier science and technology fields. For ultra-intense and ultra-short laser-matter interaction experiments, the focused peak power density (focused intensity) of the laser is one of the most important technical indexes, which requires ultra-high peak laser power and a focused focal spot close to the diffraction limit level. The ability of a laser to focus near the diffraction limit is primarily limited by its spatial phase (wavefront) distortion. In addition to the static wavefront aberration introduced by optical component processing and mounting errors, dynamic wavefront aberration during the laser amplification process is also an important influencing factor. Additionally, the near-field spatial distribution of a laser beam determines the safety of high-energy lasers during transmission. To study the dynamic phase evolution of the 100 PW laser OPCPA high-energy main amplifier, this study focuses on the three-wave beam quality evolution in the process of OPCPA amplification. Furthermore, the influence of the intensity distribution and wavefront distribution of different pump light on the wavefront distortion of the amplified signal is studied.

Solving the three-wave coupling equation in the spatial domain is important for studying the spatial phase evolution characteristics in high-energy, ultra-wideband OPCPA processes. The split-step Fourier method is important for numerically solving the three-wave coupling equations. The basic idea was to divide the nonlinear crystal into multiple parts, in which the free propagation of light is considered first, and then the nonlinear effects were considered. Once a reasonable mathematical model was developed, the characteristics of the signal light under the experimental conditions of a 100 PW laser device were first calculated. Subsequently, the phase mismatch and intensity distribution of the pump light were considered. Furthermore, the effect of the spatial phase distribution and saturation effect of the pump light on the energy and spatial phase of the amplified signal was considered.

The energy of the amplified signal light can be obtained by simulating the experimental conditions of the 100 PW laser, and the spectrum and intensity distribution can satisfy the requirements of subsequent compression (energy >300 J, spectral range is 925 nm±100 nm)(Figs.2, 3). First, the phase mismatch is analyzed, and it can be concluded that the phase mismatch has a significant influence on the conversion efficiency and PV value of the amplified signal light phase; therefore, phase matching is an important condition for determining the output performance of OPCPA. Subsequently, the influence of the spatial phase distribution of the pump light on the amplified signal light is analyzed, which is proportional to the spatial derivative of the defocus of the pump light and occurs only in one dimension of the nonlinear angle (Fig.6). The influence of the intensity distribution of the pump light on the amplified signal light is analyzed. The spatial distribution of the pump light is imprinted on the phase of the amplified signal light, which is evident in the single-directional linear modulation and central-region protrusions (Figs.9, 10, 11, 12). Finally, the effect of the saturation effect on the amplified signal light is considered, and with a further increase in the pump energy, the signal light reaches saturation and the conversion efficiency decreases. The PV value of the amplified signal light phase also increases with the increase in energy, although the growth gradually decelerates (Fig.13).

It can be concluded that under the input condition of the amplifier stage, the output of ultrashort and ultra strong pulses on the order of 100 PW can be realized. The pump light phase experiences only a small overall change gradient due to the large spatial size of the pump light. Therefore, the phase distortion of the pump light has slight effect on the phase of the amplified signal, and the effect of the phase distortion of the pump light at the wavelength level of 10^-4 can be neglected in the design process. However, in a phase mismatch, the intensity distortion of the pump light has a significant impact on the intensity and phase of the signal light. Hence, the intensity distribution and phase matching of the pump light are necessary to realize a high-quality ultrashort pulse output in the design process. In subsequent studies, we will also conduct validation experiments to verify the simulation results.