In contrast to traditional lasers utilizing chirped pulse amplification (CPA), such as Ti∶sapphire, amplified signal pulses from optical parametric chirped pulse amplification (OPCPA) inherently experience excess spectral phase distortions during the parametric amplification process besides the linear phase accumulated from crystal dispersion. These excess spectral phase distortions, also known as optical parametric phases (OPP), represent a significant issue that impedes pulse compression in petawatt-level OPCPA laser systems. With this in mind, the present study seeks to examine the evolution of OPP in the SILEX-II all-OPCPA multi-PW laser facility, developed at the Laser Fusion Research Center of the China Academy of Engineering Physics (CAEP). Analytical and numerical calculations are carried out to determine the total group delay dispersion (GDD) and third-order dispersion (TOD) induced by the OPP, from the high-intensity picosecond pulse-pumped front-end to high-energy nanosecond pulse-pumped power amplifiers. These findings are expected to provide valuable insights for the temporal compression of the SILEX-II laser system and inform the design of high-peak-power laser systems (from 10 PW to 100 PW) utilizing OPCPA technology.

The OPCPA process is modeled using the classical coupled-wave equations [Eq.(3)], under the assumption of a slowly varying electric field envelope. This model is numerically solved using the split-step Fourier algorithm. The focus of this study is exclusively on the OPCPA process and evolution of OPP. Consequently, it is assumed that the initial pulse entering the OPCPA only carries a GDD, which stretches the signal in the time domain to match the pump pulse. The evolution of the OPP is deduced by subtracting the initial GDD and the material dispersion of the parametric crystal from the spectral phase of the amplified pulse. The numerical results are compared with the analytical ones, obtained using Eq.(1) for both high-intensity picosecond pulse-pumped front-end and high-energy nanosecond pulse-pumped power amplifiers. Table 1 details the parameters used in the pump simulation, Table 2 outlines those used for the signal, and Table 3 itemizes those used for the nonlinear crystals.

The high-intensity picosecond pulse-pumped front end exhibits an OPP with a GDD of 71 fs2 and a TOD of 1092 fs3 [Fig.2(a)]. These values are obtained by fitting a third-order polynomial to the numerically calculated OPP within the wavelength range of 740-880 nm, which is the output spectrum range based on the numerical calculations [Fig.2(b)]. The GDD and TOD values obtained by fitting a polynomial to the analytically calculated OPP are 83 fs2 and 1370 fs3, respectively. Therefore, compared to the numerically calculated OPP, the main difference between the two lies in the TOD for the high-intensity picosecond pulse-pumped front end. For high-energy nanosecond pulse-pumped power amplifiers, including the preamplifier, booster amplifier, and main amplifier, the numerically calculated OPP is almost the same as the analytically calculated OPP [Figs.3(a) and 4(a)]. For the preamplifier, the GDD and TOD obtained from the OPP are 158 fs² and 2398 fs³, respectively, whereas for the booster and main amplifier, the total GDD and TOD induced by the OPP are 302 fs² and 2405 fs³, respectively. These results reveal that for the SILEX-II laser system, the OPP induces a GDD of 532 fs² and a TOD of 5782 fs³ [Fig.5(a)], and the peak intensity of the compressed pulse is only 43% of that of the Fourier transform-limited pulse [Fig.5(b)]. By compensating for the GDD of the OPP, the peak intensity of the compressed pulse can be increased to 94% compared to that of the Fourier transform-limited pulse [Fig.5(b)].

In conclusion, a thorough study of the OPP evolution in the SILEX-II full OPCPA system at the China Academy of Engineering Physics is conducted. The OPP evolution across the entire SILEX-II laser system is obtained by numerically solving coupled wave equations combined with analytical formulas. The results reveal that the SILEX-II laser system accumulates a GDD of up to 532 fs2 and a TOD of up to 5782 fs3 due to the optical parametric amplification process. Consequently, the peak intensity of the compressed pulse is only 43% of that of the Fourier transform-limited pulse. Further calculations indicate that after compensating for the GDD induced by the OPP, the peak intensity of the compressed pulse increases to 94% of that of the Fourier transform-limited pulse. These findings offer invaluable theoretical guidance for the temporal compression of the SILEX-II laser system. In practical applications, the grating distance in the compressor can be precisely adjusted to offset the extra GDD. Additionally, this study paves the way for the design of future 10-100 PW peak-power lasers utilizing full OPCPA technology, suggesting that global OPP control should be taken into consideration during the design process.