Considering that the broadband laser amplification system employs a pump power density of 12 kW/cm² and adopts room-temperature water cooling for heat dissipation, an increase in water flow rate can effectively enhance heat dissipation. On the one hand, the thicker gain medium is not conducive to heat dissipation. On the other hand, the gain medium should not be excessively thin. Otherwise, it will be difficult to meet the needs of structural strength, and deformation is prone to occur after water cooling. Therefore, in this scheme, a 6 mm thick Yb∶YGG with a doping level (atomic number fraction) of 1.75% is selected as the gain medium to yield a maximum single-pass gain of 1.87. According to simulation calculations, the highest peak power can be obtained via seeding by 30 μJ/5 nm/2 ns. The normalized time waveform of the chirp pulse outputs an uncompressed pulse duration of 0.79 ns [Fig. 2(a)]. The normalized spectrum of the chirp pulse has an output spectrum bandwidth of 1.86 nm [Fig. 2(b)]. The Fourier transform limited (FTL) pulse duration of the output pulse is 0.84 ps [Fig. 2(c)]. During the amplification process, the output energy and B integral change with the number of amplifier stages [Fig. 2(d)], with B integral always kept in the safe range. Assuming that the compression efficiency of each grating is 95%, the overall compression efficiency is about 80% by employing four grating compressors. After compression, the output pulse energy is about 20 J with an FTL pulse duration of 0.84 ps, and the peak power is higher than 20 TW.

The most widely employed gain medium based on Yb³⁺ is Yb∶YAG. There are primarily two approaches for developing table-top high-power pulse lasers based on Yb∶YAG high repetition frequency with low pulse energy (repetition rate >1 kHz) scheme and low repetition frequency with high energy (single pulse energy >5 J) scheme. Based on the former scheme, reported by Colorado State University, the average power was currently scaled up to 1100 W with a pulse of 1.1 J/4.5 ps/1 kHz. The maximum peak power, achieved by TRUMPF Scientific Lasers GmbH in Germany, was 0.78 TW with a pulse of 0.72 J/0.92 ps/1 kHz. The mode with a high repetition rate and low pulse energy generally adopts a thin-disk gain medium, which has a large body surface ratio. Limited by the system scale and thermal effect, the average power is difficult to be further improved. Based on the latter scheme, the maximum single pulse energy was created by the Petawatt?Field?Synthesizer (PFS) system with an output of 8.6 J/0.8 ps/10 Hz. Under the limitation of scale and thermal management, it is difficult to further increase the single pulse energy and average power. Therefore, in recent years, the DiPOLE device of Rutherford Appleton Laboratory, STFC, UK, as a representative has been successfully developed based on the low-temperature gas-cooled laminated Yb∶YAG amplifier configuration. However, the scale is huge, mainly for laser fusion related applications with limited applicability. To generate radiation sources such as X-rays, and efficiently study the phenomena of ultra-fast dynamics and high-energy density physics in plasma, we develop table-top, high repetition frequency, and high-energy picosecond lasers.

In response to the requirements of a table-top, high repetition frequency, and high-energy sub-picosecond laser system, we propose a novel amplification configuration based on spatial displacement?angle encoding. It has the potential to achieve an output of 20 J/1 ps/10 Hz. We introduce the amplification calculation model, utilizing a first-order approximation equation in broadband laser amplification dynamics based on Maxwell’s equations, and then analyze the design and characteristics of the proposed scheme. Initially, gain medium selection is conducted to identify a Yb-doped Y₃Ga₅O₁₂ suitable for room temperature. Next, the gain characteristics of the amplifier are optimized, with an analysis of the chirped pulse amplification (CPA) spectrum and dispersion properties carried out.

In the proposed scheme, Yb∶YGG is selected as the gain medium. Yb∶YGG not only possesses a suitable saturation fluence but also has a longer fluorescence lifetime and a larger absorption cross-section, which facilitates efficient energy storage. Additionally, the broader emission bandwidth enables the amplified pulses with a pulse duration of picosecond or even sub-picosecond.

We theoretically analyze the quasi-three-level Yb∶YGG broadband laser amplification scheme via numerical simulation by adopting dynamics equations in laser amplification. Meanwhile, a multi-pass Yb∶YGG-based amplifier with spatial displacement-angle encoding is proposed. The simulation results show that under the pump power density of 12 kW/cm² and pump duration of 790 μs, the most promising candidate is a 1.75% (atomic number fraction) doping Yb∶YGG with 6 mm thickness. A 30 μJ/5 nm/2 ns seed pulse can be amplified to 25 J, and the compressed pulse achieves an output of 20 J/0.84 ps with a peak power of 20 TW. To the best of our knowledge, the single-pulse energy is state-of-the-art in picosecond solid-state Yb medium lasers. Yb∶YGG is expected to play a key role in the development of 1030 nm lasers with high average power and high pulse energy. Therefore, our study has great significance for designing table-top, high repetition frequency, and high-energy picosecond lasers with peak powers greater than 10 TW.