# Multistage Smoothing Compressor for Multistep Pulse Compressors
## 1 Introduction  
Owing to the great progress in chirped-pulse amplification (CPA) [1] and optical parametric chirped-pulse amplification (OPCPA) techniques [2], ultrahigh peak-power lasers have achieved significant improvements in recent years; more than fifty lasers worldwide have achieved peak powers of several hundred terawatts (TWs) [3; 4; 5; 6; 7] and even petawatts (PWs) [8]. Very recently, 2 10-PW lasers were in operation in the Shanghai Super-intense Ultrafast Laser (SULF) facility in China and the Extreme Light Infrastructure (ELI) in Europe [9; 10; 11; 12]. Furthermore, several 10 s to 100 s PW laser facilities have been proposed based on OPCPA [13; 14; 15; 16]; for instance, the SEL-100 PW facility [17; 18] is currently being constructed and is expected to reach 100 PW in the next few years.  
The CPA or OPCPA has broken through the bottleneck whereby amplification crystals are damaged due to their limited damage thresholds and confining size. However, as the laser's peak power reaches 10 s to 100 PW, a new problem arises in the pulse compressor: damage to the compression grating due to the limited damage threshold and size. Previously, optical designs in XCELS-200 PW, ELI-200 PW, and SEL-100 PW were all based on the multi-beam tiled-aperture combing method [19]. This beam-combing optical design is very complex and difficult to execute; it is highly sensitive to differences in the optical delay, pointing stability, wavefront, and dispersion among all of the beams [20; 21]. Recently, anovel method called the multistep pulse compressor (MPC) was proposed to solve the compression problem, in which the limited input/output pulse energy problem is transferred to the spatiotemporal properties of the input/output laser beam [22]. Furthermore, an asymmetric four-grating compressor was proposed to simplify the MPC [23]. However, these methods only directly protect the first or last grating, and there is a risk of damage to other critical optics.  
In this study, we propose a multistage-smoothing-based MPC (MS-MPC) not only to directly protect critical and costly optics such as the amplification crystal and compression gratings, but also to reduce the requirements for prism parameters. Unlike the typical symmetric four-grating compressor, the MS-MPC employs an asymmetric four-grating compressor as the main compressor, offering several notable advantages. First, the pre-compressor with a prism pair induces a relatively small and appropriate spatial chirp width, which is sufficient to smooth the laser beam for the safety of the first grating. It is easy and convenient to achieve this using a prism pair with a small apex angle and short prism-pair distance. Second, an asymmetric four-grating compressor can induce a suitable spatial chirp width with a small grating-pair distance difference to directly protect the last grating. Third, every grating in the asymmetric four-grating compressor is well protected, as the spatial chirp is induced directly in every stage. Therefore, even if there are defects/damages on one grating, they will not be transferred to the next grating due to the spatial chirp induced in every stage. However, in a traditional symmetric four-grating compressor, defects or wavefront-aberration at high/middle spatial frequencies before or on the first grating may cause hotspots to cause damage to the last grating. Furthermore, an additional prism-pair-based beam-smoothing stage can be added before the main amplifier to protect the important and expensive amplification crystal.