# Multistage Smoothing Compressor for Multistep Pulse Compressors
## 3 Multistage-Smoothing-Based MPC  
To address the limitations of a single typical MPC or a single asymmetric four-grating compressor, a new approach, called a multistage-smoothing-based MPC (MS-MPC), has been developed. This approach combines two beam-smoothing optical designs into a single compressor, where beam smoothing is separated into multiple stages. The operation of an MS-MPC can be separated into two optical setups. First, the input is a laser beam with no spatial chirp, and the spatial chirp width is increased step by step at every stage. The largest spatial chirp width and smoothest beam are obtained in the compressed output laser beam. This is called the forward MS-MPC, as shown in Figure 4a. In contrast, the second setup starts with the input laser beam having the largest spatial chirp, and the spatial chirp width decreases step by step at every stage until the output laser beam has the smallest or even zero spatial chirp width. This setup is called backward MS-MPC, as shown in Figure 4b. Here, only forward MS-MPC is discussed in detail. For the forward MS-MPC, a suitable spatial chirp is induced in the pre-compressor by using one or two prism pairs with a small apex angle and relatively short distances. According to the simulation results, the LSIM reduced rapidly from 2 to approximately 1.3 with a relative short distance between the 2 prisms [22]. Since the first grating has a relatively long nanosecond-pulse duration and has a high damage threshold, a relatively small spatial chirp is sufficient for protecting the first grating directly. In comparison to a spatial chirp line induced in one direction, the beam-smoothing effect is more effective when the spatial chirp induced in two directions [24]. To shield the compressor from all the random hotspots, one prism pair would be better located directly before the grating-based compressor. However, for laser beams larger than 500 mm, the prisms used here would  
Figure 4: Scheme showing the principles of (**a**) forward MS-MPC with Lb2 > Lb1, and (**b**) backward MS-MPC with La1 > La2. The post-compressor based on spatiotemporal focusing is not shown. Figure 3: Schematic diagram of wavefront aberration smoothing. (**a**) A near-field laser beam with a wavefront aberration without spatial chirp induces a hotspot in the far field; (**b**) the hotspot is smoothed into a line using a one-dimensional spatial chirp. be too thick and expensive. The prism pair can also be located before the relay imaging system for smaller beam sizes, imaging the well-smoothed laser beam directly onto the first grating. The asymmetric four-grating compressor is employed as the main compressor, and it induced a suitable spatial chirp width on the last grating. This directly induced spatial chirp effectively protects the last grating from the risk of damage. After beam smoothing in the pre-compressor stage, a suitable spatial chirp width is sufficient, corresponding to a small difference in distance between the two grating pairs. Note that the asymmetric four-grating compressor will induce the same amount of spectral dispersion to the compressed laser pulse as the symmetric four-grating compressor if the total distance of the two grating pairs is equal. Finally, a post-compressor is utilized, based on the spatiotemporal self-focusing effect, to compensate for the induced spatial chirp from both the prism pairs and the asymmetric four-grating compressor. Owing to the smoothed beam profile, the self-compression process in bulk-medium plates using negatively chirped pulses can also be added to the post-compressor to shorten the output pulse duration in the near future [27]. In addition to the compressor, the main amplifier may also experience crystal damage risk. Therefore, an additional beam-smoothing stage based on prism pairs can be added before the main amplifier to mitigate this risk. The laser beam in the main amplifier of 10 s to100 s PW laser systems should be more than 200 mm in diameter or side length.