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-100PW 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-200PW, ELI-200PW, and SEL-100PW 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, a novel 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/middling 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.
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 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. An induced spatial chirp width of approximately 5 to 10 mm will not affect the main amplification. In fact, inducing a spatial chirp width of about 5 mm in one direction (X or Y) is enough to improve the LSIM of the amplified beam and protect the largest and most expensive crystal. Note that the beam smoothing at this stage is not essential because usually a 4f-system-based spatial filter is used before the main amplifier, and it is optional according to the requirements and conditions of every laser system.
The whole optical scheme of an MS-MPC is shown in
Figure 5; it includes a pre-compressor, a main compressor, and a post-compressor. Since the induced spatial chirp can smooth the laser beam in both the near field and far fields, the MS-MPC will significantly improve the safety of the important and expensive optics, and then increase the long-term operational efficiency of the laser system. Here, the PS_I, together with BE_1, will protect the largest crystal in the main amplifier; the spatial chirp induced by PS_II will protect DM_2, G1 and other important optics after PS_II. The spatial chirp induced by the asymmetric four-grating compressor will protect G4 and DM_3 directly. Furthermore, the DM_1 ensures that the wavefront before PS_II is perfect; the DM_2 guarantees the reflective wavefront by G1 is flat; the CP will compensate the wavefront distortions from G2 and G3, which is optional; and, finally, the DM_3 will be well controlled to obtain the highest focal intensity on the focal point FP.
4. Sample Design for a 100 PW Laser
To date, the central wavelengths of the proposed 100 s PW femtosecond laser facilities have mainly been located at approximately 925 nm. The optical schematic of a sample design for a 100 PW laser is also shown in
Figure 5. Since the PS_I is not indispensable in this MS-MPC, it will not be discussed in detail here. The laser beam after the main amplifier is assumed to be a 370 × 370 mm
2 beam with a 10th-order super-Gaussian profiles in both the X and Y directions. The laser pulse is positively chirped to approximately 4 ns, of which the transform limited pulse duration is approximately 14.3 fs. The central wavelength is 925 nm, and the spectral bandwidth is about 200 nm.
A spatial chirp width of approximately 5 mm is applied to the laser beam using two perpendicular prism pairs (PS_II) with a 15° apex angle and a separation distance of approximately 6 m. Then, a smoothed laser beam (~375 × 375 mm
2) is obtained, where the center of the 365 × 365 mm
2 region has full spectral bandwidth. A beam-expander and relay-imaging system BE_2 is used to expand the laser beam by 1.73 times (approximately) on both sides to ~650 × 650 mm
2, where the center 633 × 633 mm
2 region possesses full spectral bandwidth. Since the first grating G1 has a relatively high damage threshold owing to the nanosecond chirped pulse, which is approximately 2.7-folds higher than that of the last grating G4 with a femtosecond pulse, the bearable LSIM of G1 should be 1.6-folds higher than that on the last grating G4, considering 60% total compression efficiency. Then, the reserved intensity space for G1 is ~2.0 times (1.6 × 1.3) that of its damages threshold, which is a typical design value for a safe operation of most PW laser systems, if 1.3 times of the damage threshold fluence is reserved for the last grating. This means that G1 should usually be safe if we only consider the near-field affect. The PS_II can also remove the far-field affect from the laser beam before PS_II. Except for beam smoothing, the two prism pairs with a small apex angle may also be used to precisely correct the pulse front tilt and angular dispersion of the whole PW laser system. This is because all the transmitted plane optics in PW laser system, such as crystals in the amplifier, intentionally induced a wedge with a small angle to avoid the temporal contrast of the output laser pulse decreasing [
28]. These wedges induce angular dispersion and a pulse front tilt to the output laser beam, which affect the final focal intensity. The weak reflected beam from the surface of the prisms can also be used to monitor the spectrum, pointing stability, beam profile, time jitter, and wavefront of the laser beam.
After the pre-compressor, the spatiotemporal modified laser beam is guided into an asymmetric four-grating compressor with four identical 1400 lines/mm gold-coated gratings. The incident angle on the grating is set to approximately 61°, and this allows the beam size on the grating in the diffraction direction to be about 650/cos(61°) = 1340 mm. The perpendicular distances of the first and second grating pairs are set to 1215 mm and 1285 mm, respectively. As a result, there is a 70 mm length difference between the two grating pairs, and this induces a spatial chirp width of approximately 25 mm on the last grating. The approximate size (1365 × 650 mm2) of the beam on the last grating is still smaller than that of the largest grating with an approximate size of 1450 × 700 mm2. With this 25 mm spatial chirp width, the possible LSIM or hotspots, coming from both near-field and far-field effects of the optics after PS_II, can be effectively smoothed according to the previous simulation. When considering that the pre-compressor has already induced approximately 5 mm × 5 mm in the X and Y directions, which equals a 25 mm spatial chirp width in one direction, the LSIM with a period of less than 3 mm in the middling spatial frequency can also be smoothed well. As a result, a highly smoothing laser beam is achieved at the output of the asymmetric four-grating compressor. Note that the length difference between the two grating pairs can be conveniently varied according to different requirements; thus, different spatial chirp widths can be induced using the asymmetric four-grating compressor.
Since the total induced spatial chirp width on G2 is approximately 440 mm, it should be noted that the second grating G2 can cut light by a width of about 160 mm on both edges. The light cutting by the grating sharp edges induce diffraction and then LSIM to the laser beam after G2. According to the diffraction theory at a straight edge [
29], the diffracted light intensity varies with the distance between the diffracted light source and the receiving screen. The maximum diffraction intensity can reach approximately 1.5 times that of the initial intensity. Based on the above input parameters, the red dotted line in
Figure 6 shows the one-dimensional beam profile after G2 without light cutting. In the asymmetric four-grating compressor, the distance between G2 and G3 is variable. In our case, the shortest distance of the upper edge is set to 3 m, whereas the longest distance of the bottom edge is set to 5.5 m. The one-dimensional beam intensity profile on the G3 grating can be obtained by summing all the diffraction profiles at different wavelengths, as shown by the blue solid line in
Figure 6. This shows that the intensity of the light cutting on both edges is about one-fifth of the maximum intensity of the laser beam. According to the calculation, the LSIM induced by the edge diffraction does not exceed or affect the top-hat region; therefore, it does not cause damage risks to G3. The energy loss induced by light cutting is calculated to be approximately 1.9%. Note that the diffraction-induced LSIM by G2 is absolutely smoothed after G4 owing to the large spatial chirp width induced by the grating pair of G3 and G4. The spectral cutting of G2 has been used in many grating-based compressors. A kHz Ti:sapphire laser system with a beam diameter of 15 mm is used to prove the light cutting induced diffraction effect, as shown in
Figure 6c,e, where the light cutting occurs at the peak intensities of approximately 0.2 and 0.5. The simulation results of the edge diffraction are shown in
Figure 6b,d. The red lines and blue lines are one-dimensional beam intensity profiles without and with light cutting, respectively. The insets of
Figure 6c,e are the corresponding 2D beam profiles. The good agreement between the experimental and simulated results confirms the accuracy of the simulation program. It means the light-cutting-induced influence by G2 in the 100PW sample laser can be neglected.
Since the full-spectral-bandwidth regions on each grating will experience the strongest laser fluence, only the laser fluence of this region is considered. In the first grating, the effective beam size on the grating is approximately 1320 mm in the X-direction and 640 mm in the Y-direction. For an amplified laser pulse with 2500 J input, the laser fluence is 2500/(132 × 64) ≈ 296 mJ/cm
2, which is twofold lower than the grating damage threshold of approximately 600 mJ/cm
2 with a nanosecond pulse duration [
22,
30]. In the asymmetric four-grating compressor, the strongest laser fluence on the last grating G4 is decreased to approximately 296 × 0.60 = 178 mJ/cm
2 if the total compression efficiency is 60%. It is 1.28-fold lower than the damage threshold of a compressed femtosecond laser pulse, which is approximately 229 mJ/cm
2 [
22,
30]. Then, the 2500 × 0.60 = 1500 J compressed pulse can support 100 PW peak-power with a 15 fs pulse duration. Since the LSIM of the output laser beam can be smoothed to less than 1.1 after 3 stages of beam smoothing processes, it is theoretically possible to achieve 100 PW using this MS-MPC. However, in practice, achieving approximately 75 PW would be safer and more feasible for a real 10 s to 100 s PW laser system. This is because the laser fluence on the last grating would be almost 1.70 times lower than its damage threshold when the beam LSIM is smoothed to less than 1.2. Note that we only demonstrate the capabilities of this MS-MPC method for 10 s to 100 s of the PW system; the proposed parameters are not the optimized values, where enough margins have already been saved on many parameters, such as the beam size and light or spectral cutting.
After the main compressor with the asymmetric four-grating compressor setup, the output laser beam with smoothed spatial intensity and diffused wavefront aberration is focused by PM. At the focal point, the spatial chirp is automatically compensated owing to spatio- temporal focusing. Note that the damage threshold of the optics after the asymmetric four-grating compressor can be several times higher than that of the gratings. This is because the grating with a broad diffraction spectral bandwidth can only be coated with gold, which is the weakest film, whereas the reflective optics after asymmetric four-grating compressor can be coated with other kinds of coating film, of which the damage fluence threshold is several times higher. In the future, using a negative chirped pulse, this smoothed laser beam can be used to induce further pulse self-compression in a glass plate after the PM [
22,
27].
5. Discussion and Conclusions
Owing to the fixed and random hotspots induced by diffractions from dust, defects in the optics, and the spatially inhomogeneous pump beam, the LSIM of an amplified laser in a PW laser system is usually very high. To avoid laser-induced damage to important optics, especially gratings, the laser fluence on the grating must usually be kept below half of its damage threshold, which undoubtedly affects the maximum output pulse energy of a compressor. Aside from the peak power, the operating safety is also very important to maintain an economical PW laser system and increase its experimental efficiency.
As an improvement of MPC, the MS-MPC was proven to be able to achieve laser pulses with 10 s to 100 PW using a single laser beam. Based on the spatial chirp induced by grating pairs or prism pairs, both the LSIM in the near field and wavefront-aberration-induced hotspots in the far field can be effectively smoothed. Thus, the MS-MPC design can significantly improve the operating safety and increase the output peak power of PW laser systems. The proposed MS-MPC can directly protect important optics, such as the large crystal, all four gold-coated gratings, and deformable mirrors, from laser induced damage. Since the distances of the prism pairs or grating pairs can be easily varied, compressed laser beams with different spatial chirp widths can be conveniently achieved; these may induce different laser fields around the focal point and benefit laser physics experiments. Furthermore, this MS-MPC optical design can be easily applied to all existing PW laser facilities to improve their output pulse energy and operational safety.