The fabrication of meter-sized-gratings limits the rapid development of worldwide femtosecond ultra-intense lasers with 10PW or higher peak power, and the grating tiling method is an alternative to this problem. But the unreliability and complexity of the traditional grating tiling, which has already been widely used in picosecond Petawatt lasers, challenges its application in femtosecond ultra-intense lasers for wider bandwidth and more sensitive grating attitude. In this paper, we demonstrate an experiment to compress an 800nm centered nanosecond deep-chirped-pulse to around 30fs by an object-image-grating self-tiling compressor, to the best of our knowledge, which is the shortest pulse compressed by a tiled grating compressor. Both the compression pulse and the focal spot are stable and close to the theoretical limits. We believe it is a feasible solution to the grating-size-limited problem for recent femtosecond 10PW Ti:sapphire or OPCPA laser projects.
© 2015 Optical Society of America
Recently, petawatt (PW), exawatt (EW) and even zettawatt (ZW)  femtosecond lasers are urgently required by several kinds of high-field physics applications, including material sciences, particle physics, nuclear physics, plasma physics, gravitational physics, and laboratory astrophysics. Over the last decade, different power-level femtosecond PW lasers have been demonstrated and planned worldwide. In 2003, a 0.85PW-33fs laser pulse was produced by Japan Atomic Energy Research Institute . In 2012, a 1.5PW-30fs laser pulse was generated by Advanced Photonics Research Institute in South Korea . In 2013, a 2.0PW-26fs laser pulse was achieved by Shanghai Institute of Optics and Fine Mechanics in China . And in 2015, a 5PW high-energy large-aperture Ti:sapphire amplifier was finished in Shanghai Institute of Optics and Fine Mechanics in China . Besides, several 10PW femtosecond lasers are under construction, for example ELI-Beamlines [6, 7 ], ELI-NP [6, 8 ], Apollon-10PW , and Vulcan-10PW . Furthermore, two EW laser facilities are in the planning stage, whose peak intensity will reach to as high as 0.2EW [11, 12 ]. At present, the chirped-pulse amplification (CPA)  or the optical parameter chirped-pulse amplification (OPCPA)  is expected to support a femtosecond PW output, and the next step the stimulated Raman backscattering in plasma is considered as an alternative method for further pulse compression and amplification . In a CPA or OPCPA PW laser, the temporal compression of chirped long-pulses is a key process to obtain ultra-short ultra-high lasers. The parallel grating pair method proposed by E. B. Treacy usually is used to introduce a large amount of negative chirp to reconstruct an unchirped original short pulse . To avoid the nonlinearity and the damage within the amplification process, the chirped-pulse stretching/compression ratio of the stretcher/compressor generally is larger than 10,000. And to prevent from the damage of gratings, the diameter of the final laser beam usually is expanded to a sub-meter-sized level. Therefore, very large gratings are required at the end of a PW laser, which challenges the manufacture of such gratings. At present, 1.3m gold gratings are urgently required by our femtosecond 10PW laser , and 2-meter-sized gratings are needed by the 10PW design of the ELI-beamlines in Czech Republic . Unfortunately, the world largest available size of gold gratings produced by Lawrence Livermore National Laboratory (U.S.A) is only 1m . Then the grating tiling method is proposed to meet the requirement by tiling multiple small-sized individual gratings coherently to form a large-sized tiled grating [18, 19 ]. Up to now, tiled gratings have been widely used in high-energy picosecond petawatt-class lasers for improving pulse energies as well as peak powers [20–23 ].
An ideal tiled grating for an ultrashort pulse laser requires that identical small-scale gratings should be added with no orientation or position errors. However, as shown in Fig. 1(a) , this will be challenged by six degrees of freedom between two adjacent small-scale gratings: line-density variation Δd (fabrication error), angular tilt (rotation about grating line), angular tip (rotation about grating vector), line rotation (in-plane rotation), longitudinal piston (out-of-plane piston), and lateral shift (in-plane shift). Because of the existence of six tiling errors, the focal spot and the compression pulse will deviate from the initial status spatially and temporally. The tiling errors will cause the focal spot degradation in three ways: horizontal separation, vertical separation and coherent splitting, which has been explained in . And the relationship between the six tiling errors and the three focal spot distributions is given in Fig. 1(a). It means the spatial distortion of the focal spot can be corrected by adjusting the three of the six tiling errors conveniently. But the temporal characteristics of the compression pulse require that angular tilt, angular tip and longitudinal piston must be removed completely . Especially, the temporal distortion of the compression pulse is very sensitive to the longitudinal piston between two adjacent small-scale gratings, however this tiling error is very hard to be detected [24, 25 ]. Let’s make a simple calculation, for a 800nm center wavelength laser and 1480g/mm gratings, taking a 36.3° Littrow configuration for example, a 1μm longitudinal piston error will cause an around 8.3fs time delay between two parts of the beam diffracted by two small-scale gratings within a tiled grating. Generally, high-energy picosecond petawatt-class lasers are based on Nd:glass amplification materials, and accordingly the final pulse durations vary from 300fs to 1ps. In this condition, the influence of a several-femtosecond time delay can be neglected. To the best of our knowledge, the shortest pulse compressed by a tiled grating compressor is 150fs, which is a 100TW fully diode-pumped solid state laser centered at 1030nm . However, if a tiled grating is used in a 30fs Ti:sapphire laser, this several-femtosecond time delay is too large to be ignored. And we think this is one main reason why no tiled grating has been introduced in femtosecond PW lasers until now.
The object-image-grating self-tiling method presented by our group, as shown in Fig. 1(b), could completely eliminate three tiling errors (line-density variation, angular tip, and longitudinal piston) in six due to the relationship between the object and the image, and the three left tiling errors can be detected directly by observing the focal spot . Thereby the near ideal tiled grating condition could be achieved and maintained conveniently. We think this method proposes a chance to introduce tided gratings into femtosecond PW-class lasers for solving the grating-size-limited problem. In 2014, we have demonstrated the capability of chirped-pulse compression and beam focusing of this grating tiling configuration in a sub-picosecond OPCPA laser, and a 490fs near-transform-limit pulse duration and a 90μm near-diffraction-limit focal spot are obtained, synchronously . With the rapid development of recent femtosecond PW-class lasers, especially the construction of our femtosecond 10PW laser facility, in this paper we demonstrate the temporal and spatial performance of a tiled grating compressor in a deep-chirped 30fs Ti:sapphire CPA laser for the first time. The object-image-grating self-tiling configuration is used, related simulations are proposed, the experiment process is described, and the result and the long-term performance are reported.
2. Simulations of two types of grating tiling
Compare the traditional grating tiling with the object-image-grating self-tiling, the object-image-grating self-tiling has two advantages for a femtosecond CPA laser: three tiling errors (angular tilt, angular tip and longitudinal piston) contributing to temporal distortions are reduced to only one (angular tilt); and, as shown in Fig. 1(b), angular tilt can be carefully removed by detecting the horizontal separation of the focal spot. However, the object-image relationship will double the vibration amout of angular tilt between the grating and its image. In this condtion, we simulate the spatial and temporal performances of the traditional grating tiling and the object-image-grating self-tiling for a 30fs laser in a same vibration situation, firstly. The simulation is based on a single-pass four-grating compressor, and only the second grating is chosen as the tiled grating for simplifying the simulation process. The center wavelength is 800nm, the grating is 1480g/mm, the incident angle is 52°, and the beam diameter is 15mm. The line-density variation between gratings is an immovable error that cannot be affected by the external environment. Then we assume the vibration of five motion tiling errors follows the Gaussian distribution with a zero mean. In an actual use condition, grating grooves are usually perpendicular to the horizontal plane to make sure input and output beams are parallel to the platform; therefore the values of angular tip and longitudinal piston are generally larger than those of the other three tiling errors due to the effect of the gravity, and similar results can be found in [29, 30 ]. Then, in this simulation the standard deviation of angular tilt, angular tip, line rotation, longitudinal piston and lateral shift is chosen as 1μm, 2μm, 1μm, 100nm and 50nm. When the five motion tiling errors are vibrating randomly, we simulate the evolutions of the focal spot and the compression pulse of two types of grating tiling, synchronously. And the focal spot and the compression pulse of the traditional grating tiling are illustrated in Figs. 2(a) and 2(c) , and those of the object-image-grating self-tiling are given in Figs. 2(b) and 2(d). The movie shows the compression pulse is more sensitive to the vibration rather than the focal spot, and the object-image-grating self-tiling could support a much better performance than the traditional grating tiling. Then, we believe it is reasonable to introduce this grating tiling into a short-pulse CPA laser.
3. Experiment platform
The demonstration experiment is accomplished in the branch beamline of our 200TW (30fs-6J) Ti:sapphire CPA laser, and this branch beamline could support a 1TW (30fs-30mJ) output. The main and the branch beamlines share a same front part including an oscillator, an Offner stretcher and an Ti:sapphire amplifier chain. An around 5% power is extracted by a splitter to the branch beamline at the end of the amplifier chain, and the split beam is delivered to a double-pass grating compressor to remove the temporal chirp for pulse compression. The oscillator is a commercial Ti:sapphire femtosecond source, which could support a 20fs output at the 800nm center wavelength. The Offner stretcher consists of a gold coated grating (Jobin Yvon, Horiba), a concave mirror, a convex mirror, a roof mirror, and a roof prism. The incident angle is 52°, the grating density is 1480g/mm, and the radii of curvature of the concave and convex mirrors are 1000 and 500mm, respectively. The grating is 250mm away from the center of curvature. The roof mirror and the roof prism are used to finish a fourth-pass. After the stretcher, the duration of the seed pulse is stretched to be more than 1ns. The amplification chain consists of a regenerative amplifier and three stages of multi-pass amplifiers, and the single pulse energy is amplified to be around 8.5J at the end of the amplification chain. Then around 5% pulse energy is split to the branch beamline and injected into the compressor, and the beam aperture at the compressor is around 15mm.
The compressor is a standard treacy configuration, which consists of two gold coated gratings (Jobin Yvon, Horiba) and a roof mirror. As shown in Fig. 3 , the surfaces as well as the grating grooves of two gratings are parallel to each other, and the roof mirror is perpendicular to the beam diffracted by the second grating and retro-reflects the beam back into the grating pair for the second-pass. The double-pass configuration could reduce the size of the compressor, decrease the number of gratings, and remove the spatial chirp of the beam. The second grating, as shown in Fig. 3, is an object-image-grating self-tiling grating, which contains a grating and a mirror. The mirror is carefully positioned perpendicular to the grating, and accordingly the grating can be used twice due to the reflection of the mirror. The angular dispersion at the first grating leads to a pulse spatial profile laterally broadening. Then at the second grating, the shorter wavelength components are directly diffracted by the grating to complete the first-pass, and the longer wavelength components are reflected and then diffracted by the mirror and the grating, respectively, and experience a secondary mirror reflection to complete the first-pass. Actually, the longer wavelength components can be considered as being directly diffracted by the image of the grating formed by the mirror. Then the grating and its image form a two-segment tiled grating, and there are no orientation or position errors within this tiled grating due to the right angle configuration of the grating and the mirror. Thereby, the actual optical paths for longer wavelength components exactly equal to the virtual paths directly diffracted by the image of the grating. In this condition, the object-image-grating self-tiling has a same optical performance with the traditional grating-grating tiling, and it has been explained and verified in our previous works [27, 28 ].
4. Experiment results
In order to examine the performance of the object-image-grating self-tiling (hereinafter to be referred as the tiled grating), the pulse compression experiments are carried out twice in a same laser condition for comparison: one with a single grating and the other with a tiled grating. Meanwhile a simple beamline is set up for the measurement of the spatial and temporal results. The output beam of the compressor is split into two, one is focused by a focal lens (f = 1010mm) into a CCD camera, and the other is injected into an ultrafast pulse measurement device (FASTLITE, Wizzler) . The focal spots captured by the CCD camera are given in Fig. 4 , and the pulse profiles and the corresponding spectral phases measured by the Wizzler are shown in Figs. 5(a) and 5(b) , respectively.
In the first round experiment, a 220mm (width) × 165mm (height) single grating is used as the second grating, which is large enough to avoid spectrum clipping. Before the experiment, the incident angle as well as the grating pair slant distance is carefully optimized. And the shortest pulse or best compression condition is obtained while the incident angle and the grating pair slant distance are around 52.8° and 1m. Figure 4(a) shows the captured focal spot, and its detail profile in the horizontal direction (perpendicular to the tiling gap) is illustrated by the blue dash line in Fig. 4(d). The spot size is 155μm, which is around 1.18 × diffraction-limit (illustrated by the gray solid line). The measured pulse profile is shown by the blue dash line in Fig. 5(a), and the spectrum and the spectral phase are given by the blue and green dash lines in Fig. 5(b). And the Fourier-transform-limit pulse calculated based on the spectrum is shown by the shadow in Fig. 5(a), as well. The pulse duration (FWHM) is around 26.8fs, which is 1.06 × Fourier-transform-limit. And the spectral phase distortion over the 80nm spectrum of the pulse is around 3rad.
In the second round experiment, we insert a 200mm (width) × 165mm (height) silver coated mirror close to the middle of the second grating to set up an object-image-grating self-tiling grating. The mirror is perpendicular to the grating, and the mirror-grating gap is controlled as small as possible, which is around 3mm. Then half the size of the grating is blocked by the mirror, but the effective optical size of the tiled grating is still 220mm which equals to the size of the single grating in the first round experiment. At the beginning, as shown in Fig. 4(c), we find the focal spot in the CCD camera separates into two. Then we carefully adjust the angular tilt (rotation about the vertical axis) and the angular tip (rotation about the horizontal axis) of the mirror to remove the horizontal and vertical separations between two spots, and a single focal spot is achieved as shown in Fig. 4(b). This means the mirror is perpendicular to the grating and parallel to the grating grooves, and in other words the tiling errors within this tiled grating are removed . We can find that the difference between two focal spots shown in Figs. 4(a) and 4(b) is very small. The detail horizontal profile of the focal spot obtained in this round experiment is given by the red solid line in Fig. 4(d), and the spot size is around 160μm (1.22 × diffraction-limit). The pulse profile, the spectrum and the spectral phase measured by the Wizzler are illustrated by the red solid line in Fig. 5(a), the red solid line and the green solid line in Fig. 5(b). The pulse duration (FWHM) is around 27.3fs (1.08 × Fourier-transform-limit), and the spectral phase distortion over the whole spectrum of the pulse is around 4rad.
The results obtained in the two sets of experiments, as given in Table 1 , show that the tiled grating cannot achieve as excellent spatial and temporal performances as the single grating. However, the differences in our demonstration experiment are small, and we believe a 160μm (1.22 × diffraction-limit) focal spot, a 27.3fs (1.08 × Fourier-transform-limit) pulse duration and a 4rad spectral phase distortion could meet the design and application requirements of most femtosecond PW-class lasers.
Besides, the long-term stability is another problem for a tiled grating. During our experiment, we find that the stability of pulse durations is much more sensitive to the environment rather than that of focal spots. We measured the variation of pulse durations in the two sets of experiments more than 100 shots independently, and the result is illustrated by blue squares and red circles in Fig. 6(a) . The result shows that the pulse duration in the first and the second round experiment jitters around 27fs and 30fs, respectively, and which is more stable in the first round than in the second round. Figure 6(b) gives the possibility density functions of Fig. 6(a), and we can find that the mean of the pulse duration in the first and the second round experiment is 27.4fs and 30.0fs, respectively, and the corresponding standard deviation is 0.80fs and 1.24fs. It is very easy to understand that a single grating could achieve more stable compression pulses rather than a tiled grating. However, the comparison experiment shows the difference between two sets of experiments is small, and the tiled grating compressor could support an around 30fs pulse duration. We should emphasize that the stability experiment is carried out in free conditions without any active feedback controls. And then, the performance could be improved while a close-loop control system is added to the tiled grating.
During our experiment, as shown by the red solid line in Fig. 5(b), the grating-mirror gap within the tiled grating leads to a spectral gap around the center wavelength in the spectrum of the pulse. According to previous works , this spectral gap is relevant to the beam diameter. In our experiment, the beam diameter is around 15mm, and the spectral gap is obvious. However, for larger beam diameters, this spectral gap will be smeared out. Besides, we can find that the reflection efficiency of the mirror within the tiled grating reduces the intensities of longer wavelength components. These two factors cause a modulation to the spectrum of the pulse compressed by the tiled grating compressor. The influence of this spectral modulation on the pulse profile has already been simulated in our previous works , and it will not lead to an obvious pulse distortion, except a tiny pulse broadening. However, the overall energy throughput for the compressor will decrease, and an around 13% extra energy loss is observed in our experiment. This energy loss could be reduced to only around 5% by increasing the reflection efficiency of the mirror, for example replacing the silver mirror with a multilayer dielectric mirror.
As shown in Fig. 5(a), for measurement pulses in the two sets of experiments, there is a small pre-pulse before the main pulse, which is caused by the small amount of the uncompensated third-order dispersion. For the tiled grating (in the second round experiment), the power of the pre-pulse increases, and an overlap in time domain occurs between the pre-pulse and the main pulse. This small distortion is mainly relevant to the spectral phase distortion, as well as the tiny broadening of the main pulse caused by the spectral modulation. As shown in Fig. 5(b), compared with the spectral phase obtained in the first round experiment (with the single grating), the spectral phase achieved in the second round experiment (with the tiled grating) has several sharp changes around the center wavelength. This spectral phase distortion is caused by the grating-mirror gap, which cannot be completely avoided for a tiled grating. Therefore, this temporal and spectral phase distortion should be considered while a tiled grating design is introduced in a femtosecond laser.
In this demonstration only the second grating in the compressor is an tiled grating due to a small beam diameter. In a 10PW femtosecond laser, the beam diameter will be around 600mm, and accordingly the effective optical size of each grating should be doubled by this method. For the engineering consideration, we have already discussed and analized the potential problems: pulse overlap , zeroth-order reflection beam [30, 34 ], tiling stability  and spectrum amplitude modulation [28, 33 ] theoretically and experimentally in our previous works, and these will not lead to unacceptable adverse influences.
In conclusion, we have introduced the demonstration result of a pulse compression experiment with a tiled grating compressor in a deep-chirped Ti:sapphire CPA laser. A >1ns chirped pulse is compressed to 27.3fs, which is 1.08 × Fourier-transform-limit. And the spectral phase distortion over the 80nm spectrum of the pulse is only 4rad. The long-term test shows the pulse duration could operate at 30fs with a standard deviation of 1.24fs. And the beam outputted by the tiled grating compressor could be focused to a 160μm focal spot, which is 1.22 × diffraction-limit. To the best of our knowledge, this is the shortest compression pulse achieved by a tiled grating compressor in a high power femtosecond CPA laser. In the future, this compressor structure will be introduced in our femtosecond PW-class laser to solve the grating-size-limited problem for achieving a higher peak power.
This work was supported by the National Basic Research Program of China (Grant no. 2011CB808101), National Natural Science Foundation of China (NSFC) (Grant nos. 11304296, 61078037, 11127901, 11134010, and 11204328).
References and links
1. T. Tajima and G. Mourou, “Zettawatt-exawatt lasers and their applications in ultrastrong-field physics,” Phys. Rev. Accel. Beams 5(3), 031301 (2002). [CrossRef]
3. T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20(10), 10807–10815 (2012). [CrossRef] [PubMed]
4. Y. Chu, X. Liang, L. Yu, Y. Xu, L. Xu, L. Ma, X. Lu, Y. Liu, Y. Leng, R. Li, and Z. Xu, “High-contrast 2.0 Petawatt Ti:sapphire laser system,” Opt. Express 21(24), 29231–29239 (2013). [CrossRef] [PubMed]
5. Y. Chu, Z. Gan, X. Liang, L. Yu, X. Lu, C. Wang, X. Wang, L. Xu, H. Lu, D. Yin, Y. Leng, R. Li, and Z. Xu, “High-energy large-aperture Ti:sapphire amplifier for 5 PW laser pulses,” Opt. Lett. 40(21), 5011–5014 (2015). [CrossRef] [PubMed]
7. D. Kramer, J. Novák, and B. Rus, “Hybrid compressor design for a 10PW laser,” EPJ Web Conferences 48, 00010 (2013). [CrossRef]
8. R. Dabu, “High power femtosecond lasers at ELI-NP,” AIP Conf. Proc. 1645, 219–227 (2015). [CrossRef]
9. D. N. Papadopoulos, C. L. Blanc, G. Chériaux, P. Georges, J. P. Zou, G. Mennerat, F. Druon, A. Pellegrina, P. Ramirez, F. Giambruno, A. Fréneaux, F. Leconte, D. Badarau, J. M. Boudenne, P. Audebert, D. Fournet, T. Valloton, C. Greverie, J. L. Paillard, J. L. Veray, M. Pina, P. Monot, P. Martin, F. Mathieu, J. P. Chambaret, and F. Amiranoff, “The Apollon-10P project: Design and current status,” in Advanced Solid-State Lasers Congress, OSA Technical Digest (Optical Society of America, 2013), paper ATu3A.43. [CrossRef]
10. A. Lyachev, O. Chekhlov, J. Collier, R. Clarke, M. Galimberti, C. Hernandez-Gomez, P. Matousek, I. Musgrave, D. Neely, P. Norreys, I. Ross, Y. Tang, T. Winstone, and B. Wyborn, “The 10PW OPCPA Vulcan Laser Upgrade,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2011), paper HThE2.
11. G. A. Mourou, G. Korn, W. Sandner, and J. L. Collier, WHITEBOOK ELI-Extreme Light Infrastructure, Science and Technology with Ultra-Intense Lasers (Andreas Thoss, 2011).
12. The Institute of Applied Physics, the Russian Academy of Sciences, “Exawatt Center for Extreme Light Studies (XCELS),” http://www.xcels.iapras.ru/
13. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985). [CrossRef]
14. A. Dubietis, G. Jonušauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4), 437–440 (1992). [CrossRef]
15. J. Ren, W. Cheng, S. Li, and S. Suckewer, “A new method for generating ultraintense and ultrashort laser pulses,” Nat. Phys. 3(10), 732–736 (2007). [CrossRef]
16. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5(9), 454–458 (1969). [CrossRef]
17. J. Britten, “Gratings Guru,” https://lasers.llnl.gov/about/who-works-at-nif/people-profiles/jerry-britten.
18. T. Zhang, M. Yonemura, and Y. Kato, “An array-grating compressor for high-power chirped-pulse amplification lasers,” Opt. Commun. 145(1–6), 367–376 (1998). [CrossRef]
19. T. J. Kessler, J. Bunkenburg, H. Huang, A. Kozlov, and D. D. Meyerhofer, “Demonstration of coherent addition of multiple gratings for high-energy chirped-pulse-amplified lasers,” Opt. Lett. 29(6), 635–637 (2004). [CrossRef] [PubMed]
21. J. Qiao, A. Kalb, M. J. Guardalben, G. King, D. Canning, and J. H. Kelly, “Large-aperture grating tiling by interferometry for petawatt chirped-pulse-amplification systems,” Opt. Express 15(15), 9562–9574 (2007). [CrossRef] [PubMed]
22. H. Habara, G. Xu, T. Jitsuno, R. Kodama, K. Suzuki, K. Sawai, K. Kondo, N. Miyanaga, K. A. Tanaka, K. Mima, M. C. Rushford, J. A. Britten, and C. P. J. Barty, “Pulse compression and beam focusing with segmented diffraction gratings in a high-power chirped-pulse amplification glass laser system,” Opt. Lett. 35(11), 1783–1785 (2010). [CrossRef] [PubMed]
23. N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coïc, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010). [CrossRef] [PubMed]
25. Y. Zuo, X. Wei, X. Wang, Q. Zhu, R. Ren, Z. Huang, H. Liu, and C. Ying, “Eliminating the longitudinal piston error between tiled gratings by angle tuning,” Opt. Lett. 32(3), 280–282 (2007). [CrossRef] [PubMed]
26. M. Hornung, R. Bödefeld, M. Siebold, M. Schnepp, J. Hein, R. Sauerbrey, and M. C. Kaluza, “Alignment of a tiled-grating compressor in a high-power chirped-pulse amplification laser system,” Appl. Opt. 46(30), 7432–7435 (2007). [CrossRef] [PubMed]
28. Z. Li, T. Wang, G. Xu, X. Ouyang, D. Li, H. Wei, J. Yu, L. Chen, and Y. Dai, “Demonstration of chirped-pulse compression with an object-image-grating self-tiling grating compressor,” J. Mod. Opt. 61(6), 495–499 (2014). [CrossRef]
29. J. Qiao, A. Kalb, T. Nguyen, J. Bunkenburg, D. Canning, and J. H. Kelly, “Demonstration of large-aperture tiled-grating compressors for high-energy, petawatt-class, chirped-pulse amplification systems,” Opt. Lett. 33(15), 1684–1686 (2008). [CrossRef] [PubMed]
30. Z. Li, T. Wang, G. Xu, D. Li, J. Yu, W. Ma, J. Zhu, L. Chen, and Y. Dai, “Research on potential problems of object image grating self-tiling for applications in large aperture optical systems,” Appl. Opt. 52(4), 718–725 (2013). [CrossRef] [PubMed]
31. FASTLITE Ultrafast Scientific Instrumentation, “Wizzler,” http://www.fastlite.com/en/
32. M. Hornung, R. Bödefeld, M. Siebold, A. Kessler, M. Schnepp, R. Wachs, A. Sävert, S. Podleska, S. Keppler, J. Hein, and M. C. Kaluza, “Temporal pulse control of a multi-10TW diode-pumped Yb:Glass laser,” Appl. Phys. B 101(1), 93–102 (2010). [CrossRef]
33. Z. Li, “Application problems of object-image-grating self-tiling in ultra-short pulse lasers,” Proc. SPIE 9255, 925515 (2015). [CrossRef]
34. Z. Li, D. Rao, Y. Leng, L. Chen, and Y. Dai, “Third-order dispersion compensation for petawatt-level lasers employing object-image-grating self-tiling,” Quantum Electron. 45(10), 891–896 (2015). [CrossRef]