Abstract

A novel chromatic aberration pre-compensation scheme for ultrashort petawatt laser systems was proposed. The pre-compensation scheme consists of a convex lens, group of concave lenses, and a spherical reflector combined with a conventional vacuum chamber. It provides a versatile method to accurately compensate the chromatic aberration of an entire laser system via controlling the amount of propagation time delay (PTD) induced by the compensator without changing the input and output beam size. A compensator, tailored based on the proposed scheme, was designed and experimentally evaluated for the Shen-Guang-II 5PW (SG-II 5PW) laser system at Shanghai Institute of Optics and Fine Mechanics (SIOM). The experimental results verified that chromatic aberration in the laser system was almost fully compensated: the size of laser beam focused by an f/2.42 off-axis parabolic mirror (OAP) was reduced tremendously from 32×18μm2to about 4×4μm2at full width at half maximum (FWHM). The proposed scheme provides the flexibility to accurately correct chromatic aberration in high-power laser systems within a wide dynamic range.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Owing to rapid development in the chirped pulse amplification (CPA) and optical parametric CPA (OPCPA) techniques, the output power of ultra-intense ultrashort laser systems has grown dramatically, achieving high-output laser intensity in the range of 1021–1022 W/cm2 [1–5]. Such an intense laser provides a powerful tool for the experimental study of laser–matter interactions in the relativistic regime [6–9]. In most high-power laser systems, the beam size is gradually expanded by Keplerian telescope beam expanders along with energy scaling to avoid optical damage and clear unwanted intensity modulation with high spatial frequency. However, lens-based beam expanders unfavorably introduce chromatic aberration, which could significantly reduce focal-spot intensity by spatially enlarging the focal spot size and temporally distorting the laser pulse profile [10–18].

One aspect of chromatic aberration is referred as “propagation time delay (PTD),” or “longitudinal chromatic aberration.” In [18], Bor et al pointed out that a beam traveling through the center of the lenses in a system is delayed compared to traveling through other portions of the lenses, resulting in a curved pulse front that is radially symmetrical across the beam and quadratically dependent on the beam size. Consequently, the accumulated PTD of the entire laser systems leads to the broadening and distortion of the temporal beam profile when the beam is focused—especially if the total PTD is comparable to, or broader than, the ideal pulse width. Another aspect of chromatic aberration is defocus dispersion (DD). DD is usually inevitable in transmission-based beam expanders, because different light wavelengths travel on different paths through the expanders because of angular dispersion. Consequently, they focus at different focal planes, leading to deterioration of the spatial intensity distribution when the beam is focused. DD is relatively insignificant in nanosecond high-energy laser systems with narrow bandwidths, but remarkable in ultrashort laser systems with ultra-broad spectral bandwidths as it is strongly affected by the bandwidth of the spectrum. Consequently, chromatic aberration tremendously reduces the output intensity of ultrashort high-power laser systems by deteriorating the spatial-temporal focusing performance. A careful compensation of the chromatic aberration greatly contributes both to the optimization of the temporal and spatial beam profile, and consequently, to the optimization of the output intensity.

Chromatic aberration can be entirely avoided using all-reflective or achromatic beam expanders [19]. A conventional reflection-type beam expander can be built using spherical or off-axis parabolic mirrors in a vacuum chamber. However, spherical beam expanders introduce astigmatism because of their geometric setup while off-axis parabolic mirrors are quite expensive and difficult to implement [13]. Although achromatic lenses can be used to replace singlet lenses in beam expanders, their application is limited because of the introduction of higher-order dispersion that arises from the combination of different glasses. A straightforward solution to this problem is applying a chromatic aberration pre-compensator. Many types of compensation schemes have been proposed and utilized in high-power laser systems by introducing opposite chromatic aberration: a diffractive chromatic corrector—made from a Fresnel lens imprinted on one surface of a negative lens—was designed and utilized for the PETEL and OMEGA EP laser systems [20,21]; a combination of a biconcave lens and aspherical mirror was experimentally evaluated at the Texas Petawatt Laser facility [22]; an Offner triplet imaging system combined with a negative lens was presented and applied in the MTW-OPAL system at the Laboratory for Laser Energetics (LLE) [23]. Although these compensation methods have proved to be capable of correcting chromatic aberration, their performance and application are limited. For example, the quality of a beam transmitted through a diffractive chromatic aberration corrector tends to deteriorate; the capability of compensation methods with a single-pass configuration is restricted, while a double-pass configuration is not easily applied with a large beam size because of the requirement of beam switching. Furthermore, the above methods all suffer from a common insufficiency—the degree of freedom to continuously control the value of chromatic aberration within a sufficiently large dynamic range. As such, the accurate and complete compensation of chromatic aberration of an entire laser system is difficult.

In this paper, a promising chromatic aberration pre-compensation scheme with a wide dynamic compensation range was proposed to overcome the drawbacks of current compensation methods. The proposed scheme consists of a convex lens, group of concave lenses, and spherical mirror combined with a conventional vacuum chamber. It provides the flexibility to compensate the chromatic aberration of an entire laser system via continuously controlling the amount of PTD induced by the compensator without changing the input and output beam size. The performance of the proposed scheme was experimentally validated in the SG-II 5PW laser system. The pre-compensation scheme is capable to be applied in high-power ultrashort laser systems as a pre-compensator to correct chromatic aberration of the entire system accurately and effectively.

2. Chromatic aberration pre-compensation scheme

Theoretically, the chromatic aberration in a given laser system is stable and can be fully compensated by introducing a corresponding negative chromatic aberration value. However, most laser systems in reality suffer from a deviation between the theoretical and practical chromatic aberration values, which generally results for two primary reasons. The first relates to the material mismachining of optical components. Poor mismachining tolerance in processing leads to material errors in many optical parameters such as surface shape, roughness, thickness, and refractive index. Consequently, a discrepancy between the theoretical and real chromatic aberration occurs. The second reason is usually ascribed to the misalignment of optical systems. This misalignment may arose from either the misplacing of singlet optical components (position or tilting angle), or the imprecise relationship between different components. Unfortunately, the deviation of chromatic aberration is difficult to accurately measure and completely control, making it hard to fully correct systematic chromatic aberration with existing compensation methods. On this basis, a chromatic aberration compensator with the degree of freedom to continuously control the value of compensation is proposed to provide the flexibility to accurately control the value of chromatic aberration induced by the compensator and consequently, optimize the compensation performance.

The main purpose of the pre-compensation scheme presented in this paper is to provide a dynamic range of PTD. According to Z. Bor [16], PTD introduced by lens systems is defined as:

PTDtotal=i=1:Nri22cfi(ni1)(λdnidλ)
Where fi and ni represent the focal length and corresponding refractive index, respectively, of each lens; while ri describes the beam radius passing through them. According to Eq. (1), PTD is proportional to ri2ri2 and inversely proportional to fi; thus, a straightforward way to dynamically change the value of PTD is to continuously adjust the beam radius or focal length of each lens. The following describes the proposed pre-compensation scheme. A schematic image of the scheme is illustrated in Fig. 1, where the input beam is shown being reflected by the beam splitter (BS) and transmitted through the first quarter-waveplate (P1) and positive lens (L1). As shown in Fig. 1, a real-image transfer system is composed of L1, the negative lens (L2), and spherical mirror (M1) with a co-focal spot located at point F. After being reflected by M1 and transmitted through L2, L1, and P1, the beam is transmitted through BS, and then double-transmitted and reflected by the second quarter-waveplate (P2) and plane mirror (M2), respectively. The output beam is finally reflected by BS again and travels in the same direction as the input beam. A vacuum chamber is located between L1 and L2 with a pinhole located at the co-focal plane. Thus, the PTD induced by the pre-compensation scheme comes mainly from the double-transmission of L2. The vacuum chamber is placed between L1 and L2 to avoid air breakdown and clear modulations with high spatial frequency.

 

Fig. 1 Schematic image of the chromatic aberration pre-compensation scheme.

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Dynamic adjustment of the chromatic aberration can be achieved by changing the beam radius transmitted through L2. This was performed by adjusting the distance between L1 and L2 (Z1). To maintain the real-image transform system composed of the lens system, the relative distance (Z2) should be adjusted slightly along with Z1. It is evident that the compensation limitation of the proposed scheme is determined by the clear apertures of L2 and M1. To estimate the dynamic range of PTD induced by this scheme, we assuming L1 and L2 are made from BK7 glass; L2 has a diameter of 100 mm and is far bigger than that of L1 such that PTD induced by L1 is negligible. Thus, the maximal PTD induced by L2 is 320 fs when the focal length of L2 is 800 mm; this value increases to 1.4 ps when L2 has a focal length of 200 mm (f/2). Consequently, the dynamic range of this scheme can be tremendous by wisely choosing the parameters of L1 and L2. It should be noted that L2 can be replaced by a lenses group for further improving the PTD value. One potential drawback of this pre-compensation scheme, like other pre-compensation schemes based on transmission components, is the pulse broadening induced by the effect of Group-Velocity Dispersion (GVD), although PTD can be accurately compensated. The pulse broadening of this pre-compensation scheme can be compensated by presise alignment of beam compressors in laser systems.

3. Chromatic aberration compensation for the SG-II 5PW laser system

The performance of the proposed pre-compensation scheme was verified experimentally in the SG-II 5PW laser system. Chromatic aberration in the SG-II 5PW laser system was calculated via both ray-tracing of the whole system and measuring of the chromatic defocus distance and focal spot size. The simulation results were in good agreement with the experimental data. A chromatic aberration pre-compensator—tailored based on the proposed scheme—was designed and applied in the SG-II 5PW laser system.

3.1 Chromatic aberration in the SG-II 5PW laser system

The SG-II 5PW femtosecond laser system at the Shanghai Institute of Optics and Fine Mechanics (SIOM) is a pure three-stage OPCPA laser facility aiming to deliver a peak power of 5PW with output energy of 150 J and pulse width of 30 fs [24]. The laser system consists of three optical parametric amplifier (OPA) stages and six beam expander stages in series. The 3D layout of the SG-II 5PW laser system is shown in Fig. 2.

 

Fig. 2 The 3D layout of the SG-II 5PW femtosecond laser system.

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In the SG-II 5PW laser system, the laser beam size is gradually scaled by the six spatial filter stages from 2.3 mm × 2.3 mm to 290 mm × 290 mm, along with energy amplification by the three OPA stages. All lenses of the beam expanders are made of BK7 glass so that the refractive index and derivative of wavelength of each lens are the same. Numerical calculations shown that chromatic aberration in the SG-II 5PW laser system is mainly induced by the last three stages of spatial filters: SF3, SF4, and SF5. Figure 3 shows the main parameters of the beam expanders and the corresponding chromatic aberration.

 

Fig. 3 Schematic image and the key parameters of beam expanders SF3, SF4 and SF5 in the SG-II 5PW laser system: (a) Key parameters of beam expanders; (b) Chromatic induced defocus distance: blue line represents the result calculated using matrix optics; red stars represent experimental result by measuring the distance between the corresponding focal plane of each wavelength.

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The total PTD induced by the beam expanders is about 380 fs while the chromatic induced defocus distance was calculated using matric optics and ray tracing method. As shown in Fig. 3(b), the experimental results of defocus distance are in perfect agreement with the theoretical calculations.

3.2 Chromatic aberration compensation

A chromatic aberration pre-compensator—tailored based on the proposed scheme—was designed for the SG-II 5PW laser system. The 3D layout of the compensator and its position in the system are illustrated in Fig. 4(a). As shown in Fig. 4(b), the pre-compensator consists of two concave lenses (L2, L3) with focal length and clear aperture of −391.5 mm and 100 mm; respectively, a spherical mirror (M3) with focal length and clear aperture of −175 mm and 200 mm, respectively; an achromatic quarter-wave plate, achromatic half-waveplate, and beam-splitter. The compensator was applied before the entrance pupil of SF3 to pre-correct the chromatic aberration of the whole system. To avoid other types of aberration induced by the compensator—such as spherical aberration—that could possibly affect system performance, the front surface of M3 was designed to be aspherical. High-order dispersion was compensated automatically because L1, L2, and L3 were all made from BK7 glass. L2, L3, and M3 were placed on three translation stages to accurately control the compensation performance.

 

Fig. 4 3D layout of the chromatic aberration pre-compensator and its position in the SG-II 5PW laser system. (a) Pre-compensator and SF3. (b) Experimental setup of the pre-compensator: L1, positive lens; L2 and L3, plane-concave lenses; M3, aspherical mirror; P1, broad-bandwidth quarter-waveplate; P2, broad-bandwidth half-waveplate; and BS, beam splitter.

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The compensation results after applying the chromatic aberration pre-compensator were calculated by the ray tracing method. The dynamic correction of PTD in SG-II 5PW laser system was realized by continuously adjusting the distance between L1 and L3 (defined as Z1). The distance between L2 and L3 was kept stable (50 mm). The residual PTD and spherical aberration was described in Fig. 5. As shown in Fig. 5(a), the PTD can be compensated dynamically via continuously adjusting Z1. Also, the spherical aberration induced by the pre-compensator can be maintained relatively low when Z1 varies within a wide range (550-650 mm), which indicates that the spherical aberration will not affect the system performance. The simulation results of the wavefront aberration of each wavelength—before and after pre-compensation—are described in Fig. 6.

 

Fig. 5 Dynamic compensation of the chromatic aberration via continuously adjusting Z1. (a) blue line represents the residual PTD, red line describes the focal radius (RMS) after correction; (b) Spherical aberration (Zernike coefficients defined in [25]): blue line represents the Zernike coefficient of third-order spherical aberration (Z11), red line describes the Zernike coefficient of fifth-order spherical aberration (Z22).

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Fig. 6 Simulation results of the wavefront aberration of the SG-II 5PW laser system before (a)-(c) and after (d)-(f) applying the pre-compensator at each single wavelength (from left to right: at 808 nm, 830 nm, and 780 nm).

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As shown in Fig. 6, the discrepancy of wavefront aberration between each wavelength in the SG-II 5PW laser system can be nearly fully compensated by applying the pre-compensator: the wavefront aberration discrepancy between 830 nm and 780 nm was significantly reduced from 11 waves to 0.1 waves, peak-to-valley (PV).

The performance of the pre-compensator was experimentally evaluated by measuring the focal spot size in the targeting chamber, where the laser beam with a diameter of 290 mm was focused by an off-axis parabola with f/2.42. The focal spots before and after chromatic aberration correction are shown in Fig. 7.

 

Fig. 7 Focal spot before and after applying the pre-compensator: image of the focal spot (a) before and (b) after correction; spatial profiles of focal spot in horizontal and vertical dimension (c) before and (d) after correction.

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As shown in Fig. 7, the focusing performance was improved dramatically after applying the pre-compensator: the focal spot size (FWHM) was reduced dramatically from 32μm×18μm to about 4μm×4μm, which is close to the diffractive limited spot size. The improvement of output intensity was evaluated by calculating the encircled energy of focal spot. As shown in Fig. 8, the 80% encircled energy diameter after correction decreases dramatically, which indicates that the output intensity after chromatic aberration correction has grown significantly. The residual defocus distance was calculated by measuring the distance between focal plane of each wavelength. Experimental results showed that the remaining defocus distance between the focal plane of 780 nm and that of 830 nm was largely reduced from 500μm to less than 30μm.

 

Fig. 8 Encircled energy of focal spot before and after applying the pre-compensator: blue line represents the encircled energy before correction; red line represents the encircled energy after correction.

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The experimental results also indicated that the spectral bandwidth, the compressed pulse width of amplified beam and the energy conversion efficiency of OPA-II stage were not affected by the pre-compensator, which proves that the pre-compensation scheme is capable to be applied in femtosecond high-power laser systems as a chromatic aberration pre-compensator.

4. Summary

In this paper, we proposed a novel chromatic aberration pre-compensator scheme that is able to compensate chromatic aberration with a large dynamic range. The proposed scheme consists of a positive lens, negative lens, spherical mirror, and vacuum chamber. Compared with other compensation techniques, the proposed scheme holds several advantages: first, it is capable of providing a large dynamic range of chromatic aberration, making it possible to accurately correct the chromatic aberration in femtosecond or picosecond high-power laser systems without affecting the spatial profile and spectrum of the input and output beams. Second, owing to the real-image relay structure and vacuum spatial filtering system (see Fig. 1), high frequency noise and unwanted ghost beams or prepulses can be eliminated, such that excellent beam quality can be achieved. Third, the scheme has the advantages of double-pass and beam switching configurations; consequently, it is able to correct the chromatic aberration of the whole laser system, even for a small input beam size. Finally, compared with other methods, the proposed pre-compensation scheme is low-cost and can be removed and aligned with ease without changing the systematical optical paths.

A chromatic aberration pre-compensator—tailored based on the proposed scheme—was designed for the SG-II 5PW laser system. The experimental results verified that the chromatic aberration of the system was nearly fully compensated with the focal spot size reduced significantly from 32μm×18μm to about 4μm×4μm at FWHM, which is close to the diffractive limited focal size. The chromatic defocus distance reduced from 500μmto less than 30μm. The experiential results also indicated that the pre-compensator did not affect the spectrum of the amplified beam and energy amplification capability of the OPA-II stage. The output intensity larger than 1020 W/cm2 after chromatic aberration correction was realized. In summary, a novel chromatic aberration scheme with a capability to dynamically compensate chromatic aberration with a wide range was proposed and experimentally validated in the SG-II 5PW laser system. The pre-compensation scheme is capable to be applied in high-power laser systems as a pre-compensator for it provides the flexibility to correct chromatic aberration accurately and effectively.

Funding

National Natural Science Foundation of China (NSFC) (11304332, 11704392, and 61705245), International Partnership Program of Chinese Academy Of Sciences (181231KYSB20170022).

References

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2. N. Hopps, C. Danson, S. Duffield, D. Egan, S. Elsmere, M. Girling, E. Harvey, D. Hillier, M. Norman, S. Parker, P. Treadwell, D. Winter, and T. Bett, “Overview of laser systems for the Orion facility at the AWE,” Appl. Opt. 52(15), 3597–3607 (2013). [CrossRef]   [PubMed]  

3. S. W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. A. Mourou, and V. Yanovsky, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29(24), 2837–2839 (2004). [CrossRef]   [PubMed]  

4. J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006). [CrossRef]  

5. M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014). [CrossRef]  

6. M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998). [CrossRef]  

7. B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006). [CrossRef]  

8. H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32(16), 2315–2317 (2007). [CrossRef]   [PubMed]  

9. G. A. Mourou, C. L. Labaune, M. Dunne, N. Naumova, and V. T. Tikhonchuk, “Relativistic laser-matter interaction: from attosecond pulse generation to fast ignition,” Plasma Phys. Contr. Fusion 49(12B), B667–B675 (2007). [CrossRef]  

10. S. Ameer-Beg, A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday, “An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique,” Opt. Commun. 122(4-6), 99–104 (1996). [CrossRef]  

11. H. M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006). [CrossRef]  

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22. E. W. Gaul, M. Martinez, J. Blakeney, A. Jochmann, M. Ringuette, D. Hammond, T. Borger, R. Escamilla, S. Douglas, W. Henderson, G. Dyer, A. Erlandson, R. Cross, J. Caird, C. Ebbers, and T. Ditmire, “Demonstration of a 1.1 petawatt laser based on a hybrid optical parametric chirped pulse amplification/mixed Nd:glass amplifier,” Appl. Opt. 49(9), 1676–1681 (2010). [CrossRef]   [PubMed]  

23. S. W. Bahk, J. Bromage, and J. D. Zuegel, “Offner radial group delay compensator for ultra-broadband laser beam transport,” Opt. Lett. 39(4), 1081–1084 (2014). [CrossRef]   [PubMed]  

24. J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018). [CrossRef]  

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References

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  1. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).
    [Crossref]
  2. N. Hopps, C. Danson, S. Duffield, D. Egan, S. Elsmere, M. Girling, E. Harvey, D. Hillier, M. Norman, S. Parker, P. Treadwell, D. Winter, and T. Bett, “Overview of laser systems for the Orion facility at the AWE,” Appl. Opt. 52(15), 3597–3607 (2013).
    [Crossref] [PubMed]
  3. S. W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. A. Mourou, and V. Yanovsky, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29(24), 2837–2839 (2004).
    [Crossref] [PubMed]
  4. J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
    [Crossref]
  5. M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
    [Crossref]
  6. M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
    [Crossref]
  7. B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
    [Crossref]
  8. H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32(16), 2315–2317 (2007).
    [Crossref] [PubMed]
  9. G. A. Mourou, C. L. Labaune, M. Dunne, N. Naumova, and V. T. Tikhonchuk, “Relativistic laser-matter interaction: from attosecond pulse generation to fast ignition,” Plasma Phys. Contr. Fusion 49(12B), B667–B675 (2007).
    [Crossref]
  10. S. Ameer-Beg, A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday, “An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique,” Opt. Commun. 122(4-6), 99–104 (1996).
    [Crossref]
  11. H. M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
    [Crossref]
  12. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48(6), 4721–4729 (1993).
    [Crossref] [PubMed]
  13. T. M. Jeong, D. K. Ko, and J. Lee, “Deformation of the Focal Spot of an Ultrashort High-Power Laser Pulse due to Chromatic Aberration by a Beam Expander,” J. Korean Phys. Soc. 52(6), 1767–1773 (2008).
    [Crossref]
  14. A. Federico and O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91(1–2), 104–110 (1992).
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  15. M. Kempe and W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18(2), 137–139 (1993).
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  17. P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
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  18. Z. Bor, “Distortion of Femtosecond Laser Pulses in Lenses and Lens Systems,” Opt. Acta (Lond.) 35(12), 1907–1918 (1988).
  19. T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27(14), 2960–2971 (1988).
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  20. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multipetawatt high-energy laser,” Appl. Opt. 46(9), 1568–1574 (2007).
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  21. T. J. Kessler, H. Huang, and D. Weiner, “Diffractive optics for compensation of axial chromatic aberration in high-energy short-pulse laser,” International Conferance on Ultra-high Intensity Laser Development, Science and Emerging Applications, 126–128 (2006).
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  23. S. W. Bahk, J. Bromage, and J. D. Zuegel, “Offner radial group delay compensator for ultra-broadband laser beam transport,” Opt. Lett. 39(4), 1081–1084 (2014).
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  24. J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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2018 (2)

P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
[Crossref]

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
[Crossref]

2014 (2)

S. W. Bahk, J. Bromage, and J. D. Zuegel, “Offner radial group delay compensator for ultra-broadband laser beam transport,” Opt. Lett. 39(4), 1081–1084 (2014).
[Crossref] [PubMed]

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

2013 (1)

2010 (1)

2008 (1)

T. M. Jeong, D. K. Ko, and J. Lee, “Deformation of the Focal Spot of an Ultrashort High-Power Laser Pulse due to Chromatic Aberration by a Beam Expander,” J. Korean Phys. Soc. 52(6), 1767–1773 (2008).
[Crossref]

2007 (3)

2006 (3)

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

H. M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[Crossref]

2004 (1)

1998 (1)

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

1996 (1)

S. Ameer-Beg, A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday, “An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique,” Opt. Commun. 122(4-6), 99–104 (1996).
[Crossref]

1993 (2)

1992 (1)

A. Federico and O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91(1–2), 104–110 (1992).
[Crossref]

1989 (1)

1988 (2)

Z. Bor, “Distortion of Femtosecond Laser Pulses in Lenses and Lens Systems,” Opt. Acta (Lond.) 35(12), 1907–1918 (1988).

T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27(14), 2960–2971 (1988).
[Crossref] [PubMed]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).
[Crossref]

1976 (1)

Akutsu, A.

Ameer-Beg, S.

S. Ameer-Beg, A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday, “An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique,” Opt. Commun. 122(4-6), 99–104 (1996).
[Crossref]

Arunachalam, A. K.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Bahk, S. W.

Barty, C.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Bauvier, M.

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

Becker, G. A.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Bett, T.

Blakeney, J.

Blanchot, N.

J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multipetawatt high-energy laser,” Appl. Opt. 46(9), 1568–1574 (2007).
[Crossref] [PubMed]

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Bor, Z.

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14(2), 119–121 (1989).
[Crossref] [PubMed]

Z. Bor, “Distortion of Femtosecond Laser Pulses in Lenses and Lens Systems,” Opt. Acta (Lond.) 35(12), 1907–1918 (1988).

Borger, T.

Borneis, S.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Britten, J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Bromage, J.

Buma, T.

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

Caird, J.

Chvykov, V.

Clarke, R.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

Cross, R.

Cui, Z.

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
[Crossref]

P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
[Crossref]

Daido, H.

Danson, C.

N. Hopps, C. Danson, S. Duffield, D. Egan, S. Elsmere, M. Girling, E. Harvey, D. Hillier, M. Norman, S. Parker, P. Treadwell, D. Winter, and T. Bett, “Overview of laser systems for the Orion facility at the AWE,” Appl. Opt. 52(15), 3597–3607 (2013).
[Crossref] [PubMed]

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Dawson, J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Ditmire, T.

Douglas, S.

Dromey, B.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

Duffield, S.

Dunne, M.

G. A. Mourou, C. L. Labaune, M. Dunne, N. Naumova, and V. T. Tikhonchuk, “Relativistic laser-matter interaction: from attosecond pulse generation to fast ignition,” Plasma Phys. Contr. Fusion 49(12B), B667–B675 (2007).
[Crossref]

Dyer, G.

Ebbers, C.

Egan, D.

Elsmere, S.

Erlandson, A.

Escamilla, R.

Faure, J.

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

Federico, A.

A. Federico and O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91(1–2), 104–110 (1992).
[Crossref]

Gao, Q.

P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
[Crossref]

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
[Crossref]

Gaul, E. W.

George, N.

Girling, M.

Gopal, A.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

Guo, A.

P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
[Crossref]

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
[Crossref]

Habara, H.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

Hammond, D.

Harvey, E.

Hein, J.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Hellwing, M.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Henderson, W.

Heuck, H. M.

H. M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[Crossref]

Hillier, D.

Hopps, N.

Hornung, M.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Itatani, J.

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

Jeong, T. M.

T. M. Jeong, D. K. Ko, and J. Lee, “Deformation of the Focal Spot of an Ultrashort High-Power Laser Pulse due to Chromatic Aberration by a Beam Expander,” J. Korean Phys. Soc. 52(6), 1767–1773 (2008).
[Crossref]

Jochmann, A.

Jovanovic, I.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Jungquist, R.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Kalintchenko, G.

Kaluza, M. C.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Kanazawa, S.

Kang, J.

P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
[Crossref]

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
[Crossref]

Kaplan, D.

M. Nantel, J. Itatani, A. Tien, J. Faure, D. Kaplan, M. Bauvier, T. Buma, P. V. Rompay, J. Nee, P. P. Pronko, D. Umstadter, and G. A. Mourou, “Temporal contrast in Ti:sapphire lasers, characterization and control,” IEEE J. Sel. Top. Quantum Electron. 4(2), 449–458 (1998).
[Crossref]

Karsch, S.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
[Crossref]

Kelly, J. H.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” J. Fusion Science & Technology 49(3), 453–482 (2006).
[Crossref]

Kempe, M.

Keppler, S.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Kessler, A.

M. Hornung, H. Liebetrau, A. Seidel, S. Keppler, A. Kessler, J. Korner, M. Hellwing, F. Schorcht, D. Klopfel, A. K. Arunachalam, G. A. Becker, A. Sävert, J. Polz, J. Hein, and M. C. Kaluza, “The all-diode-pumped laser system POLARIS-an experimentalist’s tool generating ultra-high contrast pulses with high energy,” High Power Laser Science and Engineering 2(3), 5–11 (2014).
[Crossref]

Kessler, T. J.

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J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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S. Ameer-Beg, A. J. Langley, I. N. Ross, W. Shaikh, and P. F. Taday, “An achromatic lens for focusing femtosecond pulses: direct measurement of femtosecond pulse front distortion using a second-order autocorrelation technique,” Opt. Commun. 122(4-6), 99–104 (1996).
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B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
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B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nat. Phys. 2(7), 449–462 (2006).
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J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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Yang, Q.

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J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
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J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Science and Engineering 6(02), 115–127 (2018).
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[Crossref]

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[Crossref]

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P. Zhu, X. Xie, J. Kang, Q. Yang, H. Zhu, A. Guo, M. Sun, Q. Gao, Z. Cui, X. Liang, S. Yang, D. Zhang, and J. Zhu, “Systematic study of spatiotemporal influences on temporal contrast in the focal region in large-aperture broadband ultrashort petawatt lasers,” High Power Laser Science and Engineering 6(1), e8 (2018).
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Figures (8)

Fig. 1
Fig. 1 Schematic image of the chromatic aberration pre-compensation scheme.
Fig. 2
Fig. 2 The 3D layout of the SG-II 5PW femtosecond laser system.
Fig. 3
Fig. 3 Schematic image and the key parameters of beam expanders SF3, SF4 and SF5 in the SG-II 5PW laser system: (a) Key parameters of beam expanders; (b) Chromatic induced defocus distance: blue line represents the result calculated using matrix optics; red stars represent experimental result by measuring the distance between the corresponding focal plane of each wavelength.
Fig. 4
Fig. 4 3D layout of the chromatic aberration pre-compensator and its position in the SG-II 5PW laser system. (a) Pre-compensator and SF3. (b) Experimental setup of the pre-compensator: L1, positive lens; L2 and L3, plane-concave lenses; M3, aspherical mirror; P1, broad-bandwidth quarter-waveplate; P2, broad-bandwidth half-waveplate; and BS, beam splitter.
Fig. 5
Fig. 5 Dynamic compensation of the chromatic aberration via continuously adjusting Z1. (a) blue line represents the residual PTD, red line describes the focal radius (RMS) after correction; (b) Spherical aberration (Zernike coefficients defined in [25]): blue line represents the Zernike coefficient of third-order spherical aberration (Z11), red line describes the Zernike coefficient of fifth-order spherical aberration (Z22).
Fig. 6
Fig. 6 Simulation results of the wavefront aberration of the SG-II 5PW laser system before (a)-(c) and after (d)-(f) applying the pre-compensator at each single wavelength (from left to right: at 808 nm, 830 nm, and 780 nm).
Fig. 7
Fig. 7 Focal spot before and after applying the pre-compensator: image of the focal spot (a) before and (b) after correction; spatial profiles of focal spot in horizontal and vertical dimension (c) before and (d) after correction.
Fig. 8
Fig. 8 Encircled energy of focal spot before and after applying the pre-compensator: blue line represents the encircled energy before correction; red line represents the encircled energy after correction.

Equations (1)

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PT D total = i=1:N r i 2 2c f i ( n i 1 ) ( λ d n i dλ )

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