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Abstract
Double deformable mirrors (DMs) with different actuator densities are cascaded to optimize the wavefront aberrations to improve the focus intensity of the Shanghai super-intense ultrafast laser facility (SULF), which plans to generate 10 PW laser pulse. The beam aberrations near the focal spot are corrected from 0.556 um to 0.112 um in RMS by a 300-mm DM with a large stroke installed after the compressor. After then, it is further optimized to 0.041 um using a 130-mm DM with a high spatial resolution working after the main amplifier. The corrected beam is focused to 2.75 × 2.87 um2 at the full width at half maximum (FWHM) with an f/2.5 off-axis parabolic mirror (OAP), which contains approximately 27.69% energy. A peak intensity of 2 × 1022 W/cm2 is achieved at the output of 5.4 PW, and it could exceed 1023 W/cm2 in the SULF 10 PW laser facility using an f/1.8 OAP.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, ultra-fast petawatt-class laser systems have undergone rapid development [1–8] by the incorporation of chirped-pulse amplification (CPA) [9] and optical parametric chirped-pulse amplification (OPCPA) technologies [10]. The focal intensity at the target plane is a critical parameter for high-field laser-matter interaction experiments. For most petawatt-class laser systems, the focal intensity is within the range of 1019–1021 W/cm2, and provides an extreme condition for physical experiments such as electron acceleration, proton acceleration, and the generation of x-rays [11–13]. With advances in physical experiments, intensities of 1022 W/cm2 and higher are required [14–16]. A peak intensity of ~1022 W/cm2 was achieved in the J-KAREN-P laser system, using an f/1.3 off-axis parabolic (OAP) mirror [17]. Increasing the pulse energy, shortening the pulse duration, and decreasing the size of the focus spot are three methods for achieving a higher intensity at the focal plane. In recent years, multi-petawatt laser systems were built with an increased pulse energy and shorter pulse duration, such as the 4.2 PW/20 fs laser in APRI, South Korea [18], and the 4.9 PW laser in CAEP, China [19]. The highest reported peak power of 5.4 PW was achieved at the SULF by our team in 2017 [20,21] and will be upgraded to 10 PW at the end of 2018 [22].
Decreasing the size of the focus spot is another essential and economic method used to increase the intensity. Moreover, the smallest focus spot is limited by diffraction. For a certain beam size, short focal length means a small diffraction limit, but also increases the difficulty for aiming target in physical experiments. Wavefront aberrations are the main limitation to the realization of the ideal focus spot. Large-aperture optic elements that are typically 250–300 mm in diameter for multi-petawatt systems and 400–500 mm in diameter for 10-PW systems [23,24] are used to prevent the damage. However, they increase the wavefront aberrations to a level higher than that of petawatt laser systems. The optimization of the wavefront aberrations of multi-petawatt laser systems is challenging, given the complex laser systems and severe aberrations.
Over the past two decades, adaptive optics systems (AOSs) have been used in high-power laser systems to improve the focusing ability of the laser pulse [14]. A suitable DM with an aperture smaller than 100 mm can satisfy the demand of a PW laser system. Double or more adaptive optics systems with cascaded correction are required in multi-PW and 10-PW systems, due to the large aperture beam size and severe aberrations [18,26]. In the 4.2PW laser system of APRI, an energy concentration of over 60% inside the Airy disk was achieved by using two AOSs [18]. The root mean square (RMS) value of the residual wavefront aberrations before the beam expander was less than 0.04 um after being corrected by the first AOS and the focal spot was optimized by the second DM with a diameter of 320 mm and 127 actuators. These applications of two-DM or multi-DM could also be found in the manipulation of the monochromatic aberrations of eyes [25], or the correction of strong phases and amplitude modulations in laser systems [26]. Typically, the first DM with a large stroke corrects large-scale low-order aberrations, and the second DM with high a spatial resolution compensates for small-scale high-order aberrations.
In this study, the evolution of the wavefront aberrations of the SULF laser system was evaluated, and the wavefront aberrations were optimized using two DMs as a two-cascaded-DM system. From the analysis of the different wavefront aberrations in the system and the correction capability of each DM, an experimental scheme was developed for the compensation of the wavefront aberrations of the laser beam, according to the function of each DM. The simulations in [27] confirmed that the scheme maximized the correction ability of the double DMs. The large-scale low-order aberrations were primarily optimized using the 300-mm DM, and then the 130-mm DM corrected the small-scale high-order aberrations, based on their actuator densities. The peak-to-valley (PV) and RMS values of the focal spot were reduced from 3.338 um and 0.556 um to 0.207 um and 0.041 um, respectively, after the wavefront correction. Focused by an f/2.5 OAP with focal length of 721 mm, the FWHM of the focal spot, which was obtained using an apochromatic objective lens with a 20 × magnification and a charge-coupled device (CCD), was 2.75 × 2.87 um2. This could result in a peak intensity of 2 × 1022 W/cm2. It is the first report that the intensity is higher than 1022 W/cm2 with an f-Number ≥2 OAP, which is significant for some experiments such as proton acceleration. A long working distance is favorable to aim target and probe at the same intensity.
2. Experimental setup and wavefront evolution
2.1 Experimental setup
The SULF laser system at present can generate a 5.4 PW laser pulse with a pulse energy of 202.8 J before the compressor, and a pulse duration of 24 fs after the compressor [20]. The layout for the wavefront measurement and correction of the laser system is presented in Fig. 1(a). The femto-second (fs) laser pulse generated by the high contrast front end was transported to the power and booster amplifiers after the Offner stretcher and spectral shaping. After reshaping by a soft edge aperture, the beam size was expanded to 65 mm and further to 115 mm by two Galilean expanding telescopes, before passing to the multi-pass Ti: sapphire amplifiers with diameters of 80 mm and 150 mm [20]. A bimorph DM with a diameter of 130 mm and 64 actuators was inserted after the 150 mm Ti: sapphire multi-pass amplifier, as the first wavefront corrector. The pulse was expanded to 290 mm with a Kepler expanding telescope before passing to the compressor. In addition, the surface of the first DM was imaged to the second one’s by this expanding telescope. The pulse duration was recompressed from 2 ns to 24 fs by the compressor consisting of four high-quality gratings. We minimized and optimized the low-order, spatial-to-spectral phase coupling, and the angular chirp, which may affects the focal spot quality [17,28]. After passing through the second DM with a diameter of 300 mm and 77 actuators, the beam was focused on the target chamber using an f/2.5 OAP (f = 721 mm) with an off-axis angle of 31°.
Fig. 1 (a). Layout of the SULF laser system. Numbers in circles ①-⑤: the measured points where the sampling optical path were inserted to survey the wavefront information of the beam. × 1.9, × 1.8, and × 2.5: the expansion ratios of the beam expanders, the first two expanders were Galilean type and the last one was Kepler type. 130 mm DM and 300 mm DM: the deformable mirrors with a diameter of 130 mm and 64 actuators, and a diameter of 300 mm and 77 actuators, respectively. Achromatic lens: contained in the beam expander before the compressor, to prevent chromatic dispersion. OAP: f = 721 mm off-axis parabolic mirror (f/2.5, off-axis angle: 31°). (b) The insertable sampling optical path for ①-④, for down-collimation of the beam to 3.4 mm. The wavefront information was measured by the WFS. FCLS: Fiber-Coupled Laser Source, an ideal source was collimated to measure and remove the sampling optical path aberrations. (c) The sampling optical path for ⑤. The OAP and aspheric lens (f1 = 32mm) constitute the first down-collimator. The second down-collimator that consists of high-quality lenses with f2 = 150 mm and f3 = 62.5 mm down-collimate the beam from 12.9 mm to 5.4 mm. WFS: Shack–Hartmann wavefront sensor. FCLS was inserted into the focus position of OAP to measure the additional aberration caused by the sampling optical path and then the measured result was used as the reference for the measurement of laser beam. The final focal spot was displayed on the CCD (12 bit, Spiricon SP620U) after expansion by the apochromatic objective lens (20 × , Olympus).
To study the evolution of the wavefront aberrations of the SULF laser system, the PV and RMS values of the wavefront aberrations were measured at critical positions in the laser system, which are indicated as ①-⑤ in Fig. 1(a). The sampling optical path for ①-④ is presented in the Fig. 1(b). Different down-collimators with optimal optical designs were used to collimate the beams at positions ①-④ to nearly 3.4 mm in diameter, to match the receiver area of the wavefront sensor (WFS). In order to avoid boundary errors during the measurement process by WFS, we define a finite mask for the analyzed image. In this experiment, the mask is defined as a circle, which covers the beam aperture with the threshold level higher than 5% of the maximal intensity.
The surface-shape error of the OAP should not be ignored, given that it is difficult to eliminate the error during the processing completely, due to the large aspheric surface. The PV and RMS values of the OAP we used were 0.206 um and 0.028 um. In the scheme, the wavefront aberrations of the entire laser system, including the OAP, were measured.
After the optimal optical design, three high-quality lenses were selected for two-stage down-collimators with the OAP, as shown in Fig. 1(c). The surface of second DM was imaged to the receptive plane of the final WFS by the two-stage down-collimating Kepler telescope. A pluggable ideal point source (Fiber-Coupled Laser Source, FCLS) running at 808 nm was set up at the focal position to collimate the lens and Shack–Hartmann WFS. The aberration of the sampling optical path in Fig. 1(c) was measured by the WFS with the ideal point source. The PV and RMS values of the additional optical system were 0.251 um and 0.057 um. The map of measured aberration was taken as the new reference of WFS to remove the additional aberrations of the sampling optical path during the measurement of laser beam. The focal spot after the OAP was obtained using an apochromatic objective lens (20 × , Olympus) and low-noise 12-bit CCD.
2.2 Wavefront evolution
With the passage of the beam through the optical elements, the wavefront aberrations became increasingly apparent. The wavefront evolution of the beam is presented in Fig. 2. The PV, RMS, and Strehl ratio (SR) values can quantitatively describe the wavefront of the beam at the measured points. For example, at ①: the wavefront was transported from the front end through several small multi-pass amplifiers; at ②: it was located between the three-pass 80-mm diameter Ti: sapphire amplifier and beam expander from 65 mm to 115 mm; at ③-④: it was before and after the DM with a diameter of 130 mm; and ⑤ represents the final spot of the laser system. In Fig. 2, the red and the blue points represent the PV and RMS values, thus indicating that the wavefront aberrations increased from 0.39 um/0.037um to 3.338 um/0.556um. With the increase in the PV/RMS values, the SR of the beam, which is represented by the black lines in Fig. 2, decreased from 0.9 to nearly 0.
The SR is the ratio of the displayed peak intensity from the WFS and the one with the same intensity profile and a flat wavefront. Although this uncorrected SR overestimates the focal spot [17], it could be used to study the variation trends of the focus spot at different measured points. The wavefront distortions resulted in an increase in satellite peaks, which lead to a decrease in the SR values of the beam and the focal spot quality. Calculated focal spots by the corresponding intensity and phase measured at position ①-③ were shown in Figs. 3(a)-3(c).
The wavefront aberrations increased as the laser pulse passed through more and larger-aperture optical elements, resulting in the dispersion of the focal spot. To control and optimize the wavefront aberrations, a 130-mm DM with 64 actuators was set up after the main amplifier and a 300-mm DM with 77 actuators was set up after the compressor, as shown in Fig. 1(a).
3. Wavefront correction of the 130-mm DM and aberrations analysis
In Section 2, the evolution of wavefront aberrations of the laser system was evaluated at several main measured points. Wavefront aberrations of the entire system, with a PV of 3.338 um and RMS of 0.556 um, resulted in a dispersed and ineffective focal spot. Two AOSs were required before and after the pulse compressor for the optimization.
The 130-mm DM was placed after the Ti: sapphire amplifier with a diameter of 150 mm, as shown in the Fig. 1(a). The PV, RMS, and Zernike polynomials coefficients of the initial and the corrected surface of the 130-mm DM were listed in the Table 1.
Table 1. The technical parameters of the initial and the corrected surface
The down-collimator consisting of f4 = 2500 mm and f5 = 75 mm lenses down collimated the beam from 115 mm to 3.4 mm. The pluggable ideal source (FCLS) was used to collimate the lens and remove the additional aberrations caused by the down-collimating telescopes. The DM surface was imaged to the sensor. The optical imaging system for the adaptive loop is presented in Fig. 1(b), which was inserted at the measured point ④. The wavefront edge with an intensity less than 5% of the maximal intensity was clipped to ensure the measurement accuracy of the WFS. The focal spot of the 115-mm beam diameter was displayed on the CCD after being reflected by a removable mirror.
After the correction of the 130-mm DM, there was a decrease in the PV and RMS values of the beam at the measured point ④ from 2.32 um and 0.339 um to 0.419 um and 0.058 um, respectively. The aberration profiles of the beam and the focal spots by the f4 = 2500 mm lens are presented in Fig. 4. The aberration distributions before and after correction are presented in Figs. 4(a) and 4(c), which indicated that the wavefront distortions were optimized by the first wavefront corrector. The satellite peaks of the focal spot significantly decreased with the closed loop calibration. The results in Fig. 4(d) revealed that the 115-mm beam after the first wavefront correction approached the diffraction limit.
Fig. 4 The phase profiles of the 115-mm beam (a) before and (c) after the correction; (b) and (d) the corresponding focal spots focused by the f4 = 2500 mm lens.
Although the wavefront aberrations were reduced to a nearly flat phase by using the 130-mm DM before the final expander, an exception occurred for the wavefront obtained at the measured point ⑤. The PV and RMS errors were 4.137 um and 0.785 um when the first AOS was on, which were higher than those when the first AOS was off (PV = 3.338 um, RMS = 0.556 um). It should be noted that the Zernike coefficients of low orders of magnitude at measured point ④ (before the final expander) and ⑤ (final spot) were changed when the first AOS was off and on, as shown in Table 2.
Table 2. The low orders of Zernike coefficients at ④ and ⑤
To analyze the wavefront aberrations caused by the system, the optical elements of the system after the 130-mm DM were regarded as a black box, which included the final expander, compressor, 300-mm DM, and f/2.5 OAP. From the Zernike coefficients presented in Table 2, the main aberrations were the astigmation_0°/_45° and spherical aberration. With an increase in the RMS value from 0.339 um to 0.556 um when the laser pulse passed through the black box; the astigmation_0°/_45° values increased from −0.195 um/0.144 um to −0.382 um/-0.814 um, and the spherical aberration decreased from 0.141 um to −0.167 um. When the first AOS was on, the Zernike coefficients of the wavefront aberrations at ④ were very low; however, they were higher after the passage of the pulse through the black box. In this process, the changes in direction of the astigmation_0°/ _45° and spherical aberration were the same as those when the first AOS was off; however, the magnitudes were higher. Except for the change introduced by the surface of the 130-mm DM, it could be concluded that the black box compensated a certain amount of aberrations caused by the elements before the black box, especially the astigmation_0°/_45° and spherical aberration, thus increasing the PV and RMS values at position ⑤ when the AOS was on. Moreover, the RMS value was 0.556 um when the first AOS was off, whereas it was 0.785 um when the AOS was on.
The wavefront aberrations after the OAP were increased when the first AOS was on, which limited the mutual optimization of the two-DM wavefront correctors in the laser system, due to the poor correction results. When the first AOS was on, the PV and RMS values of the residual distortions corrected by the final DM with a diameter of 300 mm and 77 actuators were 0.6 um and 0.112 um, respectively. The values could not be decreased due to the sparseness of the actuator distribution. To enhance the effectiveness of correctors, the two DMs were cascaded and applied to optimize the focal spot to the level of the diffraction limit.
4. Experimental results
Two AOSs were used before and after the compressor in the laser system, to correct the wavefront aberrations. A high-spatial-resolution DM with a diameter of 130 mm diameter and 64 actuators was used in the first AOS loop, and a large stroke DM with a diameter of 300 mm diameter and 77 actuators worked in the second AOS loop. Both wavefront aberrations of two AOSs were measured at position ⑤. An ideal point laser source was inserted to remove the additional aberrations caused by the sampling optical path. The second AOS was primarily used to correct the large-scale aberrations, and then the first AOS was used to correct the residual aberrations.
The comparison of Zernike coefficients (absolute values for analyzing) for the first 36 orders before and after the correction was shown in Fig. 5. The red columns represented the Zernike coefficients before the correction and the blue ones represented the coefficients after the correction by 300-DM. The most part of the large-scale aberrations were compensated by the 300-DM with a large stroke and the RMS value decreased to 0.112 um. However, the small-scale residual aberrations after the correction of 300-DM need to be further improved to achieve a high-quality focus. After the correction of the high-spatial-resolution 130-DM in the first AOS, the RMS value of the beam reduced to 0.041 um, and the Zernike coefficients were shown in Fig. 5 with the orange columns. The low-order aberrations were further compensated and the small-scale high-order aberrations were corrected to nearly zero, as shown in Fig. 5.
The distributions of the wavefront aberrations before and after the correction of the beam are presented in Figs. 6(a) and 6(c). The real focal spots, as shown in Figs. 6(b) and 6(d), were obtained using an apochromatic objective lens with a 20 × magnification and a 12-bit CCD, before and after the wavefront correction. The intensity of background in Fig. 6(d) was about 1% of the peak intensity according to the measurement of the12-bit CCD. In our opinion, although the pulse energy was attenuated by high surface quality wedges, it still caused slight nonlinear effect and chromatic aberration when a broadband pulse passed through the attenuators (3 pieces) and the apochromatic objective lens. The distributions of the focus on the x and y-axes and the encircle energy cure were presented in Fig. 7. The FWHM of the focal spot was 2.75 × 2.87 um2, which was close to the diffraction limit. The focal spot of the measured plane contained approximately 27.69% energy in the FWHM area and 59.43% energy in the e2 area.
Fig. 6 The phase profiles of the focal spots (a) before and (c) after the correction; (b) and (d) the corresponding focal spots focused by the OAP and obtained by an apochromatic objective lens (20 × , Olympus) and low-noise CCD.
Fig. 7 The distributions of the focal spot on the x and y-axes (left) and the encircle energy cure (right).
High surface quality wedges and neutral density attenuators were used to attenuate the laser pulse when the energy increased. The focal spot presented in Fig. 6(d) was measured at an energy of 5 J, and amplified by the third multi-pass amplifier at a frequency of 1 Hz. The real focal spot could not be measured when the energy increased, as it was difficult to attenuate the femtosecond pulse with an energy of 30–130 J. However, the wavefront aberrations were measured when the first single-shot amplifier was working, with an amplified energy of 40 J. The RMS value of the single-shot amplified beam was 0.043–0.05 um, which was nearly the same as that measured in the frequency amplification, as shown in Figs. 8(a)-8(b). We measured the pulse duration again after the correction by the two DMs, and it was closed to the value that the spectrum of the final amplifier could support. The final spot indicated that there was not any spatiotemporal coupling. According to the measured results, the peak intensity exceeded to 2 × 1022 W/cm2 with working distance of 721 mm for physical experiments. The peak intensity would have exceeded 1023 W/cm2 in the SULF 10 PW laser system with an f/1.8 OAP, which is suitable for the experiments of high-level ion acceleration and quantum electrodynamics effects.
Fig. 8 The phase profiles: (a) measured at a frequency of 1 Hz; (b) measured at a single-shot amplified with an amplified energy of 40 J.
5. Conclusion and outlook
In this work, the evolution of wavefront aberrations in SULF laser system was studied. Moreover, the large-scale low-order aberrations were primarily compensated using a 300-mm DM. Then the small-scale high-order aberrations were corrected by a 130-mm DM with different actuator density. Focused with an f/2.5 OAP, a focal spot close to the diffraction limit was achieved, which contained approximately 27.69% energy in the FWHM area (2.75 × 2.87 um2). This work demonstrated that two cascaded DMs with different actuator densities could compensate effectively the beam aberrations of multi-PW to 10-PW laser systems. A peak intensity of 2 × 1022 W/cm2 was achieved in the SULF laser system at output of 5.4 PW with a relatively long focal length OAP. For the next research, the 300 mm DM will be replaced with a 500 mm DM to correct the beam aberrations of SULF 10 PW laser beam, and the intensity would exceed 1023 W/cm2 with an OAP of f/1.8.
Funding
National Natural Science Foundation of China (NSFC) (61775223); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB1603).
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