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Abstract
A grism pair is utilized to control the high-order dispersion of the Shanghai Superintense Ultrafast Lasers Facility, which is a large-scale project aimed at delivering 10-PW laser pulses. We briefly present the characteristics of the laser system and calculate the cumulative B-integral, which determines the nonlinear phase shift influence on material dispersion. Three parameters are selected, grism separation, angle of incidence and slant distance of grating compressor, to determine their optimal values through an iterative searching procedure. Both the numerical and experimental results confirm that the spectral phase distortion is controlled, and the recompressed pulse with a duration of 24 fs is obtained in the single-shot mode. The distributions and stabilities of the pulse duration at different positions of the recompressed beam are also investigated. This approach offers a new feasible solution for the high-order dispersion compensation of femtosecond petawatt laser systems.
© 2017 Optical Society of America
1. Introduction
The invention of the chirped-pulse amplification (CPA) technique [1] and its analog, optical parametric chirped-pulse amplification (OPCPA) [2] have been utilized to make remarkable advances in the development of petawatt femtosecond lasers within the laboratory [3–5]. Petawatt-class lasers have been constructed or are under construction for specific research activities, including producing ultra-intense and ultra-short sources of particles (electrons, protons), and generating coherent and highly energetic X-rays or γ-rays. The first CPA petawatt laser system based on Nd:glass was built in the Lawrence Livermore National Laboratory in 1999 [6]. Since then, there has been a global race to build petawatt-class laser facilities with pulse durations of a few tens of femtoseconds. The Extreme Light Infrastructure (ELI) in Europe aims at building ultrahigh-power lasers with focusable intensities and average powers exceeding the 10 PW level before 2017 [7]. Apart from the ELI project, there are several ongoing international multi-PW projects, such as the Apollon-10 PW [8], Vulcan-10 PW [9], 4.2 PW laser in South Korea [10], multi-petawatt laser facility fully based on OPCPA [11], and Shanghai Superintense Ultrafast Laser Facility (SULF) aiming at producing peak power pulses of 10 PW [12]. The CPA technique employs the concept of laser pulse stretching in the temporal domain and compression to ultrashort durations after laser pulse amplification. This idea could reduce the damage risk related to nonlinear effects and overcome the low extraction efficiency during the amplification stage. However, it should be stressed that the construction of ultrahigh-power laser systems has not been easy. Parasitic lasing has to be addressed as it causes the decay of population inversion and limits the achievable gain in large-aperture, high-gain amplifiers [13]. The dispersion properties of optical materials should also be investigated, including the role of stretchers and compressors in achieving dispersion balance of the laser facility [14]. In this approach, we will be able to generate pulses with high energies and ultra-short durations, and reach an extreme peak power level.
In general, dispersion components based on diffraction grating pairs are adopted to compensate for the spectral phase distortions imposed on broadband laser pulses. The dispersion compensation includes second-order dispersion, i.e., group velocity dispersion (GVD), third-order dispersion (TOD), fourth-order dispersion (FOD), and higher order dispersions. If the amplifier in a CPA system exhibits large amounts of material dispersion, dispersion compensation is only feasible for the second and third orders. To improve the dispersion up to the fourth order, Kane and Squier proposed that the high-order dispersion of an aberration-free CPA system could be reduced simply by employing a grating-pair compressor with gratings possessing a higher groove density than the gratings in the stretcher [15]. In this method, it is necessary to choose the compressor gratings and determine the material path length required for fourth-order compensation. If the material path length of the laser system changes, the compressor may not match the stretcher and amplifier. The acousto-optic programmable dispersive filter (AOPDF) can be used to actively compensate for high orders of dispersion and is only capable of maintaining group delays of less than a few picoseconds [16].
In our previous studies, considerable efforts were made to completely rule out GVD, TOD, and FOD by inserting a grism pair in the front end; as a result, near-Fourier-transform-limited (FTL) pulses were achieved [17, 18]. The grism proposed by P. Tournois is a combination of a grating and a prism [19], and the grism pair can provide both negative GVD and TOD, which could be used to compensate for the material dispersion in a CPA system [20]. Based on the grism and AOPDF, an OPCPA system is expected to produce gain-bandwidth-limited, high-power, sub-two-cycle pulses [21]. However, these grism designs have not been adopted in a petawatt-class laser facility, especially a fully CPA configuration with large amounts of material dispersion.
In this report, we present the design of the dispersion control system in the Superintense-Ultrafast Lasers Facility (SULF), which was successfully implemented with a 5.4-PW output in 2016. A grism pair, inserted between the Öffner stretcher and regenerative amplifier, is utilized to reduce the high-order dispersion up to the fourth order. In section 2, the system characteristics are briefly presented, and the cumulative B-integral of the femtosecond petawatt laser facility is calculated to be 0.47, indicating that the nonlinear phase shift has little impact on the material dispersion. The grism separation is then optimized to compensate for the mismatch between the stretcher, amplifier, and grating compressor. In Section 3, the evolution of the laser spectrum through the whole CPA laser system is studied, and the pulse duration in the single-shot mode is measured to be 24 fs. Considering the recompressed pulse with an energy of 130 J, the laser facility has the ability to deliver 5.4-PW pulses. Lastly, we select three different parts of the laser beam to study the distributions and stabilities of the pulse durations and measure the spectral phase of the recompressed pulse. It is proved that the pulse durations can remain stable for long periods of time.
2. System characteristics and simulations
A double CPA architecture is employed in the Ti:sapphire laser facility, which is outlined in Fig. 1. The first CPA is a commercial, 1-kHz CPA laser system (Astrella, Coherent Inc.) delivering 6-mJ-scale, sub-30-fs pulses, and the measured temporal contrast is about 10−8 at tens of picoseconds before the main pulse. Seed pulses with a central wavelength of 800 nm are injected into the nonlinear pulse cleaner using cross-polarized wave generation (XPWG) and femtosecond optical parametrical amplification (OPA) [22]. The XPWG acts similar to a temporal filter, which could improve the temporal contrast by 4–5 orders of magnitude. The XPWG unit primarily consists of two crossed polarizers, two nonlinear crystals (BaF2), and an achromatic half-wave plate. The polarizers are made of calcite and the achromatic half-wave plate is made of K9 glass. A set of chirped mirrors can compensate for the dispersion introduced during the XPWG stage. The XPW signal with an energy of 5 μJ will serve as the seed pulse for the subsequent femtosecond OPA based on the beta-barium borate (BBO) crystal. The signal pulses are amplified to 120 μJ in the OPA process and the temporal contrast is estimated to be better than the 10−13-scale.
Next, the high-contrast seed pulses with a diameter of 4.8 mm are injected into the second CPA stage and stretched to about 2 ns by an Öffner stretcher with a 1480 lines mm–1, gold-coated grating (Jobin Yvon, Inc.). The stretcher has an eight-pass configuration. The radii of curvature of the concave and convex mirrors are 1600 and 800 mm, respectively, and are very large to reduce the aberration introduced by the stretcher. The angle of incidence is 50° and the grating is 300 mm from the center of the sphere. The GVD, TOD, and FOD of the stretcher at the central wavelength are 5.7672 × 106 fs2, –1.1746 × 107 fs3, and 3.8311 × 107 fs4, respectively. The throughput efficiency of the stretcher is measured to be over 28.5%. Before injecting into the regenerative amplifier, the stretched pulse passes through a home-made grism pair, which is used to control the high-order dispersion. A Pockels cell (PC) assembly, which consists of two Glan polarizers and a Pockels cell, is set to select single pulses at a repetition rate of 10 Hz, and another PC assembly is used for pre-pulse suppression. After that, the laser pulse is amplified in the regenerative amplifier, and another two PC assemblies are aligned for single-pulse selection and pre-pulse suppression. As a result, the repetition rate is altered to 1 Hz. The pulse repetition rate of 1 Hz is amplified in three multi-pass amplifiers. The energy is amplified to 7 J in the front end. The pump lasers are all commercial Nd:YAG lasers.
It is then reshaped by a soft-edge aperture with an energy output of 5.8 J, and is sent to the following three-pass power amplifier, which is double-end pumped by a home-made Nd:glass laser in single-shot mode with a total energy of 100 J. Subsequently, the laser pulse with an energy of 45 J is injected into the final booster amplifier. The amplifier is also double-end pumped by a home-made Nd:glass laser with an energy of 320 J. The final amplifier employs a state-of-the-art 150-mm-diameter Ti:sapphire crystal. To suppress the parasitic lasing and transverse amplified spontaneous emission, a novel temporal dual-pulse scheme is proposed [12]. The pump pulse is divided into two pulses with identical energies by a beam splitter. These two pump pulses are then further divided into two individual pulses by beam splitters with certain splitting ratios. The pump energy distribution is optimized and the time delay between each pump pulse is precisely controlled. All the pump lasers exhibit almost flat-top spatial profiles. The maximum energy of the laser pulse could reach 202.8 J after the final booster amplifier. The beam wavefront of the amplified laser pulse is corrected by an optical adaptive closed-loop composed of a wavefront sensor, a deformable mirror, and a feedback software. The deformable mirror with a diameter of 130 mm is installed between the final booster amplifier and the beam expander before the compressor. The beam diameter is expanded to 300 mm by the beam expander. The amplified pulses are then recompressed by a grating compressor composed of four 1480 grooves mm–1, gold-coated holographic gratings (Jobin Yvon, Inc.). The angle of incidence and slant distance of the compressor will be 52.18° and 1.255 m, respectively, if we only consider the GVD and TOD of the laser system. After the compressor, another optical adaptive closed-loop with a 320-mm-diameter deformable mirror is being installed to correct the wavefront of the compressed beam.
In our design, the highest amount of pulse stretching and compression is still achieved by the typical Öffner stretcher and grating compressor. The grism pair is designed to compensate for the mismatching of the stretcher, optical material, and compressor. The simultaneous compensation of the GVD, TOD, and FOD implies the solving of an optimization problem with three constraint conditions of
where is the central circular frequency, denotes the mth-order derivative of the spectral phase evaluated at , and the subscripts S, G, A, and C denote the stretcher, grism pair, amplifier, and compressor, respectively.The dispersion terms of the amplifiers need to be calculated. Table 1 presents the lengths of the optical materials in our laser system. As mentioned earlier, the dispersion introduced by the pulse cleaner (BBO, K9, CaF2, and e-calcite) has been compensated by a set of chirped mirrors. Two expanders of the laser system are made of K9 glass, while most of the expanders are made of fused silica (FS). Terbium gallium garnet (TGG) is a material commonly used in Faraday rotators. The materials used in the regenerative amplifier include a 16-mm Ti:sapphire rod, 20-mm KD*P Pockels cell, and 2-mm, BK-7, thin-film polarizer. The Pockels cell has two 4-mm, FS window plates. Because of the gain narrowing and spectral redshift in the amplifying process, a spectral shaping filter made of FS (ARO, Inc.) is inserted in the regenerative amplifier to achieve spectral evolution management, aiming to optimize the spectral profile and width compatible with high-contrast pulses less than 25 fs. The spectral shaping filter is a dielectric-coated filter with a spectral transmission curve designed to suppress the gain narrowing and spectral redshift. The magnitude of the single-pass gain can be easily controlled by adjusting the insertion depth of the spectral filter, and the center wavelength can be tuned by varying the angle of incidence of the optics. The length of the filter is about 2.85 mm. In our laser system, the number of round-trips N is generally in the range of 23–28 to fully deplete the gain. The pump energy could be increased to minimize the number of round-trips, and N is measured to be 23. It should be emphasized that the pump energy should not be too high to prevent damage to the Ti:sapphire crystals.
Table 1. Length of optical materials in the laser system.
In the presence of very intense beams, self-phase modulation (SPM) occurs because of the optical Kerr effect, which would modify the refractive index of a transparent material, defined by
where is the linear refractive index, is the nonlinear component of the refractive index, and I is the laser intensity. As for the Ti:sapphire, the nonlinear refractive index is 3.18 10−16 cm2/W. The refractive index change is thus proportional to the instantaneous intensity of the light travelling through the medium. Recompression of the amplified pulse is strongly affected by SPM. To examine this effect, the B-integral is used, which is a measure of the cumulative nonlinear phase shift through the optical material and was proposed by M. D. Perry et al. [23]. The B-integral can be given bywhere z is the position in the beam direction. It is clear that the total on-axis nonlinear phase shift can be characterized by the B-integral. To reduce the B-integral, we stretched the pulse duration to about 2 ns, and the calculated cumulative B-integral of the whole system was less than 0.47. Therefore, the optical Kerr-effect plays a minor role during amplification, and we can neglect the nonlinear phase contribution because of SPM. Based on Table 1, the GVD, TOD, and FOD of the amplifiers at the central wavelength are calculated to be 1.2478105 fs2, 9.9957104 fs3, and –4.3911104 fs4, respectively.Our grism pair unit illustrated in Fig. 2 can provide negative GVD and TOD. The red lines denote light rays at the central wavelength. The dispersion introduced by the grism pair can be calculated using the ray-tracing method [21, 24, 25]. The home-made grism pair consists of a retroreflector, two aluminum-coated reflection gratings (5050 mm2, Newport), and two antireflection-coated SF11 prisms with hypotenuses of 50 and 80 mm, respectively. The retroreflector is used to reflect the beam to the position right below the incident beam along the same path. The following parameters are used in our grism pair: insertion amount on the first grism , insertion amount on the second grism , prism apex angle 20°, and grating groove density d = 300 lines mm–1.
Fig. 2 Layout and parameters of grism pair. M1 and M2 are the reflective mirrors with different vertical heights. : insertion amount on the first grism; : insertion amount on the second grism; : grism separation; : grism tip-to-tip distance.
Three parameters are selected, grism separation, angle of incidence and slant distance of the grating compressor, to determine their optimal values through an iterative searching procedure. The total GVD and TOD of the laser system can be reduced to zero by adjusting the angle of incidence and slant distance of the compressor at the central wavelength, and the equations can be given by [17]
where d is the grating groove period, is the diffractive angle, and is the slant distance of the compressor. The residual fourth-order dispersion (RFOD) is defined aswhich is a function of the grism separation shown in Fig. 3(a). When the grism separation changes, the value of correspondingly changes to keep the insertion amount on the second grism unchanged. It is evident that the RFOD is strongly dependent on the grism separation. When the grism separation varies from 0 to 40 mm, the RFOD decreases from 1.47106 to –1.02106 fs4, and the grism tip-to-tip distance increases from 64.53 to 167.6 mm. For a grism separation of 24 mm, the RFOD is equal to zero, which indicates that the dispersions up to the fourth-order will be completely compensated. Correspondingly, the grism tip-to-tip distance is 126.3 mm. In this condition, the angle of incidence and slant distance of the compressor gratings are 50.74° and 1222 mm, respectively.Fig. 3 (a) Residual fourth-order dispersion (black line) and grism tip-to-tip distance (blue line) as a function of grism separation. (b) Residual fourth-order dispersion as a function of deviation angle between the angle of incidence and its theoretical value.
In our previous studies, the grism separation was set to be 30 mm, and the dispersion of the grism pair was tuned by adjusting the angle of incidence. There is a major disadvantage. It is a challenge to ensure the angle of incidence of the grism accurately without changing the insert amount . For a grating separation of 30 mm, the RFOD will be zero when the angle of incidence is −0.42°. But if there is a deviation angle between the angle of incidence and its theoretical value, the RFOD will be dramatically changed, which is shown in Fig. 3(b). Even if the angle of incidence is 0.05° larger than the theoretical value, the RFOD will be −4.52104 fs4. The RFOD is large enough to affect the duration of the compressed pulse. Therefore, a better approach is to adjust the grism separation and change the grism tip-to-tip distance accordingly based on the precision linear stages.
3. Results and discussion
The evolution of the laser spectrum through the whole CPA laser system is presented in Fig. 4. The commercial kilohertz output pulse exhibits a Gaussian spectrum with a bandwidth of 30 nm (full-width at half-maximum (FWHM)). After the pulse cleaner based on XPWG and OPA, the spectrum (black line) is significantly broadened. The XPW-generated pulse has a broader spectrum than the input pulse. The spectrally dependent gain in the OPA process will reshape the spectrum of the XPW-generated pulse. The spectrum (blue line) of the pulse exhibits no obvious change after the stretcher, but the intensities of the short-wavelength components are significantly weakened after the grism pair (pink line), indicating that these components have a lower throughput efficiency. By adjusting the spectral shaping filter in the regenerative amplifier, the spectrum components (green line) longer than 780 nm are significantly suppressed to pre-compensate for the redshift and gain narrowing of the spectrum, and the peak wavelength is shifted to 755 nm. After the final booster amplifier, we can see that the gain narrowing of the spectrum (red line) is controlled, and the central wavelength is, again, shifted to 800 nm. The spectral width of the final amplified pulse can support a 19.9-fs, FTL pulse.
The main compressor of the SULF is based on a typical unfolded configuration, the size of all the gratings are 565 × 360 mm2, and their diffraction efficiency was measured to be about 92%. The damage threshold should be the primary consideration. Limited by the grating manufacture technology, the damage threshold of the gold-coated gratings is generally less than 200 mJ/cm2. In our system, the peak influence on the first grating is 180 mJ/cm2 of a 300-mm diameter laser beam. The compressor throughput efficiency was measured to be 64%, thus, the peak influence on the fourth grating is only 125 mJ/cm2. Another important issue is the low-order, spatial-to-spectral phase coupling, which refers to the impact of the quality of the gratings inside the compressor; it could be minimized by placing the two highest quality gratings in the second and third positions [8]. Then, the angle of incidence and slant distance of the compressor was optimized to obtain the shortest pulse duration. The recompressed pulse was measured with a single-shot autocorrelator (SSA, Coherent Inc.) for the full energy in the single-shot mode. The typical pulse duration shown in Fig. 5 was 24 fs (FWHM). When considering the 130 J output energy and the energy proportion included in only a 24-fs envelope, the recompressed pulse had a peak power of 5.4 PW [12]. When the pulse is measured with the SSA, pre-shot setup of the SSA is necessary. We need to maximize the intensity of the non-collinear second harmonic by slow adjustments of the nonlinear crystal and time delay of the SSA. However, the energy of the laser pulse was reduced by an uncoated fused silica plate and a neutral attenuator with an attenuation coefficient of 0.1 before the autocorrelator. We could not optimize the SSA to the best state when the laser system works at 1 Hz/7 J mode, because the laser energy entering the SSA was too low. And it was difficult to optimize the SSA in the single-shot mode as well. As a result, the pulse duration we captured in the single-shot mode may be longer than the real value.
As the laser beam has a large diameter, we selected three different parts of the laser beam to study the distributions and stabilities of the pulse durations. To make the samples more representative, we chose three spots at the left, middle, and right parts of the beam along the direction of beam propagation. The beam diameter of each part is around 5 mm. For the convenience of study, the pump lasers of the power amplifier and final booster amplifiers were shut down, and the laser system with an energy of 7 J was operated at a repetition rate of 1 Hz. The spectral shaping filter in the regenerative amplifier was adjusted again to make the spectral range before the vacuum compressor similar to the spectral range after the final amplifier in Fig. 4. We used a commercial measurement device (Fastlite, Wizzler) to measure the characteristics of the recompressed pulse. A typical pulse spectrum (black line) and spectral phase (green line) are shown in Fig. 6(a). The spectral phase over the whole spectrum is less than 1.2 rad, which indicates that the phase distortion introduced by the high-order dispersion is quite small. The temporal profile of the pulse is shown in Fig. 6(b). The FWHM of the pulse duration (black line) is 21.7 fs, which is FTL (red line) by a factor of approximately 1.04. The residual uncompensated spectral phase mainly results from the calculation errors of the material dispersion as well as the unknown dispersion of all the mirror coatings. Compared with the characteristics of the compressed pulse in [17, 18], the phase distortion over the pulse spectrum is reduced from 2.25 rad to less than 1.2 rad. This experimental result demonstrates that it is more effective to optimize the grism separation to control the high-order dispersion.
Fig. 6 Characteristics of the compressed beam: (a) input spectrum (black line), measured phase of the pulse(green line) and (b) temporal profile of the measured pulse(red line) and Fourier-transform-limited pulse (black line).
The long-term stability of the pulse duration at different parts of the beam for 50 shots is shown in Fig. 7. The pulse duration fluctuates over time. The average pulse duration at the central part of the beam (black square) is 21.79 fs, and the standard deviation of the duration is less than 0.37 fs, which indicates that the pulse duration can remain stable over a long period of time. As the measuring part is moved to the right part of the beam, the average pulse duration (red diamond) is 22.01 fs, while the standard deviation of the duration is 0.41 fs. As expected, the pulse duration of these two parts has little difference. As the measuring part is moved to the left edge of the output beam, the average pulse duration (blue circle) increases to 22.40 fs, and the standard deviation of the pulse duration is less than 0.3 fs. Because of the finite size of the second and third gratings, the short wavelength components from 750 to 755 nm are clipped by the edge of the gratings. As a result, the pulse duration increases. Despite this, we can conclude that the spectral phase over the whole laser beam is well-corrected. We will receive two meter-class gratings of 995555 mm2 before November, 2017, and spectral clipping will be avoided by that time. Another amplifier with a 220-mm diameter Ti:sapphire is currently under construction, aiming at delivering pulses with an energy of 360 J.
Moreover, it should be pointed out that the laser system uses a series of beam expanders and spatial filters, consisting of pairs of refractive lenses, to expand and clean the laser beam. Because the refractive index of the glass is related to the wavelength, short-wavelength and long-wavelength components will be focused into multiple foci after passing through these lenses. As a result, the lenses could introduce an aberration known as longitudinal chromatic aberration. This aberration is dependent on the focal length of the lens and the distance of the marginal ray from the axis. Due to longitudinal chromatic aberration, the different radial positions of the pulse front arrive at the focal region at different time, thus the focal intensity of the laser pulses could be dramatically decreased. In our previous works, we proposed a scheme to measure the relative time delay between the pulse fronts [26]. This approach have been applied in the petawatt laser facility, and a compensator is being designed to improve the pulse front quality of the laser pulses.
4. Conclusion
We demonstrated the advantages of a grism pair to compensate for higher-order phase distortions. The grism pair, a combination of a grating and prism pair, was inserted between an Öffner stretcher and regenerative amplifier. We presented the system characteristics, and the B-integral was calculated to be 0.47 in total, indicating that the nonlinear phase contribution could be neglected. By adjusting the spectral shaping filter in the regenerative amplifier, the spectrum of the final amplifier could support a 20-fs compression. The grism separation, angle of incidence and slant distance of the compressor were then optimized to reduce the high-order dispersion up to the fourth order. The grism pair was successfully applied into a 5-petawatt laser facility. The pulse duration of the recompressed pulse was measured to be less than 24 fs in the single-shot mode for a pump energy of 320 J. Finally, we selected three different parts of the laser beam to study the distributions and stabilities of the pulse duration and measured the spectral phase at the same time. The experimental results indicated that the pulse duration could remain stable over a long period of time, and the pulse durations at different positions of the output beam had little difference. Moreover, the spectral phase over the whole spectrum was reduced to less than 1.2 rad. We believe that this approach offers a new feasible solution for high-order dispersion compensation of femtosecond petawatt laser pulses and will be used in our 10 PW laser facility.
Funding
National Basic Research Program of China (Grant No. 2011CB808101); Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB16); International S&T Cooperation Program of China (Grant No. 2016YFE0119300); National Natural Science Foundation of China (NSFC) (Grant Nos. 61521093, 10734080, 60921004, 60908008, 61078037).
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