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Abstract
A novel design of double chirped pulse amplification laser systems implementing a combination of negatively and positively chirped pulse amplification is proposed for the first time. Without utilizing any extra dispersion compensation element, this design can sufficiently cancel out the second-, third- and especially fourth-order dispersion simultaneously, just by optimizing the parameters of the stretcher and compressor in first chirped pulse amplification stage which applies negatively chirped pulse amplification. The numerical results indicate that near Fourier-transform-limited pulse duration about 20fs can be achieved in high-peak-power femtosecond laser systems up to multi-Petawatt level. This design not only provides a feasible solution for the dispersion control in high-contrast and high-peak-power femtosecond laser systems, but also can avoid the degradation of temporal contrast induced by seed energy loss in the presence of additional dispersion compensation components.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Thanks to the inventions of chirped pulse amplification (CPA) and optical parametric chirped pulse amplification (OPCPA) [1–2], Petawatt-class (PW) femtosecond lasers have been built up by many laboratories over the past decades [3–11]. Recently, femtosecond lasers with peak power up to 10PW have also been proposed and constructed worldwide, such as ELI-10PW [12], Appllon-10PW [13], Vulcan-10PW [14], SULF-10PW [15]. With the rapid development of high-peak-power femtosecond lasers, the peak intensity has already reached 1022W/cm2 in PW-class laser and will probably realize 1023W/cm2 in 10PW-class laser in near future [16–17]. These ultra-intense femtosecond lasers can provide many unprecedented opportunities for the researches on laser-matter interaction in relativistic and even ultra-relativistic regimes. In such laser-matter investigations, the temporal quality of laser pulses becomes crucial along with the rapidly increased peak intensity. High temporal contrast is required to prevent the destructive pre-plasma on target induced by pre-pulses. Meanwhile, short pulse duration and good pulse temporal profile are also required for the enhancement of effective peak intensity with reduced pulse energy and reduced facility cost.
Double chirped pulse amplification (DCPA) technique has been proposed and widely used for the enhancement of pulse temporal contrast. DCPA scheme includes two CPA stages with intermediate temporal pulse filtering, which has been demonstrated to be an effective method to suppress the background of amplified spontaneous emission [18]. Pulse temporal filtering plays an important role in DCPA scheme, which can generate high-contrast and large-energy seed pulses for the second CPA stage. Though significant progress on pulse temporal contrast enhancement has been realized based on the DCPA technique, there are still some problems of pulse temporal quality. Such as the high-order dispersion, especially the residual fourth-order dispersion (FOD), which is still a bottleneck of pulse duration and pulse temporal profile in conventional DCPA laser systems.
Several dispersion compensation methods have been proposed for the suppression of FOD. Such as liquid-crystal modulator [19], mechanically deformable mirror [20], grism pair [21], mismatched-grating compressor [22–23], and acousto-optic modulator [24–25]. Among them, liquid-crystal modulator and deformable mirror are generally installed at the Fourier plane of a zero-dispersion stretcher to control the spectral phase. Nevertheless, liquid-crystal modulator is limited by the spectral resolution, deformable mirror is limited by its dynamic range. Thus, both liquid-crystal modulator and deformable mirror are seldom utilized in high-peak-power lasers. Though the mismatched-grating compressor is possible to completely compensate FOD, the material dispersion imposes a serious restriction on the design of stretcher and compressor due to the limited commercial available grating groove density [26]. Acousto-optic modulator, especially the acousto-optic programmable dispersive filter (AOPDF), can realize the arbitrary dispersion compensation. It has become the most popular dispersion compensation component in high-peak-power femtosecond lasers. Recently, pulse duration of ∼20fs has been reported in two different multi-PW lasers by utilization of AOPDF [9,11]. In addition, the grism pair has also been verified to be feasible for the FOD compensation. In 2017, high-order dispersion control of a 10PW Ti:sapphire (Ti:sa) laser by utilization of a grism pair was reported, and the pulse duration of ∼24fs was obtained [27]. However, due to the large energy loss of seed pulse induced by AOPDF and grism pair, the high-order dispersion compensation in DCPA lasers is inevitably accompanied with the degradation of pulse temporal contrast [28]. In our previous experiment, the pulse temporal contrast is degraded by an order of magnitude after inserting a grism pair [29]. DCPA scheme is primarily developed for the enhancement of pulse temporal contrast, above-mentioned problem will influence or restrict the application of grism pair and AOPDF, especially when a higher pulse temporal contrast is required. In addition, the angular dispersion of AOPDF also should be carefully treated.
In this work, we proposed a novel design of DCPA laser systems based on the combination of negatively and positively chirped pulse amplification (NCPA and PCPA, NPCPA in short), which is the first time to the best of our knowledge. In such laser systems, the seed pulses are firstly negative chirp stretchered, amplified and compressed in the first CPA (i.e. NCPA) stage, and then positive chirp stretchered, amplified and compressed in the second CPA (i.e. PCPA) stage. In this NPCPA design, not only the degradation of temporal contrast induced by extra dispersion compensation components can be avoided, but also the second-order dispersion, i.e. group velocity dispersion (GVD), third-order dispersion (TOD) and FOD can be cancelled out simultaneously just by optimizing the parameters of the stretcher and compressor in the NCPA stage. The numerical results show that near Fourier-transform-limited (FTL) pulses with ∼20fs duration can be achieved in high-peak-power femtosecond laser systems up to multi-PW level. This paper is organized as follows. In section 2, the characteristics of NPCPA laser systems is briefly described based on FOD compensation. In section 3, the detailed NPCPA designs with two different types are presented, in which a regenerative amplifier and an OPCPA amplifier are employed as the high-gain preamplifier, respectively. In section 4, some discussions about this NPCPA design are illustrated. Lastly, conclusion is presented.
2. Characteristics of NPCPA laser systems
In conventional DCPA laser systems, the two CPA stages are both employing PCPA. For such a PCPA stage, both GVD and TOD can be compensated by optimizing the incident angle and grating pair distance of compressor. However, the FOD is impossible to be entirely cancelled out, and the residual FOD is generally positive. Hence, the positive residual FOD accumulated by the two PCPA stages in conventional DCPA laser systems is usually very large, which will lengthen the duration and degrade the temporal profile of output pulses. As a result, additional components, such as AOPDF and grism pair, should be applied for the FOD compensation in conventional DCPA laser systems.
Different from conventional DCPA laser systems, the NPCPA laser systems are based on a combination of NCPA and PCPA. Here, the NCPA laser system is innovatively adopted as the first CPA stage, which usually possess the characteristics of small stretching factor, low pulse energy and high repetition rate. Compared with PCPA front end, the stretcher in NCPA stage is more easily aligned due to the absence of focusing optics, the material compressor in NCPA stage has higher energy and spectral bandwidth transmission efficiency while is insensitive to small misalignment. A typical setup of NCPA laser system has been shown in Ref. [30]. The femtosecond seed pulses from mode-locked oscillator are firstly negative chirp stretched by a two-stage stretcher, which combines grating pair and prism pair for the compensation of TOD. Followed by the stretcher, multi-pass amplifier is utilized to enhance the seed pulse energy to millijoule level. Lastly, a bulk material compressor is used to recompress the amplified pulses to tens of femtoseconds.
It is worth noting that the residual FOD in NCPA laser systems is usually negative, which is contrary to that in PCPA laser systems [31]. In addition, the residual amount of negative FOD is variable, by altering the parameters of the stretcher and compressor in NCPA laser systems. Therefore, after carefully optimizing the design of the stretcher and compressor in the NCPA stage, it is potential to achieve a good result of FOD control in NPCPA laser systems based on the counteraction of the residual FOD in two CPA stages. The detailed design and numerical analysis will be presented in Section 3.
3. Design of NPCPA laser systems
In above section, we analyzed the characteristics of NPCPA laser systems based on the control of residual FOD. In this section, we will present two NPCPA design examples for high-peak- power and high-contrast femtosecond laser systems, which are expected to achieve near FTL laser pulses, without utilizing any additional dispersion control components. In our design, the laser systems are composed of three main modules: the NCPA stage, the pulse cleaner, and the PCPA stage. For the sake of simplicity, the setup of our NCPA stage is similar to that in [30], and the most amount of pulse stretching, amplification and compression are still accomplished in the PCPA stage. The key steps of our design are:
- a. According to the parameters of Öffner stretcher and all materials in the pulse cleaner and PCPA stage, calculating their total GVD, TOD and FOD, respectively.
- b. Adjusting the incident angle and grating pair distance of grating compressor in the PCPA stage to cancel out the above GVD and TOD simultaneously, based on Eq. (1) [22]. Here θ is the diffractive angle of grating compressor in the PCPA stage, and d is grating groove period. The superscripts s and m identify Öffner stretcher and all materials in the pulse cleaner and PCPA stage, respectively.
- c. Calculating the positive residual FOD in the pulse cleaner and PCPA stage, based on the parameters of above grating compressor.
- d. Optimizing the parameters of the stretcher and compressor in the NCPA stage, until the realization of zero-GVD, zero-TOD, and negative residual FOD with similar amount to that in step c.
3.1 250TW laser system, with small stretching factor and large material dispersion
The first design example is a 250TW-level NPCPA laser system, which applies a regenerative amplifier as the preamplifier in the PCPA stage. For such laser systems, the stretching factor in the PCPA stage is comparatively small while the introduced material dispersion is relatively large. A simple schematic of this laser system is shown in Fig. 1.
In the NCPA stage, the ultrashort seed pulses from Ti:sa oscillator are firstly negative chirp stretched to −20ps by a two-stage pulse stretcher, then amplified to ∼1mJ by a Ti:sa multi-pass amplifier with 10mJ pump energy, and finally compressed to ∼30.4fs by a SF18 bulk material compressor. In order to control the spectral gain narrowing in multi-pass amplifier, a specially designed mirror with variable spectral reflectivity [32] can be utilized. As referred in [30], the B-integral can be controlled by adopting proper laser beam size in the material compressor of the NCPA stage. In addition, a beam splitter can also be introduced after the NCPA stage to achieve proper pulse energy for the following stages.
The first stage stretcher is a SF57 prism pair with the apex-to-apex separation of 1030.5mm, through which the pulses make two passes. The second stage stretcher is a 600g/mm grating pair with the incident angle of 50° and the grating pair distance of 5.45cm. The compressor is a SF18 bulk material with the total traversing length of 337mm. All the materials introduced in this NCPA stage includes 72mm Ti:sa, 36mm calcite, 20mm KDP, 11mm fused silica, and 40mm terbium gallium garnet. Dispersion at 800nm central wavelength of this NCPA stage is listed in Table 1. The residual GVD and TOD are almost 0 and the residual FOD is −216449fs4, which is the main factor that prevents the recompression to FTL pulse duration. In addition, the fifth-order dispersion (FiOD) is also calculated, whose residual amount is about −5×104fs5. It is worth noting that the stretcher and compressor in above NCPA stage is designed based on the dispersion parameters in the subsequent pulse cleaner and PCPA stage.
Table 1. Dispersion at 800nm central wavelength of the NCPA stage.
After the NCPA stage, a pulse cleaner is employed to enhance the temporal contrast of seed pulses. For the sake of simplicity, two ultrafast Pockel cells and a saturable absorber are used in the pulse cleaner, which has been verified to be an effective method for the improvement of pulse temporal contrast in high-peak-power laser systems [7–8]. All the material dispersion at 800nm central wavelength introduced by this pulse cleaner is about 3942fs2, 3317fs3, −1653fs4 and 4485fs5, respectively.
The following PCPA stage includes an Öffner stretcher, four stages of Ti:sa amplifier and a grating compressor. High-contrast seed pulses from the pulse cleaner are firstly positive chirp stretched to ∼700ps by the Öffner stretcher and amplified to about 1.5mJ by the regenerative preamplifier, then amplified to 8J-level by three cascaded multi-pass amplifiers. The design of these amplifiers can be referred to an existing 200TW Ti:sa laser [33–34]. Finally, compressed pulses with the energy above 5J can be obtained. The spectral gain narrowing and redshift can be suppressed by adjusting the spectral shaper in regenerative cavity [35].
In this PCPA stage, the Öffner stretcher is designed based on a 1200g/mm grating with the incident angle of 50°. The curvature radii of concave and convex mirrors are 0.88m and 0.44m respectively, and the distance between the grating and the center of spherical mirrors is 0.22m. The materials used in this PCPA stage includes 200mm KDP, 175mm fused silica and 440mm Ti:sa. In order to simultaneously cancel out the GVD and TOD of the Öffner stretcher and all materials in the pulse cleaner and PCPA stage, the grating compressor is designed in terms of Eq. (1). The grating groove density is 1200g/mm, the incident angle is 52.771°, and the distance of grating pair is 893.15mm. The dispersion at 800nm central wavelength of the pulse cleaner and PCPA stage are listed in Table 2. As a result, the residual GVD and TOD are nearly 0, the residual FOD is 2168295fs4, and the residual FiOD is about −1.12×106fs5.
Table 2. Dispersion at 800nm central wavelength of the pulse cleaner and PCPA stage.
In all, the residual GVD, TOD and FOD at 800nm central wavelength of the whole NPCPA laser system are 0fs2, −8fs3, 380fs4 respectively, while the residual FiOD is about −1.17×106fs5. A simulated super-Gaussian pulse spectrum ranges from 750nm to 850nm and the calculated spectral phase of this designed NPCPA laser system are shown in Fig. 2(a). The spectral phase over the whole spectrum is below 0.93rad, which indicates that the phase distortion caused by residual high-order distortion is quite small in this design. The temporal profile of compressed pulses is also calculated, with a duration of ∼20.1fs, which is nearly the same with FTL pulse duration, as shown in Fig. 2(b). Consequently, the peak power >250TW can be realized in this laser system.
Fig. 2. (a) Simulated pulse spectrum and calculated spectral phase (b) FTL and corresponding compressed pulses of the 250TW NPCPA laser system.
3.2 4PW laser system, with large stretching factor and moderate material dispersion
Another design example is a multi-PW NPCPA laser system, which employs an OPCPA/Ti:sa hybrid amplification scheme. Compared to the 250TW laser system above, a larger stretching factor is required for this laser system, while a moderate material dispersion is introduced due to the utilization of OPCPA preamplifier in the PCPA stage. Figure 3 shows the schematic of this multi-PW NPCPA laser system, the setup of its NCPA stage and pulse cleaner is similar to that in the 250TW laser system above. But the parameters of the stretcher and compressor in this NCPA stage is redesigned, in order to make its residual FOD matching with that in the following pulse cleaner and PCPA stage.
In this new NCPA stage, the SF57 prism pair is designed with an apex-to-apex separation of 778.4mm, the 600g/mm grating pair is designed with an incident angle of 55° and a grating pair distance of 4cm, while the SF18 bulk material is designed with a total traversing length of 237.75mm. Dispersion at 800 nm central wavelength of this NCPA stage is listed in Table 3, and the residual amounts are 3fs2, −2fs3, −162106fs4 and −46154fs5, respectively. Consequently, compressed pulses with ∼25.5fs duration are outputting from this NCPA stage.
Table 3. Dispersion at 800nm central wavelength of the NCPA stage.
This PCPA stage is referred to the second CPA stage of the existing 4.2PW laser system [9], which consists of an Öffner stretcher, an OPCPA preamplifier, four-stage Ti:sa amplifiers, and a grating compressor. High-contrast seed pulses from the pulse cleaner are firstly stretched to ∼1.9ns by the Öffner stretcher, then amplified to 50mJ by the two-stage OPCPA preamplifier with 200mJ pump energy. The following four amplifiers are designed to output 1.8J, 4.5J, 50J and 110J pulse energy, with the pump energy of 4.5J, 8J, 100J and 170J, respectively. After compression, pulse energy >80J can be achieved. Different from the regenerative preamplifier, the OPCPA preamplifier can directly realize spectral shaping by adjusting the phase-matching angle of nonlinear crystal and changing the temporal profiles of its pump lasers. Moreover, high temporal contrast can also be ensured by this OPCPA, which is operated at a low-gain of ∼250 to minimize the parametric fluorescence [36–37]. In addition, to suppress the transverse parasitic lasing in boost amplifiers, an index-matching fluid with absorbing dye and extraction during pumping technique are used [4–9]. To decrease the lenses induced pulse front distortion, the large-aperture telescopes are designed as achromatic [38–39].
For this Öffner stretcher, the grating groove density is 1480g/mm, the incident angle is 50°, the curvature radii of concave and convex mirrors are 1.32m and 0.66m, while the grating is 0.33m from the center of sphere mirrors. The materials introduced in this PCPA stage includes 19mm beta barium borate (BBO), 310mm Ti:sa, and the glasses of all telescopes (80mm fused silica, 20mm ZF6 and 30mm F4). The grating compressor consists of four 1480g/mm gratings, with the incident angle of 50.493° and the grating pair distance of 1215.4mm, which are also designed based on Eq. (1). The dispersion at 800nm central wavelength of this pulse cleaner and PCPA stage are listed in Table 4, and the residual amounts of GVD, TOD, FOD and FiOD are −1fs2, 2fs3, 161706fs4 and −1.21×106fs5 respectively.
Table 4. Dispersion at 800nm central wavelength of the pulse cleaner and PCPA stage.
For the whole NPCPA laser system, the residual GVD, TOD, FOD, FiOD at 800nm central wavelength are 2fs2, 0fs3, −400fs4 and −1.25×106fs5 respectively, and the phase distortion over whole spectrum is below 1rad. As a result, the degradation of pulse temporal profile induced by phase distortion is slight and ignorable. The temporal profile of compressed pulses output from this NPCPA laser system is also calculated based on the pulse spectrum in Fig. 2(a). As Fig. 4 shows, near FTL pulse duration of ∼20.1fs duration can be obtained. Consequently, this NPCPA laser system can potentially realize >4PW peak power output.
Fig. 4. Calculated spectral phase and according compressed pulse of the 4PW level NPCPA laser system.
Based on above results, we can find that this novel NPCPA design is not only applicable to high-peak-power laser systems with small stretching factor and large material dispersion, but also suitable for high-peak-power laser systems with large stretching factor and moderate material dispersion.
4. Discussion
In above NPCPA designs, the GVD, TOD and FOD are almost completely cancelled out, then near FTL pulses are achieved. However, a large residual amount of negative FOD may induce temporal distortion of compressed pulses output from the NCPA stage. In order to alleviate this problem, some methods have also been proposed.
In the NCPA stage, an appropriate compromise between the temporal quality of compressed pulses and the residual amount of negative FOD can be made. We redesign the NCPA stage of above 250TW laser system: the incident angle and grating pair distance of 600g/mm grating pair stretcher are 60° and 2.85cm respectively, the apex-to-apex separation of SF57 prism pair stretcher is 572.2mm, and the total traversing length of SF18 material compressor is 154.9mm. In this design, the ultrashort seed pulses are firstly stretched to −11.5ps, then amplified to 1mJ, and finally compressed to 22.5fs, with the residual FOD of −118548fs4. As shown in Fig. 5(a), compared with the design in Section 3.1, the temporal profile of the compressed pulses output from the newly designed NCPA stage is obviously better than that with 30.4fs. As the residual negative FOD in this new NCPA stage can only partially cancel out the residual positive FOD in the following stages, the pulse duration of this new NPCPA laser system is lengthened from previous ∼20.1fs to current ∼21.3fs, as shown in Fig. 5(b). This pulse duration is less than 1.1 times of FTL, which is still a quite good result in high-peak-power femtosecond laser systems.
Fig. 5. (a) Compressed pulses of the NCPA stage in 250TW NPCPA laser system with fully and partially FOD compensation, (b) compressed pulses of newly designed 250TW NPCPA laser system.
Another method based on the global optimization of high order residual dispersion may also be effective. Instead of cancelling out the dispersion order by order, a proper tradeoff between different orders of dispersion is found to make the whole spectral phase as flat as possible [40]. In this scheme, the pulse temporal quality degradation in the NCPA stage induced by residual FOD is probably alleviated. The detail of this method is still under investigation.
5. Conclusion
In conclusion, a novel DCPA laser system based on NPCPA scheme is proposed and designed for the first time to the best of our knowledge. The NPCPA scheme makes it possible to cancel out the GVD, TOD and FOD simultaneously, while without utilizing any additional dispersion compensation component. The numerical calculations for two different design examples show that near FTL pulse duration around 20fs can be achieved in laser systems with peak power of hundreds-TW to multi-PW level. In addition, the NPCPA scheme can avoid the degradation of temporal contrast induced by extra dispersion compensation components in traditional DCPA laser systems. Therefore, the NPCPA scheme should be a feasible solution for the dispersion control in high-contrast and high-peak-power laser systems. In the following work, a further investigation of NPCPA scheme aims at the dispersion control over larger spectral bandwidth will be carried out.
Funding
Natural Science Foundation of Shanghai (20ZR1464600); National Natural Science Foundation of China (11127901, 61505234, 61521093); International Science and Technology Cooperation Programme (2016YFE0119300); Strategic Priority Research Program of Chinese Academy of Sciences (XDB160301); Science and Technology Commission of Shanghai Municipality (2017SHZDZX02); Youth Innovation Promotion Association of the Chinese Academy of Sciences.
Disclosures
The authors declare no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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