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Abstract
Pre-pulses caused by the post-pulses in the optical parametric chirped-pulse amplifier were comprehensively studied for the first time, including the underlying mechanism for the delay-shift of pre-pulses, the intensity variation of pre-pulses affected by the initial delay of post-pulses and the pump energy, and also the nonlinear beat noise. The simulation and measurement confirmed that the high-order dispersion of the pulse stretcher was the main cause for the delay-shift of pre-pulses, which should be similar with the chirped-pulse amplifiers. The intensity of pre-pulses would decrease significantly as the initial delay of post-pulses increased, but would increase with the growth of pump energy. Moreover, the temporal position of the nonlinear beat noise in the experiment was successfully predicted by our simulation. This work could help us better understand the pre-pulses in OPCPA and provide helpful guidance for designing high-contrast laser systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultra-intense and ultra-short lasers are powerful tools for secondary radiation generation, particle acceleration, and other strong-field physics experiments [1–4]. In past decades, a lot of petawatt-level systems have been constructed worldwide based on the chirped-pulse amplifier (CPA) [5–7]. Since the invention of the optical parametric chirped-pulse amplifier (OPCPA), its advantages of low thermal effect, large bandwidth and the absence of parasitic lasing effect have attracted researchers’ attention [8–12]. Towards giant peak power, EP-OPAL 75PW laser [11] and Station of Extreme Light (SEL) 100PW laser [12] are under construction based on the OPCPA. With the pursuit of the higher laser peak power, temporal contrast becomes more and more crucial because it is easier for noise to reach the laser ablation threshold and destroy the laser-target interaction [13,14].
In this paper, temporal contrast degradation by pre-pulses in the OPCPA system is concerned. Actually, this kind of pre-pulses has been firstly studied in CPA systems [15,16]. Its origination can be understood that the post-pulse interferes with the main chirped pulse and forms temporal modulation. Then the modulation would produce the pre-pulse after the compressor due to the B-integral in CPA. Although the B-integral is smaller in OPCPA, pre-pulses can also be produced due to the nonlinear gain and coupled interaction between the signal and pump [17,18]. In the previous study on the CPA system [19], the pre-pulses far from the main pulse were temporally distorted compared to the corresponding post-pulses. Additionally, the temporal positions of these pre-pulses were delayed to the symmetrical positions of the post-pulses, which would be described as ’delay-shift’ in the following content. Recently, these phenomena were numerically explained by considering the high-order dispersion introduced by the stretcher [20]. However, the asymmetry of pre-pulses has not been studied in the OPCPA systems. In addition to the pre-pulses generated by the nonlinear mixing of main pulse and post-pulses discussed above, another type of pre-pulses generated by the mixing of pre-pulses and post-pulses was theoretically predicted in [21], which was named as nonlinear beat noise. But, the experiment on this type of pre-pulses is absent to our knowledge.
In the following paragraphs, the delay-shift of pre-pulses in OPCPA would be demonstrated based on a broadband system. According to our experiment and simulation, the high-order dispersion could also be the key factor to the delay-shift of pre-pulses in OPCPA. The intensity evolution of pre-pulses versus the initial delay of post-pulses and pump energy has also been studied in detail. Finally, the nonlinear beat noise in the experiment would be reported. We find that the nonlinear beat noise is not generated at the position as predicted in [21], which could be explained by the high-order dispersion according to our simulation. The numerical results considering the high-order dispersion can agree well with the experiment.
2. Numerical method and experimental setup
In order to numerically investigate the post to pre-pulses process in OPCPA, following coupled-waves equations were solved [22],
The experiment was based on the SEL-100PW frontend [12]. In this facility, an ultra-broadband seed ranging from 820 nm to 1030 nm was temporally expanded to 3 ns (full width) by a double-grating Offner stretcher. The GDD, TOD, FOD, and FiOD provided by the stretcher was 6,082,694 fs$^2$, −16,724,320 fs$^3$, 75,375,209 fs$^4$, and −471,857,241 fs$^5$, respectively [24]. Then the seed energy was amplified from 15 $\mu$J to 9 mJ after the first amplifier stage, and to 488 mJ after the second amplifier stage based on the type-I LBO. The energy of the 532nm pump lasers in two stages was 90 mJ and 2.8 J, respectively. In this experiment, the pump laser of the third amplifier stage was not used. The output repetition rate was 1 Hz, and the beam diameter was 9 mm. After the compressor, the pulse was compressed to about 16 fs which was near the FTL duration.
Plane-parallel plates made of uncoated BK7 with the thickness of 1 mm, 5 mm, 10 mm, and 15 mm were used to generate post-pulses with different initial delay to the main pulse. The surface reflectivity is $\sim$ 4%, so the relative intensity of post-pulses to the main pulse is $\sim$ $10^{-3}$. Plane-parallel plates were separately inserted between the first and second OPCPA amplifier to study the pre-pulses generated by the second OPCPA amplifier. Above experimental parameters were used in the simulation. The nonlinear beat noise was investigated by simultaneously inserting two plane-parallel plates. Temporal contrast was measured by the commercial third-order correlator (Amplitude, Sequoia).
3. Results and discussion
3.1 Delay-shift of the pre-pulses
Figure 1(a) illustrated the output temporal profile when we inserted the plane-parallel plate with the thickness of 1 mm. It should be noticed that the small pulses at −6 ps and 6 ps existed even when plane-parallel plates were not inserted. The post-pulse at 11 ps delayed to the main pulse was created due to the double reflection in the 1mm plate. Correspondingly, the pre-pulse at −11 ps was produced symmetrically with the post-pulse, and the delay-shift was not observed. However, the delay-shift appeared after we replacing the 1mm plate with the 5mm plate. As shown in Fig. 1(b), the post-pulse was generated at 52 ps, and the pre-pulse was generated at $-51\,{\rm ps}$. Since the symmetrical position of the corresponding post-pulse was −52 ps, the delay-shift was $1\,{\rm ps}$ for the −51ps pre-pulse.
Fig. 1. The temporal profile when inserting the plane-parallel plates with the thickness of 1 mm (a), 5 mm (b), 10 mm (c), and 15 mm (d). The blue and green lines in (d) represented the simulated pre-pulses with and without considering the high-order dispersion, respectively.
When we inserted the 10mm plate, the post-pulse was generated at 103 ps, and the pre-pulse was generated at −99 ps, as shown in Fig. 1(c). Besides, the ghost pulse at −103 ps was observed symmetrically with the post-pulse. Its relative intensity to the main pulse was the square of the post-pulse’s relative intensity. The appearance of the ghost pulse was caused by the mixing of the second harmonics of the post-pulse and the fundamental of the main pulse in the measurement device [19]. It could be deduced that the delay-shift of the −99ps pre-pulse was 4 ps. Figure 1(d) depicted the temporal profile when the 15mm plate was inserted. The post-pulse was generated at 154 ps, and the pre-pulse was generated at −145 ps. The ghost pulse at −154 ps was also observed. As the plate was thicker and the initial delay of the post-pulse was larger, the delay-shift of the pre-pulse increased to 9 ps. There was another pre-pulse generated at −271 ps due to the quartic reflection in the 15mm plate. The corresponding post-pulse should be produced at 308 ps, but it was beyond the time window of the measurement device. The corresponding delay-shift could be as large as 37 ps. The pre-pulses due to the quartic reflection were also observed when other plates were inserted, but they were not discussed here for simplicity.
The delay-shift of pre-pulses was numerically investigated by considering two dispersion conditions of the pulse stretcher. The green line in Fig. 1(d) depicted the simulated pre-pulse when only the GDD was considered. In this condition, the pre-pulse overlapped with the ghost pulse in the experiment, and the delay-shift did not occur. However, the pre-pulse became delayed and temporally distorted if the high-order dispersion was also taken into account, as depicted by the blue line in Fig. 1(d). Obviously, the latter case was closer to the real system. It worth mentioning that the positions of post-pulses were almost the same before and after the amplification both in the simulation and experiment.
The simulated delay-shift of pre-pulses considering the high-order dispersion was compared to the experimental results in detail in Fig. 2. It was clear that the pre-pulse had a larger delay-shift when the corresponding post-pulse had a larger initial delay to the main pulse. The biggest deviation of the delay-shift between the simulation and experiment was 3 ps when the initial delay of the post-pulse was as large as 308 ps. The similar trend of the delay-shift was investigated only numerically in the CPA system without the comparison of experimental results [20]. The good agreement between our simulation and experiment could further indicate that the delay-shift was mainly induced by the high-order dispersion of the pulse stretcher, and it would occur both in the CPA and OPCPA system. In order to properly locate the optical component which produced the pre-pulse in the real system, the delay-shift of the pre-pulse needed to be considered especially when the component was very thick.
Fig. 2. The delay-shift of pre-pulses versus the initial delay of post-pulses. The red line represented the numerical results. The black diamond represented the experimental results.
3.2 Intensity of the pre-pulses versus the initial delay of post-pulses
Then the intensity of pre-pulses was investigated. We measured that the relative intensity of the pre-pulses at −11 ps, −51 ps, −99 ps, and −145 ps was $1.3\times 10^{-3}$, $4.6\times 10^{-4}$, $1.6\times 10^{-4}$, and $5.4\times 10^{-5}$, respectively, as depicted by the black diamond in Fig. 3. The −145ps pre-pulse was 20 times weaker than the −11ps pre-pulse. It was partly due to that the corresponding post-pulse had less temporal overlapping with the main pulse. In the simulation, the relative intensity of the pre-pulses at −11 ps, −51 ps, −99 ps, and −145 ps was $7.7\times 10^{-4}$, $4.4\times 10^{-5}$, $4.5\times 10^{-6}$, and $1\times 10^{-6}$, respectively, as depicted by the red line in Fig. 3. Compared to the experimental results, the numerical results had faster decline as the initial delay of the post-pulse grew. For example, the intensity of the −11ps pre-pulse in the simulation was similar with that in the experiment, but the difference between the simulated and measured intensity of the −145ps pre-pulse reached nearly two orders of magnitude.
Fig. 3. The relative intensity and the simulated pulse duration of pre-pulses versus the initial delay of post-pulses under the pump energy of 2.8 J. The black diamond represented the measured intensity. The red and blue lines represented the simulated intensity considering that the full spectrum and the limited spectrum of the output pulse was measured, respectively. The green line represented the simulated duration of pre-pulses.
The difference could be mainly because the third-order correlator only allowed the characterization of part of spectrum due to the second harmonic generation and the sum frequency process [25], which leaded to the longer duration and smaller energy for the measured main pulse. The typical phase-matching bandwidth for the measurement was $\sim$ 15 nm [26,27]. Considering that the input pulse had the spectral width of 210 nm, the peak intensity of the main pulse would be reduced by approximately two orders of magnitude. As for the pre-pulses, they could be not well compressed like the main pulse especially for the pre-pulses that were far from the main pulse, which was mostly caused by the high-order dispersion. As depicted by the green line in Fig. 3, the pulse duration of the pre-pulse increased dramatically as the initial delay of the corresponding post-pulse grew. So that, the absolute intensity of the pre-pulses that were far from the main pulse might be much less affected in the measurement, and their relative intensity would be higher compared to the numerical results when the full spectrum of the output pulse was considered. We multiplied the final $\widetilde {E}_s(\omega )$ by the sinc function in the simulation assuming that the output pulse was centered at $925\,{\rm nm}$ with a FWHM bandwidth of 15 nm. The corresponding relative intensity of the pre-pulses was depicted by the blue line in Fig. 3. In this case, the numerical results were close to the experimental results. In order to compare with the experimental results, we would consider the limited measurement capability of the third-order correlator in the following content.
Usually, the pre-pulse could be improved by adding the wedge to the corresponding optical component. However, it would introduce angular dispersion especially for broadband lasers. According to the above analysis, increasing the thickness of the optical component could be the alternative method for effectively decreasing the intensity of the pre-pulse without degrading the beam quality.
3.3 Intensity of the pre-pulses versus the pump energy
The pre-pulses under different pump energy were also investigated. The output signal energy was 275 mJ, 367 mJ, 449 mJ, and 488 mJ when the pump energy of the second amplifier stage was $1.6\,\rm {J}$, 2 J, 2.4 J, and 2.8 J, respectively. Figure 4 illustrated the corresponding temporal profile when the 15 mm plane-parallel plate was inserted. The measured relative intensity of −145ps pre-pulse was $5.7\times 10^{-6}$, $6.1\times 10^{-6}$, $2.1\times 10^{-5}$, $5.4\times 10^{-5}$ for the pump energy of 1.6 J, 2 J, $2.4\,\rm {J}$, and $2.8\,{\rm J}$, respectively, as shown in Fig. 4(a). While, the simulated intensity was $1.2\times 10^{-5}$, $2.9\times 10^{-5}$, $5.1\times 10^{-5}$, $7.3\times 10^{-5}$, respectively, as shown in Fig. 4(b). There was 10 times and 6 times growth of the pre-pulse’s relative intensity in the experiment and simulation respectively when increasing the pump energy from 1.6 J to 2.8 J. Both the experiment and simulation revealed that the pre-pulse was more intense as the pump energy grew. It could be understood that the higher pump energy deepened the saturation and nonlinear modulation [17].
Fig. 4. (a) The measured and (b) simulated temporal profile when the 15 mm plane-parallel plate was inserted under different pump energy. In the simulation, we considered that the output pulse was centered at 925 nm with the spectral width of 15 nm.
3.4 Nonlinear beat noise
Finally, the nonlinear beat noise was investigated. By increasing the pump energy over 2 J, the nonlinear beat noise could be obviously observed. Figure 5 depicted the output temporal profile under the pump energy of 2.8 J when the 10mm and 15mm plane-parallel plates were inserted simultaneously. According to the previous theoretical study [21], the nonlinear beat noise should be generated at −42 ps which was calculated by the sum of −145ps pre-pulse and 103ps post-pulse. However, it was generated at −47.5 ps both in our experiment and the simulation, as shown in Fig. 5. We attributed the difference to the high-order dispersion of the pulse stretcher, which was not considered in the previous study. There also exists nonlinear beat noise at 48.5 ps in the simulation due to the interaction of the −99ps pre-pulse and the 154ps post-pule. However, it was buried by the laser trailing edge in the experiment.
Fig. 5. (a) The measured and (b) simulated temporal profile when simultaneously inserting the plane-parallel plates with the thickness of 10 mm and 15 mm. The inset was the nonlinear beat noise. In the simulation, we considered that the output pulse was centered at 925 nm with the spectral width of 15 nm.
The measured intensity of the nonlinear beat noise at −47.5 ps was $2.2\times 10^{-6}$, and the simulated intensity was $1\times 10^{-6}$. Compared to the −99ps and −145ps pre-pulses, it was about two orders of magnitude weaker. It was the first time to experimentally observe the nonlinear beat noise. Although it was less intense, it could still be harmful especially to hundreds-petawatt lasers in the future. We noticed that the laser noise could be more complicated when inserting more than two plates, and the identification of the noise source would be difficult. In the real systems, we suggested eliminating the most intense pre-pulse firstly, and the weaker noise such as nonlinear beat noise could be eliminated automatically.
4. Conclusion
In this article, the pre-pulses caused by the post-pulses in the OPCPA system was studied in detail. Similar with the CPA systems, the delay-shift of pre-pulses was also observed in OPCPA. The simulated delay-shift by considering the high-order dispersion could agree well with the experiment, and it increased as the initial delay of the corresponding post-pulses grew. The intensity of pre-pulses was also investigated. It was observed that the pre-pulse had lower intensity when the initial delay of the post-pulse was larger. We measured that the −144ps pre-pulse was one order of magnitude weaker than the −11ps pre-pulse. According to the simulation, there could be additional two orders of magnitude reduction due to the limited spectral measurement capability of the third-order correlator. So that, the pre-pulse could be improved by increasing the thickness of the corresponding optical component in the real system. We also adjusted the pump energy, and the relative intensity of the pre-pulse was stronger at higher pump energy. Furthermore, the nonlinear beat noise generated by the nonlinear mixing of the post-pulse and pre-pulse was investigated. The temporal position of the nonlinear beat noise was successfully predicted by the simulation which considered the high-order dispersion. The nonlinear beat noise was weaker than the pre-pulse generated by the mixing of the post-pulse and main pulse, but it should also be stressed in the future laser system with higher peak power. This comprehensive work was believed to not only deepen our understanding on the pre-pulses but also provide guidelines for the design of OPCPA systems with high temporal contrast.
Funding
National Key Research and Development Program of China (2019YFF01014401, 2022YFA1604401, 2022YFE0204800); Shanghai Sailing Program (21YF1453800); National Natural Science Foundation of China (11127901, 61925507); The International Partnership Program of Chinese Academy of Sciences (181231KYSB20200040); Science and Technology Commission of Shanghai Municipality (22560780100, 23560750200); Chinese Academy of Sciences President's International Fellowship Initiative (2023VMB0008); Youth Innovation Promotion Association of the Chinese Academy of Sciences.
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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