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Abstract
In this paper, we report that the conversion efficiency and spectrum of femtosecond optical parametric amplification (fs-OPA) can be significantly enhanced by employing a compact cascaded femtosecond OPA (CF-OPA) scheme with the self-compensation of the temporal walk-off between two nonlinear gain media. Correspondingly, the gain related temporal contrast can also be improved. The feasibility of the CF-OPA method using three cascaded BBO crystals is numerically and experimentally analyzed. Moreover, by replacing the conventional fs-OPA with the CF-OPA and optimizing the design, the performance of a nonlinear temporal filter combining cross-polarized wave generation and fs-OPA is comprehensively improved. The experimental results demonstrate the superiority of the CF-OPA scheme, which can generate high-performance cleaned pulses at 1 kHz repetition rate with energy of 340μJ, energy fluctuation below 0.9% (RMS), spectral width of 97 nm (FWHM), Fourier-transform-limited pulse width of 12 fs and temporal contrast better than 10−12. To the best of our knowledge, this is the first reported temporal walk-off self-compensated quasi-collinear CF-OPA geometry adopting three cascaded BBO crystals, which can be easily generalized to other wavelengths or nonlinear crystals. The above nonlinear temporal filter with a CF-OPA scheme has the rarest comprehensive parameters, which can provide excellent seed pulses for PW and 10 PW class femtosecond laser systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the great advances in chirped pulse amplification (CPA) [1], optical parametric chirped pulse amplification (OPCPA) [2] technologies and corresponding breakthroughs in key optical components [3–6], the marvelous developments have been achieved in femtosecond (fs) superintense laser systems [7,8]. So far, the highest peak power of the femtosecond superintense laser systems have reached to 10 petawatt (PW) for CPA laser [9,10] and 4.9 PW for OPCPA laser [11]. And the highest focused peak intensity has reached $10^{23}\;\textrm {W/cm}^2$ [12]. Furthermore, the laser systems with a higher peak power of 100 PW or even exawatt are already under planning or construction [13,14], and the corresponding focused peak intensity of such femtosecond laser systems will exceed $10^{23} \textrm {W/cm}^2$ in the near future. However, any pre-pulses or amplified spontaneous emission (ASE) with intensities above $10^{11}\; \textrm {W/cm}^2$ level will generate unwanted low-density plasma prior to the main pulse and thus dramatically influence the laser-plasma interactions [15]. Therefore, it is indispensable to adopt the pulse cleaning techniques in high-peak-power femtosecond laser systems.
Temporal filters used in the front-end are one of the mainstreams since they can avoid a lot of energy loss compared with techniques implemented after the compressor. In the past decades, many pulse cleaning techniques for front-end, such as saturable absorber (SA) [16,17], self-diffraction (SD) [18], nonlinear ellipse rotation (NER) [19,20], cross-polarized wave generation (XPWG) [21,22], second-harmonic generation (SHG) [23], sum-frequency generation (SFG) [24], and optical parametric amplification (OPA) [25–27], have been proposed to improve the temporal contrast. Although these techniques can effectively enhance the temporal contrast of femtosecond pulse, each of them still more or less has shortcomings [28]. Hence, improvements are still required when these technologies are used. In 2013, an energy-scalable temporal filter based on spatial filtering through a hollow-core fiber (HCF) followed by a nonlinear crystal for XPWG was reported, which was capable of supporting up to a 1.6 mJ output at 11 mJ input [29]. This is the highest energy reported in temporal filters. Nevertheless, the temporal contrast is limited by extinction ratio of the polarizers in XPWG process and the setup has to be implemented in vacuum. In 2018, to seed a few-cycle OPCPA laser system, cleaned pulses with pulse duration of 5 fs were generated through spectral broadening in two consecutive HCFs and temporal cleaning via XPWG [30]. This is the shortest pulse width reported in temporal filters. However, both the pulse energy (only $4\;\mu \textrm {J}$) and the temporal contrast (only $\sim 10^{-11}$ at 10 ps before main pulse) are restricted. In 2019, a more than 8 orders of magnitude contrast enhancement was realized by combining self-phase modulation (SPM), OPA and SFG [24]. Although contrast ratio over $10^{-12}$ at 5 ps before main pulse and $250\;\mu \textrm {J}$ output energy were obtained, the reported pulse width was only 40 fs. In our previous works [28], a novel nonlinear temporal filter was developed by combining XPWG with femtosecond OPA (fs-OPA), which can generate ultrahigh contrast seed pulses with energy of $110\;\mu \textrm {J}$ and spectral width exceeding 60 nm (full width at half-maximum, FWHM). Although the comprehensive performance of this temporal filter is pretty good, the conversion efficiency and the energy scaling are still problems, which are mainly restricted by the temporal walk-off between the pump and signal pulses in the fs-OPA process (see Section 2.).
In order to break through the restriction imposed by temporal walk-off and realize a high-efficiency broadband fs-OPA, many techniques have been developed. The dual-chirped OPA (DC-OPA) scheme can reduce the impact of temporal walk-off by separately increasing the pulse duration of pump and signal pulse through two stretchers [31,32], while the dual-crystal OPA (D-OPA) geometry can compensate the temporal walk-off by using a pair of wedged material which have opposite group-velocity relationship to the OPA crystal [33,34]. Dual-pump OPA (DP-OPA) and multi-stage OPA (M-OPA) are another ways to avoid temporal walk-off, which is achieved by setting a series of pump-to-signal temporal delays [23,35]. Although these methods are available, the DC-OPA, DP-OPA and M-OPA is complicated in structure while the D-OPA is troubled by finding suitable materials for a complete compensation. Fortunately, the degenerate and quasi-collinear fs-OPA in our case provides great convenience for adopting a temporal walk-off self-compensation scheme. Specifically, the temporal walk-off is self-compensated through using the same material as the fs-OPA crystal by just changing the orientation of the optical axis.
In this work, a compact CF-OPA scheme adopting temporal walk-off self-compensation between two nonlinear gain media is proposed for achieving a higher conversion efficiency, a broader bandwidth and a higher temporal contrast. The feasibility and superiority of the CF-OPA geometry using three cascaded BBO crystals (${\beta }$-BBO + ${\alpha }$-BBO + ${\beta }$-BBO) has been numerically studied with a one-dimension computational model, and experimentally investigated based on a nonlinear temporal filter combining XPWG and fs-OPA. By replacing the conventional fs-OPA with the CF-OPA and optimizing the design, the comprehensive performance of the nonlinear temporal filter can be significantly improved. Compared with our previous work [28], the output energy increases from $110\;\mu \textrm {J}$ to $340\;\mu \textrm {J}$, while the energy fluctuation reduces from 1.8% to 0.9% (RMS); The bandwidth of output pulses expands from 60 nm to 97 nm (FWHM) and correspondingly the supported Fourier-transform-limited (FTL) pulse width decreases from 17 fs to 12 fs. Moreover, the temporal contrast can be enhanced by more than 6 orders of magnitude and the measured contrast ratio can reach $10^{-12}$, which is limited by the maximum dynamic range of the measurement. To the best of our knowledge, this is the first reported temporal walk-off self-compensated quasi-collinear CF-OPA geometry adopting three cascaded BBO crystals, which can be easily generalized to other wavelengths or nonlinear crystals. The nonlinear temporal filter with CF-OPA scheme features ultrahigh contrast, large energy, ultra-broadband spectrum and good stability simultaneously, which has the rarest comprehensive parameters and can provide excellent seed pulses for PW and 10 PW class laser systems, such as the 1 PW and 10 PW laser systems in SULF facility [5,9,28].
2. Numerical and experimental study of CF-OPA
In this work, a one-dimension numerical model is adopted to simulate the fs-OPA and CF-OPA process [36,37]. In this model, the phase-mismatching, the material dispersion (the temporal walk-off results from group-velocity mismatch), the second-order nonlinear interaction and third-order nonlinear terms (SPM and cross-phase modulation) have been considered. The initial simulation parameters for the signal and pump pulse are listed in Table 1, which is similar to the experimental case (see Section 3. for details). Here, $P$ is the polarization, $\lambda _0$ is the central wavelength, $\Delta \lambda _{1/2}$ is bandwidth in FWHM of the signal spectrum and $\Delta \tau _{1/2}$ refers to the pulse duration. Both temporal and spatial profile of signal and pump are Gaussian. Please note that, in the following section, all ${\beta }$-BBO crystals are Type-I cut ($\theta = 29.2^{\circ }$) for both SHG and OPA processes, while all ${\alpha }$-BBO crystals are X-cut ($\theta = 90^{\circ }$) for compensating the temporal walk-off. In addition, a quasi-collinear geometry with a noncollinear angle equal to $0.5^{\circ }$ (internal) is adopted in both simulations and experiments to separate the signal and idler pulse.
Table 1. Initial parameters used in the simulations.
2.1 Influence of the temporal walk-off on the conversion efficiency of fs-OPA
To investigate the limitation on the conversion efficiency of fs-OPA, the simulations are executed in a single 0.5 mm thick ${\beta }$-BBO using above parameters. Moreover, some experiments also have been carried out by using a single ${\beta }$-BBO with 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm thickness, respectively. As can be seen from Fig. 1(a), a saturation in single ${\beta }$-BBO crystal is observed at around 0.3 mm for both simulated and experimental cases. Since the ${\beta }$-BBO crystal is very thin and the OPA is quasi-collinear Type-I geometry, the phase mismatching and spatial walk-off should contribute little to the saturation. In order to clearly reveal the contribution of temporal walk-off to the saturation, the case without considering the temporal walk-off effect is also illustrated as the dashed blue line in Fig. 1(a). In this case, the saturation occurs when the crystal thickness exceeds 0.35 mm and the maximum output energy is much larger than the case with temporal walk-off effect. The calculated temporal walk-off (peak-to-peak) between signal and pump versus the ${\beta }$-BBO length is also plotted in Fig. 1(b). It can clearly be seen that the temporal walk-off occurs before the back-conversion, and the temporal walk-off is already obvious when the thickness of ${\beta }$-BBO exceeds 0.3 mm. Therefore, a promising solution to improve the conversion efficiency of fs-OPA is to compensate the temporal walk-off between the signal (idler) and pump pulse.
Fig. 1. (a) Dependence of the output signal energy on the ${\beta }$-BBO length. The red solid line refers to the case with temporal walk-off, while the blue dashed line represents the case without temporal walk-off. (b) Calculated temporal walk-off between signal and pump versus the ${\beta }$-BBO length.
2.2 Design of the CF-OPA scheme using three cascaded BBO crystals
As mentioned in Section 1., although D-OPA geometry can compensate the temporal walk-off, it is difficult to find a suitable compensation material which has the opposite group-velocity characteristic as the OPA crystal. Fortunately, the degenerate and quasi-collinear in our fs-OPA provide a convenience for implementing a temporal walk-off self-compensation scheme through using the same material as the fs-OPA crystal by just changing the orientation of the optical axis (ie, use ${\beta }$-BBO for amplification, ${\alpha }$-BBO for compensation). In order to evaluate the feasibility of this temporal walk-off self-compensation scheme using ${\alpha }$-BBO, the relationship between the angle $\phi$ (the angle between optical axis of ${\alpha }$-BBO and vertical direction), the thickness of ${\alpha }$-BBO and the thickness of ${\beta }$-BBO has been numerically studied. As shown in Fig. 2(a), for a ${\beta }$-BBO crystal with any given thickness, a ${\alpha }$-BBO crystal with suitable thickness and angle $\phi$ can be found to achieve a complete compensation of the temporal walk-off in theory. In general, it is a good choice to use a relatively thin ${\alpha }$-BBO with the same thickness as ${\beta }$-BBO, which is beneficial to weaken the self-focusing effect.
Fig. 2. (a) The angle $\phi$ and thickness of ${\alpha }$-BBO for perfect compensation the temporal walk-off of ${\beta }$-BBO (pseudocolor). The area covered by gray color indicates that the ${\alpha }$-BBO is too thin to fully compensate the temporal walk-off. (b) The schematic setup of CF-OPA.
Based on the above analysis, a compact CF-OPA scheme using three cascaded BBO crystals is proposed, which is illustrated in Fig. 2(b). Here, the first and third BBO crystals are ${\beta }$-BBO to achieve broadband amplification, while the second BBO crystal is ${\alpha }$-BBO for compensating the temporal walk-off between the signal (idler) and pump pulses. For degenerate case, the temporal walk-off between the three interacting pulses can be simultaneously compensated. For non-degenerate case, although only the temporal walk-off between signal (or idler) and pump can be totally compensated, this will also inhibit the back-conversion and further improve the conversion efficiency [38]. Compared with the D-OPA geometry, this CF-OPA scheme greatly reduces the difficulty of finding suitable materials, which can realize a perfect compensation. Moreover, the simultaneous adjustment of the crystal thickness and rotation angle $\phi$ greatly increases the flexibility of the application. This compact and efficient CF-OPA scheme can be easily extended to other quasi-collinear fs-OPA that use different wavelengths or nonlinear crystals.
2.3 Numerical analysis of the CF-OPA scheme with different crystal combinations
In order to evaluate the feasibility of the CF-OPA scheme using three cascaded BBO crystals and find a suitable crystal combination, numerical simulations have been carried out on some crystal combinations and demonstrated in Fig. 3. Here, a crystal combination 33n means that the thickness of the first ${\beta }$-BBO, the ${\alpha }$-BBO and the second ${\beta }$-BBO are 0.3 mm, 0.3 mm, and 0$\sim$0.3 mm, respectively, and so on. Please note that only the thickness of ${\beta }$-BBO is demonstrated in Fig. 3. Take the curve of 33n case as an example, the 0 mm–0.3 mm part represents the amplification in the first ${\beta }$-BBO crystal, while the 0.3 mm–0.6 mm part represents the amplification in the second ${\beta }$-BBO crystal. Compared with the efficiency of fs-OPA in a single ${\beta }$-BBO crystal (see Fig. 1(a)), an obviously improvement on conversion efficiency can be observed. The simulations also show that the 33n (n=1.6, indicates 0.16 mm thickness) crystal combination is the optimal one. Since we only have BBO crystals with a thickness of 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm in the experiment, the 332 crystal combination is the most promising choice. In addition, in the case of 332 crystal combination, the saturation amplification appears in the second ${\beta }$-BBO crystal, which is also useful for improving the energy stability.
Fig. 3. Dependence of the output signal energy on the ${\beta }$-BBO length for CF-OPA scheme using different BBO crystal combinations. Please note that only the thickness of ${\beta }$-BBO is demonstrated in the figure.
3. Performance improvement of the upgraded nonlinear temporal filter by employing CF-OPA
The layout of upgraded nonlinear temporal filter based on XPWG and CF-OPA is shown in Fig. 4. Several important improvements are introduced compared to our previous work [28]. First and the most important is that the fs-OPA is replaced by CF-OPA. Second, the total optical path of signal pulse has been significantly shortened from 4.9 m to 3.6 m for alleviating the beam quality degradation resulting from long-distance transmission in air. Third, in order to get the widest possible signal spectrum from XPWG, the dispersion introduced by transmission materials has been more precisely compensated by optimizing the chirped mirrors. Finally, to ensure a good extinction ratio, the GL2 is placed after the collimated mirrors (M12). According to subsection 2.3, the thickness of the first ${\beta }$-BBO, the ${\alpha }$-BBO and the second ${\beta }$-BBO in CF-OPA are 0.3 mm, 0.3 mm, and 0.2 mm, respectively. In addition, the thickness of ${\beta }$-BBO for SHG is 0.1 mm.
Fig. 4. Layout of the upgraded nonlinear temporal filter based on XPWG and CF-OPA. M, mirrors; BS, beam splitter; CM, chirped mirror pair; GL, polarizer; HWP, half-wave plate; TDL, time delay line; DM, dichroic mirror.
The entire nonlinear temporal filter only covers a 2 m$\times$0.4 m area on an optical table, and the 6 mJ output energy of the first CPA stage (Coherent, Astrella) is fully used. After the beam splitter, the incident 6 mJ pulse is divided into two beams: one beam with $150\;\mu \textrm {J}$ energy is injected into the XPWG stage for producing clean broadband signal pulses, while the other beam with 5.85 mJ energy is used to generate the pump pulse through SHG. However, limited by the available aperture of Glan-Laser Polarizers and the energy loss on the mirrors, the effective energy used for XPWG and SHG are only $120\;\mu \textrm {J}$ and 5.7 mJ, respectively. After fine adjustment, the output energy for XPWG and SHG are $10\;\mu \textrm {J}$ and 2.4 mJ, respectively. In order to determine the performance improvement of the upgraded nonlinear temporal filter, some key parameters relevant to the application to high-peak-power femtosecond laser systems are examined and illustrated in Fig. 5. They are the spectrum evolution (Ocean optic, USB4000), pulse duration (Fastlite, Wizzler), temporal contrast (Amplitude Technology, Sequoia 800), energy stability (Coherent, Labmax-TOP and PM10), and beam quality (Spiricon, CCD).
Fig. 5. Performance of the upgraded nonlinear temporal filter: (a) Spectral evolution: the gray, green, blue and red lines represent the spectrum of kHz, XPWG, OPA1 and OPA2, respectively. (b) Spectral phase (right top axis), pulse duration (left bottom axis, red solid line) and FTL pulse duration (left bottom axis, green dashed line). (c) Measured temporal contrast before (blue line) and after (red line) filtering. (d) Energy stability over the duration of one hour. The evolution of beam profile: (e) XPWG, (f) OPA1, and (g) OPA2. Please note that the entries kHz, XPWG, OPA1 and OPA2 in here represent the output of the first CPA stage, the XPWG, the first ${\beta }$-BBO in CF-OPA and the second ${\beta }$-BBO in CF-OPA, respectively.
Compared to our previous work [28], there is a comprehensive performance improvement in the upgraded nonlinear temporal filter. As can be seen from Fig. 5(a), thanks to the optimization on dispersion control, the output spectral width (FWHM) of XPWG has been broadened from 56 nm to 71 nm. This broadband signal pulse is fully amplified in the CF-OPA stage by finely tuning the phase-matching geometry of the two ${\beta }$-BBO crystals. Therefore, the output spectrum bandwidth (FWHM) has been expanded from 60 nm to 97 nm. Correspondingly, the supported FTL pulse duration has been decreased from 17 fs to 12 fs as shown in Fig. 5(b). However, due to the residual high-order material dispersion, the measured pulse duration is only 16 fs. Moreover, benefiting from the compensation of temporal walk-off, the increase of pump energy and the gain saturation in the CF-OPA geometry, the output signal energy has been increased from $110\;\mu \textrm {J}$ to $340\;\mu \textrm {J}$, while the energy stability in one hour has been improved from 1.8% to 0.9% (RMS) as demonstrated in Fig. 5(d). According to literature [4], this increased signal energy means that the ASE contrast of PW laser system can be promoted. In addition, for fs-OPA with a single 0.5 mm ${\beta }$-BBO crystal, an output energy of ${\sim }150\;\mu \textrm {J}$ can be inferred from the experimental curve in Fig. 1(a). Therefore, compared with the fs-OPA in single crystal, a more than twice increase in efficiency can be obtained by using a CF-OPA scheme.
In addition to the enhancement of conversion efficiency and bandwidth, the amplification gain also has been increased from 22 times of fs-OPA to $\sim$34 times of CF-OPA, which augments the ability of temporal contrast improvement in the fs-OPA process. Considering the high extinction ratio of the polarizers (Newport, 10GL08AR.16, $\sim 10^{5}:1$) and the enhanced gain in the CF-OPA process, the estimated enhancement of the temporal contrast ratio should reach $\sim 10^6$ in theory. As shown by the red line in Fig. 5(c), the measured contrast ratio of the temporal filter approaches $10^{-12}$, which is limited by the maximum dynamic range of the third-order cross correlator. The temporal contrast of the initial pulses from the 1 kHz CPA laser is also presented by blue line. Both the comparison between the intensity of the post-pulses (for example, post-pulse A and C), and the contrast ratio at $1\sim 2$ ps before main pulse (see the insert in Fig. 5(c)) in the two curves indicates that the enhancement of temporal contrast can reach 6 orders of magnitude in the temporal filter. The newly generated post-pulse B ($1.5\times 10^{-6}$) is originated from the multi-reflections in dichroic mirror, which can be eliminated by introducing a wedged angle. The evolution of output beam profile of XPWG, and the first and second ${\beta }$-BBO in CF-OPA are illustrated in Fig. 5(e)–5(g), respectively. As can be seen from Fig. 5(g), a back-conversion is occurred at the central position in the second ${\beta }$-BBO of CF-OPA due to the spatially inhomogeneous gain resulted from the Gaussian profile of the pump pulse. By choosing the optimal thickness ($\sim$0.16 mm) of the second ${\beta }$-BBO crystal, both the conversion efficiency and beam profile of CF-OPA should be further improved.
4. Conclusion
In this work, we demonstrated that the conversion efficiency and bandwidth of fs-OPA can significantly be enhanced by employing a compact CF-OPA scheme using three cascaded BBO crystals (${\beta }$-BBO + ${\alpha }$-BBO + ${\beta }$-BBO). Both numerical and experimental investigations show the feasibility and superiority of CF-OPA geometry with the temporal walk-off self-compensation between two OPA crystals, which can easily be generalized to other wavelengths or nonlinear crystals. By replacing the conventional fs-OPA with the CF-OPA and optimizing the design, the comprehensive performance of the nonlinear temporal filter combining XPWG and fs-OPA can obviously be improved. Specifically, cleaned pulses at 1 kHz repetition rate with energy of $340\;\mu \textrm {J}$, energy fluctuation below 0.9% (RMS), spectral width of 97 nm (FWHM), FTL pulse width of 12 fs and temporal contrast better than ${10^{-12}}$ is achieved. This nonlinear temporal filter with rarest comprehensive performance can provide excellent seed pulses for PW and 10 PW class laser systems. After improving the engineering design, the high-performance nonlinear temporal filter will be applied to the SULF laser facility.
Funding
National Key Research and Development Program of China (2017YFE0123700); The Strategic Priority Research Program of the Chinese Academy of Sciences (XDB1603); National Natural Science Foundation of China (61925507); Program of Shanghai Academic Research Leader (18XD1404200); Shanghai Municipal Science and Technology Major Project (2017SHZDZX02); Shanghai Sailing Program (19YF1453100); Natural Science Foundation of Shanghai (20ZR1464600); Youth Innovation Promotion Association of the Chinese Academy of Sciences; International Partnership Program of Chinese Academy of Sciences (181231KYSB20200040).
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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