Herein, a theory for modeling the problem of scattering pulse-induced temporal contrast degradation in chirped-pulse amplification (CPA) lasers is introduced. Using this model, the temporal evolutions of the scattering and signal pulses were simulated, the temporal contrasts for different cases were compared, and finally the theoretical prediction was verified by an experimental demonstration. The result shows that the picosecond and the nanosecond temporal contrast is mainly determined by the scattering pulses generated in the stretcher and the compressor, respectively. In addition, the B-integral accumulation will further degrade the temporal contrast, especially the picosecond temporal contrast. We believe it is helpful for solving the problem of the picosecond pedestal contrast (i.e., noise limit). With reference to these results, some suggestions for the temporal contrast improvement are presented.
© 2017 Optical Society of America
Extreme lasers, such as petawatt (1015 W) lasers , have been demonstrated worldwide and are used in various high-field physics applications. The first picosecond petawatt laser; indeed, the first petawatt laser; was the Nova system at Lawrence Livermore National Laboratory that achieved a 1.1 petawatt output in 1996 . Next, the first femtosecond petawatt laser with a 0.85 petawatt output was demonstrated at Japan Atomic Energy Research Institute in 2003 . After that, several petawatt lasers were completed in different laboratories. Currently, the strongest petawatt laser is the LFEX system at the Institute of Laser Engineering in Osaka University , which can deliver 2 petawatt (3-kJ pulse energy in 1.5-ps pulse duration) . Another 2 petawatt laser that possesses a 26 fs short pulse duration has been demonstrated at the Shanghai Institute of Optics and Fine Mechanics in 2013 . Several 10 petawatt lasers are currently under construction; for example, the Extreme Light Infrastructure (ELI) , Apollon-10-petawatt , the Shanghai Super-intense Ultrafast Laser Facility (SULF)  and the Vulcan-10-petawatt laser . Furthermore, two exawatt laser facilities are in the planning stage, whose peak intensity will reach as high as 0.2 exawatt (1018 W) [11, 12]. In engineering, chirped-pulse amplification (CPA)  and optical parametric chirped-pulse amplification (OPCPA)  techniques are widely used to obtain a high peak power output. As the next step, stimulated Raman backscattering in plasma is considered to be an alternative method for further pulse compression and amplification .
In a CPA or OPCPA petawatt laser, the pulse is temporally stretched and compressed in front of and behind main amplifiers, respectively. To achieve a large amount of stretching or compression ratio, both the stretcher and compressor are designed based on high-groove-density diffraction gratings . The parallel grating pair is used as a compressor , and the symmetric grating pair with a telescope is generally used as a stretcher . At a grating, apart from the required diffraction rays, the reflection and scattering rays cannot be completely avoided. According to recent experiments, the scattering effect in a CPA laser is an important factor in the degradation of temporal contrast [19–21]. It is well known that the temporal contrast is a key parameter and a significant problem for high-peak power lasers, especially for recent petawatt and/or future exawatt lasers, and will directly determine their possible applications. However, it is an exceedingly complex problem owing to the multitudinous influences involved, including the oscillator itself , spectral phase distortion [23, 24], spectral amplitude modulation , amplified spontaneous emission , optical parametric fluorescence [27–30], element-surface-reflection and refractive index nonlinearity [31, 32], among others. According to these factors, many novel methods for temporal contrast enhancement have already been proposed [33–43].
Regarding the problem of the scattering pulse-induced temporal contrast degradation, although some experiments have already been demonstrated [20, 21], to the best of our knowledge, theoretical models or detailed theoretical analyses have not yet been presented. Moreover, the influence of the scattering pulse respectively generated in the stretcher and the compressor on the temporal contrast also has not been carefully researched. Especially, the scattering pulse may be the main reason for the generation of the picosecond contrast pedestal around the signal, which is one of the biggest headaches in ultra-intense lasers (named as noise limit) . A clean seed, which passes through the CPA configuration (i.e., stretcher, amplifier and compressor), will be superimposed a picosecond contrast pedestal , even without any amplifiers . And this picosecond contrast pedestal cannot be removed by available methods. Previous result shows that this picosecond contrast pedestal could be experimentally reduced by controlling the noise induced by the imperfection of the stretcher [19, 20, 46]. Consequently, in this paper, we discuss the scattering pulse problem in CPA lasers, classify all possible scattering-diffraction processes in a stretcher/compressor, and propose a simplified theoretical model for description. Using this model, we simulate the evolution of the scattering and signal pulses, compare the temporal contrasts in various cases, and determine the majority influence of each key parameter. Furthermore, the theoretical results were verified by experimental demonstrations, and finally several suggestions to improve the temporal contrast and some relevant discussions are ultimately presented.
2. Scattering pulses in a grating stretcher/compressor
The optical structures of the stretcher and the compressor generally used in a CPA system are shown by upper and lower illustrations in Fig. 1(a). Because of the complete dispersion-matching, a pair of conjugate temporal chirps/dispersions can be introduced, and thereby the pulse can be stretched and re-compressed in the time region. In the ideal condition, the incident pulse at a grating is expected to be totally diffracted. However, in actuality, scattering lights induced by structural imperfection, intrinsic composition inhomogeneity, impurity ions, etc. cannot be avoided; and, as shown in Fig. 1(b), they are very difficult to be completely removed from the signal in space. It is noticeable that the generated scattering pulse is a source of noise in the signal for a CPA system. Generally, scattering rays possess an angular spatial distribution, however, for simplification, a uniform distribution in the concerned region (i.e., spatial region of the diffraction rays) is used in this paper. The residual reflection of transmission lenses (i.e., non-ideal anti-reflection coating) and the scattering at imaging elements in the telescope (e.g., concave and convex mirrors in an Offner stretcher) would also produce noise pulses. The first factor can be efficiently avoided by using an all-reflection telescope. And the second factor, comparing with the scattering at gratings, is much weaker. In this condition, for simplification, these two factors are neglected in this paper.
Due to the complexity of the scattering pulse problem, in Section 2.1 we discuss all possible ray trajectories of a scattering-diffraction process, and summarize ones possessing majority influences; in Section 2.2 the temporal evolution of the scattering and signal pulses is qualitatively described; and in Section 2.3 a theoretical model is proposed.
2.1 Possible ray trajectories of a scattering–diffraction process
Figure 1(a) illustrates that, when a multiple-pass and symmetrical configuration is used in a grating stretcher and compressor, respectively, the input pulse is diffracted by gratings for several times. For simplification, as shown in Fig. 2(a), the propagation within a stretcher is divided into two parts. The first-pass begins at the input and goes to the first grating G1, the telescope, the second grating G2 and finally the end mirror M. The second-pass is from the end mirror M to the second grating G2 (G2’ to distinguish from the first-pass), the telescope, the first grating G1 (G1’ to distinguish from the first-pass) and finally the output. The signal will experience an all-diffraction (i.e., diffraction–diffraction–diffraction–diffraction; DDDD) process from the input to the output, and meanwhile noise will be generated within a scattering–diffraction process. There are a number of permutations and combinations of the scattering–diffraction process, and all possible ray trajectories are listed in Table 1.
Refer to multilayer dielectric diffraction gratings, we make a simple estimation of the intensity weight relative to the signal. Excluding the efficiency of the negative-first-order diffraction (>96%), the zeroth-order reflection (~1%), the absorption, etc ; the total scattering light may actually be only around ~1%. Moreover, as shown in Fig. 1(b), the scattering rays propagate into a solid angle region, from which only a limited amount will be collected by the optical elements that come after. If we assume that the average efficiency at each grating is 0.1% (i.e., 10−3), the intensity weights of ray trajectories are listed in Table 1, which (and influence on the temporal contrast) decrease with increasing the scattering events.
For the case of one scattering event, Fig. 2(b) illustrates a possible ray trajectory: the scattering–diffraction–diffraction–diffraction (SDDD) process along the propagation path. The output rays at G1’ can be divided into two types. On the one hand, rays in Type (1) propagate exactly along the reverse direction of the input. By comparing Figs. 2(a) with 2(b), it is easy to see that these rays have experienced a wavelength-dependent optical path that is equivalent to the signal (i.e., DDDD), and that consequently possesses the same temporal chirp and spatial distribution as the signal and that can be considered as part of the signal instead of the noise. On the other hand, rays in Type (2) possess output positions and propagation directions that are completely disordered owing to the uncompensated angular dispersion caused by odd times of scattering. In this condition, these rays can be filtered conveniently by the spatial filters and the compressor, and their adverse influence can thereby be eliminated.
For the case of two scattering events, Fig. 2(c) shows a possible ray trajectory whereby both two scattering events occur in the first-pass (i.e., SSDD). Unlike the earlier case with SDDD, the output rays at G1’ can be divided into three types. In addition to the Types (1) and (2), rays can also be in Type (3) and possess parallel propagation directions that are also parallel to the output of the signal (i.e., DDDD). According to the illustration in Fig. 2(c), these rays are produced from the incident scattering rays at G2’ that are anti-parallel to the input at G1. In the space domain, although the spatial chirp at G1’ is not compensated, once a finite beam aperture is used a portion of the Type (3) rays can pass through the spatial filters as well as the compressor and arrive at the target successfully. In the time domain, these pulses are temporally delayed by various amounts and temporally chirped due to a same incident angle (comparing with the signal at G2’) in the first- and second-pass, respectively. Thereby, the stretcher–compressor matching is destroyed, and these pulses cannot be temporally compressed. Consequently, rays/pulses in Type (3) are noise sources that will degrade the temporal contrast.
When two scattering events occur in the first- and the second-pass, respectively, a possible ray trajectory of SDSD is shown in Fig. 2(d). After the first-pass, the positions and directions of rays are disordered by the scattering-diffraction process, and after the second-pass which are further disordered. Comparing with the case of SSDD, the disorder would be further exacerbated. Therefore, the number of rays in Type (3) will be reduced, and those in Type (2) will be increased. In this way, most of the rays can be filtered by the following spatial filters, and comparing SSDD the influence of SDSD is therefore weaker.
For the other possible ray trajectories (i.e., SDDS, DSSD, DSDS and DDSS), the situations are similar to the two previously discussed (i.e., SSDD and SDSD) and we will not repeat again. Besides that, for SDSD, SDDS, DSSD and DSDS, these is a strong spatio-temporal-spectral coupling, which possesses randomicity and would make the analysis extremely complex. In this condition, to achieve a general result and for simplification, influences of these ray trajectories are neglected in this paper.
To verify the validity of the simplification, a simple beamline model [see Fig. 3(a)] is set up based on a commercial optical software (ZEMAX) with following parameters: grating density 1740 g/mm, focal length of lenses 100 mm, Gaussian beam with an aperture of 2 mm, and 11 spectral components from 1048 to 1058 nm with a same weight. Diffraction and scattering is interchangeably considered at gratings of G1, G2, G2’ and G1’, respectively. In the case of scattering, the grating is replaced by a ground glass mirror with a Lambertian scattering model, and the perfect reflection direction of the mirror is the original diffraction direction of the center wavelength. A 10 mm focal lens and a 0.5 mm pinhole is used to filter the scattering lights, and rays which could arrive at the detector positioned 3 mm after the pinhole are shown in Fig. 3(b). The result indicates that, the throughputs of SSDD and DDSS are relatively high, and, to a certain extent, our simplification is reasonable.
For the case of three scattering events, for example SSSD illustrated in Fig. 2(e), the output rays at G1’ can also be divided into three types. And, only rays in Type (3) can influence the temporal contrast. However, the intensity weight of 10−9 is small. Moreover, because no temporal chirp is introduced but only different amounts of time delay, in the time domain the pulses will be stretched by the compressor instead of compressed. In this condition, for a general >1000 × stretching–compression ratio (e.g., stretching from <1 ps to >1 ns), the induced temporal intensity contrast degradation will be around 10−12, which is lower than the usual requirement (10−10 to 10−11) and can be neglected in this paper.
For the case of four scattering events (i.e., SSSS), as shown in Fig. 2(f), although the intensity weight is even lower than that in SSSD, because of the ease of simulating, its influence will be considered.
Considering the above discussion, the temporal contrast is mainly influenced by pulses generated in two ray trajectories (i.e., SSDD and DDSS). To simplify the above explanation, the Martinez type stretcher with transmission lenses are used, however the above discussion absolutely is also suitable for other types of grating stretchers (e.g., Offner stretcher). For the compressor [Fig. 1(a), lower image], if we define the propagation processes G1 to G2 and G3 to G4 as the first- and second-pass, respectively, the scattering–diffraction process in theory is quite similar to that of the stretcher. Generally, after the compressor the beam is focused by a focusing element to a tiny target, which can be considered as a spatial filter to filter most of the scattering pulses. Consequently, the above discussion based on the stretcher also applies to the compressor, and we therefore will not repeat it.
2.2 Signal and scattering pulses in the time domain
Based on the discussion in Section 2.1, we qualitatively introduce the temporal evolution of the signal and scattering pulses in a CPA laser consisting of a two-pass stretcher and a two-pass compressor. The total stretching amount is defined as τ, and the temporal distributions of signal and scattering pulses are illustrated in Fig. 4.
In the stretcher, Fig. 4(b) shows, after the first-pass, the signal is stretched to τ/2 with a positive temporal chirp. The scattering pulses follow different propagation paths, however, and different time delays are introduced. Because no dispersion has occurred, a time-delayed scattering pulse sequence without any temporal chirp is generated in the time range of τ/2. Figure 4(c) shows, after the second-pass, the signal and each pulse in the scattering pulse sequence generated in the first-pass is chirped and stretched to τ and τ/2, respectively. In addition, another time-delayed scattering pulse sequence is generated that can be considered as time-delayed replicas of the input signal.
It is well known that a spectral amplitude modulation will be induced by the interference between the signal and the scattering pulses [see Fig. 4(d)], which will degrade the temporal contrast of the compression pulse. This degradation will be further increased by a nonlinear amplification process [25, 26].
In the compressor, Fig. 4(e) shows, after the first-pass the signal is compressed to τ/2 and the scattering pulses generated in the stretcher are compressed to the Fourier transform limit. However, the time delays of the scattering pulse sequence cannot be changed. Similarly, a third time-delayed scattering pulse sequence will be generated where each pulse is a replica of the input signal with a pulse duration of τ. Figure 4(f) shows, after the second-pass, the signal is compressed to the Fourier transform limit. However, the scattering pulses generated in the stretcher will be stretched from the Fourier transform limit to τ/2 with a negative temporal chirp. Moreover, the scattering pulses generated in the first-pass of the compressor will be compressed from τ to τ/2, which possesses a positive chirp. Likewise, the fourth time-delayed scattering pulse sequence will appear, which is a time-delayed replica of the input signal.
According to the above qualitative description, it is reasonable to assume that the scattering pulse sequences generated in the stretching-compression process and the induced spectral amplitude modulation of the signal are two important factors in the temporal contrast degradation of a CPA laser. For simplification, the spatial chirp has been neglected in the above description, which is acceptable for the condition with a finite beam aperture. In the next section, a temporal intensity ratio of the scattering to the signal pulse r will be defined, and the influence of the spatial chirp can also be represented by this coefficient.
2.3 Simplified theoretical model
In this section, we develop a theoretical model for the process described in Section 2.2. For the first-pass of a stretcher, given a Fourier transform limit seed A0(t), the corresponding spectral amplitude can be calculated by the Fourier transform A0(Ω) = FT[A0(t)], where Ω is the difference between the angular frequency and the central angular frequency of the spectrum (Ω = ω - ω0). Similar to the process used in , a coefficient r is defined that equals the temporal intensity ratio of a single scattering pulse to the incident pulse. Then, for an input, the output can be described byEq. (1), the first term on the right side indicates the temporal chirp effect (diffraction–diffraction process), and the second term represents the scattering effect (scattering–scattering process). In Eq. (1), the higher-order dispersion terms are neglected, though interested readers could conveniently add them if necessary. For each pass of a stretcher/compressor the output of the previous pass is the input of the recent pass. By using the inverse Fourier transform of Eq. (1) Aout(t) = FT−1[Aout(Ω)], the temporal amplitude of the output after one particular pass in a stretcher/compressor can be calculated. The nonlinear amplification of the stretched pulse can be approximately described byEq. (1) for the required times. Then, by substituting this result into Eq. (2), the influence of a nonlinear amplification can be calculated. Finally, the pulse evolution in a two-pass compressor can be obtained by re-using Eq. (1) twice.
Using the proposed model, we quantitatively simulate the signal and scattering pulses in a CPA laser. Two configurations comprising a two-pass-stretcher-two-pass-compressor and a four-pass-stretcher-two-pass-compressor are compared. To ensure consistency, the total stretching/compression amount and the grating quality are exactly the same.
3.1 Temporal distributions of signal and scattering pulses
The signal and scattering pulses in a CPA laser consisting of a two-pass stretcher and a two-pass compressor are simulated based on the following parameters: The input signal is a Gaussian pulse centered at 1053 nm with a 2 nm bandwidth (FWHM, full width at half maximum), the total stretching/compression amount is 4.8 ns (FW, full width), the grating density is 1740 g/mm, the incident angle is 61°, the B-integral accumulation is 2 rad, the time delay between two adjacent scattering pulses Δt is chosen as 50 ps, and the temporal intensity ratio of the scattering to the signal pulse r is −80 dB. Using Eq. (1), the signal and scattering pulses after the first-pass of the stretcher are calculated and illustrated in Fig. 5(a). The signal is stretched to 2.4 ns (FW), and a time-delayed scattering pulse sequence is generated in the time range of 2.4 ns. Additionally, Fig. 5(a) shows the amplitude modulation of the signal caused by the interference. Re-using Eq. (1), we obtain the result after the second-pass, as shown in Fig. 5(b), where the signal is stretched to 4.8 ns (FW) and the superimposed profile of the scattering pulse becomes very complex. Moreover, as shown in Fig. 5(b), the amplitude modulation of the signal is increased. Using Eq. (2) to introduce the B-integral accumulation of 2 rad and substituting the result into Eq. (1) again, the output of the first-pass of the compressor can be obtained. Figure 5(c) shows the signal is compressed to 2.4 ns (FW) and the superimposed profile of the scattering pulse exhibits increased complexity. Compared with Fig. 5(b), Fig. 5(c) shows that the amplitude modulation of the signal is further increased. Finally, using Eq. (1) the output after the second-pass of the compressor is calculated. When the dispersion is removed, the signal is re-compressed to around 1.1 ps [see Fig. 5(d)], and the temporal distortion is mainly caused by the B-integral accumulation. Clearly, as shown in Fig. 5(d), the signal is surrounded by the scattering pulses in the time range of 4.8 ns (FW), which will degrade the temporal contrast. In addition, the amplitude modulation of the signal itself caused by the interference between the signal and scattering pulses, which is further amplified by the Kerr nonlinearity (i.e., the B-integral accumulation), is another factor in the temporal contrast degradation.
Similarly, the situation in a CPA laser with a four-pass stretcher and a two-pass compressor is simulated based on the same model and same parameters, and the result is given in Fig. 6. Comparing Fig. 6 with Fig. 5, it is easy to see that the profiles of the signal and scattering pulses after the corresponding passes of the stretcher/compressor are similar, and we will not explain the details again. However, the major differences are also obvious when comparing Fig. 6(b) with Fig. 5(a), Fig. 6(d) with Fig. 5(b), and Fig. 6(e) with Fig. 5(c), wherein the amplitude modulation of the signal shown in Fig. 6 is greater than that in Fig. 5, which means that the final temporal contrast will become even worse. In addition, comparing Figs. 5(b) with 6(d) it can be seen that the scattering pulses after the stretcher are mainly concentrated around the position of the zero delay, which is another unfavorable factor in the temporal contrast degradation.
3.2 Comparison of temporal contrasts
To achieve a detailed understanding of the influences, the temporal contrasts are calculated and compared for different cases. The initial parameters are changed individually while all other parameters are held to the same values used in the initial simulation in Section 3.1. Figure 7(a) shows when the stretcher configuration is changed from two-pass to four-pass the temporal contrast within ± 1 ns will be degraded but that outside ± 1 ns can be improved. In actual applications, we mainly focus on the temporal contrast near the main pulse; and in this condition a stretcher with a small pass number should be preferred. However, to reduce the size of the grating and stretcher, sometimes we have to increase the pass number, and the four-pass stretcher (widely used) is therefore mainly discussed in this paper. Figure 7(b) shows, when the temporal intensity ratio of the scattering to the signal pulse in the stretcher rs is reduced to −90 dB, the temporal contrast within ± 1 ns is improved. When the temporal intensity ratio of the scattering to the signal pulse in the compressor rc is reduced to −90 dB, the temporal contrast outside ± 1 ns is improved [see Fig. 7(c)]. If we reduce the B-integral accumulation B from 2 to 0.5 rad, both the temporal contrast within and outside ± 1 ns is improved [see Fig. 7(d)], and the improvement within ± 1 ns is very significant. If we hold B at 0.5 rad, the temporal contrast within and outside ± 1 ns can be improved while rs and rc is reduced, respectively [see Figs. 7(e)and 7(f)]. However, compared with Fig. 7(b) where B is 2 rad, the amount of the improvement in Fig. 7(e) is relatively less.
According to the above result, it is easy to conclude that rs, rc and B are the three key parameters influencing the temporal contrasts in different time ranges. Besides that, an uniform distribution of scattering pulses in time [i.e., fixed Δt in Eqs. (1) and (2)] is considered in this paper. Once, a Gaussian distribution for example is used, Δt will be another key parameter determining the shape of the temporal contrast. Due to the complexity, Δt will be considered in future works. For rs, rc and B, the temporal contrast within ± 1 ns is mainly determined by rs, and is also sensitive to B; that outside ± 1 ns is mainly determined by rc, and is not very sensitive to B.
In Fig. 8, we calculated the evolution of the temporal contrast −10 ps and −2 ns before the main pulse for various rs, rc and B values. Identical to the result concluded from Fig. 7, Figs. 8(a)–8(c) and Figs. 8(d)–8(f) show that the −10 ps and the −2 ns temporal contrast is mainly determined by rs and rc, respectively. As shown in Figs. 8(b), 8(c), 8(e) and 8(f), both the −10 ps and the −2 ns temporal contrasts degrade with increasing B. When rs is around −80 dB, Fig. 8(b) shows that as B is reduced the sensitivity of the −10 ps temporal contrast to rs is also reduced. However, when rc is around −80 dB, as shown in Fig. 8(f), for different values of B the sensitivity of the −2 ns temporal contrast to rc is almost constant. That is B possessing a higher influence on the −10 ps temporal contrast (mainly induced by rs) than the −2 ns temporal contrast (mainly induced by rc). The corresponding theoretical explanation can be found in . In addition, from Figs. 8(b), 8(c), 8(e) and 8(f) we find that the degradation speed of the temporal contrasts for various values of B decreases while B is greater than 3. This is because the breakup of the main pulse itself caused by a large B. In physical and/or engineering applications, the nanosecond temporal contrast can be conveniently improved by using ultrafast Pockels cells and/or saturable absorbers [39, 42]; however, the picosecond temporal contrast, for example −10 ps before the main pulse, is very difficult to enhance. According to the above analysis, for the scattering pulse-induced temporal contrast degradation, the stretcher must be optimized and the nonlinear should be reduced for the enhancement of the picosecond temporal contrast.
4. Experimental verification
To verify the previous theoretical analysis, a simple verification experiment was designed based on our recent upgraded HALNA (High Average-power Laser for Nuclear Fusion Application) laser system . A seed pulse centered at 1053 nm with a bandwidth around 15 nm (FWHM) was generated by a homemade Yb-doped fiber oscillator. A four-pass Offner grating stretcher, whose configuration and photograph are given in Fig. 9, was used to stretch the pulse duration to around 4.5 ns (FW). However, the pulse bandwidth was clipped to only about 5 nm (FW) owing to a limited grating size. Then the chirped pulse was amplified by a laser diode (LD)-pumped Yb:CaF2 regenerative amplifier and a LD-pumped glass slab amplifier, respectively. Finally, the temporal chirp was completely removed by a two-pass Treacy grating compressor, and the compressed pulse duration was around 1.1 ps (FWHM).
For comparison, verification experiments were carried out twice in different amplification conditions (different B-integral accumulations). First, the pump of the slab amplifier was turned off and that of the regenerative amplifier was increased to achieve an output around 370 µJ. Second, the output of the regenerative amplifier was decreased to 40 µJ by reducing its pump, and the final output was held at 370 µJ by turning on the pump of the slab amplifier. In the regenerative amplifier, the beam size and the total propagation length inside the gain material (Yb:CaF2) was 0.1 mm and 1.22 m, respectively, and in the slab amplifier those parameters within the gain glass (HOYA Corporation USA, HAP-4) were 5.3 mm and 1.35 m, respectively. Because of the gain narrowing and the spectral clipping in the Pockels cell, the pulse duration after the regenerative amplifier was around 2.5 ns (FWHM). Taking this effect into account, the B-integral accumulation in the two-round experiments was about 0.31 and 0.04 rad, respectively. The temporal contrasts were measured by a commercial third-order cross-correlator (Amplitude Technologies, Sequoia), and the measurement results in the first-round experiment is given in Fig. 10(a) (blue line). To reduce the scattering pulses generated in the stretcher, as shown in Fig. 9, a homemade mask was positioned at the concave mirror to filter scattering pulses but allow all of the signal to be collected by the telescope (concave and convex mirrors). The temporal contrast was then re-measured and the result is illustrated in Fig. 10(a) (red line). Comparing the two results, it is clear that the picosecond temporal contrast is improved, which corroborates the result concluded in the previous theoretical section: the picosecond temporal contrast could be improved by reducing the scattering pulses generated in the stretcher [see Fig. 7(b)]. In the second-round experiment, the B-integral accumulation was reduced and the temporal contrasts were also measured twice, once without [Fig. 10(b) blue line] and once with [Fig. 10(b) red line] the mask. Comparing the data in Fig. 10(b) shows that the temporal contrast is also slightly enhanced by the spatial filtering of the scattering pulses, however the amount of the enhancement is not as obvious as that seen in Fig. 10(a). This phenomenon is caused by different B-integral accumulations: in the case of same scattering pulses generated in the stretcher, a large B-integral accumulation would further increase the picosecond temporal contrast degradation [see Figs. 7(b) and 7(e)]. Figure 8(b) also shows that, when the B-integral accumulation is reduced, the sensitivity of the picosecond temporal contrast to rs will decrease and, correspondingly, the temporal contrast enhancement of the mask will decrease.
In Fig. 10, we can identify some post- and pre-pulses after and before the main pulse that are generated by the multiple-reflection of a 0.8 mm-thick ¼-wave plate in the regenerative amplifier and the refractive index nonlinearity. The theory behind this problem is very clear, so we will not repeat it again here . Comparing Figs. 10(a) with 10(b), when the B-integral accumulation is reduced the peak of the first pre-pulse decreases slightly. Correlating with the theory, the first pre-pulse is proportional to the square of the B-integral accumulation. In Fig. 10(b) we can also see that the noise in the range of −400 to −200 ps before the main pulse increases, which we believe is caused by the amplified spontaneous emission (ASE) generated in the slab laser. ASE has already been well researched and is neglected in our model. Although the signal pulse itself in our demonstration is not as clean as is ultimately possible, which limits the temporal contrast enhancement amount by filtering scattering pulses, the result of the experiment does agree well with the theoretical prediction proposed in Section 3.2, and verifies the reliability of the proposed theoretical model and simulation results. Next step, we will optimize our regenerative amplifier to clean the signal pulse for even obvious comparison demonstrations.
5. Suggestions and discussions
To reduce the temporal contrast degradation, especially picosecond contrast pedestal, induced by the scattering pulse in a CPA laser, several suggestions are presented based on our theoretical simulations and experimental demonstrations. The pass number in the stretcher should be carefully controlled to reduce the possibility of generating scattering pulses. Transmission gratings, such as those demonstrated by Tang et al. , are recommended for use in the stretcher to reduce the total amount of scattering pulses collected by the telescope. As illustrated in Fig. 1(b), it is reasonable that at the transmission and reflection grating the scattering pulse is generated in a 4π and 2π space, respectively. A mask should therefore be introduced inside the stretcher to spatially filter the scattering pulses, as demonstrated herein, which should be positioned near the Fourier plane of the telescope. The B-integral accumulation of the entire system should be carefully optimized because of pulse duration distortion as well as temporal contrast degradation.
In Section 3, the time delay between two adjacent scattering pulses Δt was fixed as 50 ps, whereupon about 100 scattering pulses were simulated in the stretcher/compressor for a total amount of 4.8 ns stretching/compression. When rs or rc = −80 dB, the energy ratio of the total scattering to the signal pulse generated in the stretcher/compressor was −60 dB. Obviously, for a theoretical simulation, Δt, rs and rc are three key parameters that directly determine the total energy of the scattering pulses, and which should be carefully chosen according to the actual conditions. In fact, variation/random Δts and Δtc values for a stretcher and a compressor can be used, especially for a non-uniform distribution of scattering rays, which would make the simulation closer to the real condition. However, in this paper we mainly focus on the general influences of the stretcher and the compressor; and so for simplification the Δt for both the stretcher and the compressor are chosen as a fixed identical value.
Actually, the scattering-diffraction processes in stretchers/compressor are very complex. To simplify this complexity and set up a theoretical model, in Section 2.1 only three ray trajectories of SSDD, DDSS and SSSS are considered. Compared with the other ray trajectories of SDDD, DSDD, DDSD, DDDS, SDSD, SDDS, DSSD, DSDS, SSSD, SSDS, SDSS and DSSS, although the individual influence of considered three ray trajectories on the temporal contrast is relatively higher, that of the other ones still is not too weak to be completely neglected. In this case, to improve the theoretical model and accurately estimate the scattering pulse-induced temporal contrast degradation, the influence of each possible ray trajectory should and will be considered in our next-step work.
In conclusion, a simplified theoretical model was developed for the first time to address the problem of the scattering pulse-induced temporal contrast degradation in a CPA laser. Based on the proposed model, we simulated the evolution of the scattering and signal pulses in a CPA laser consisting of an Offner stretcher and a Treacy compressor. Further, we calculated the variation of the temporal contrast for the scattering effect in the stretcher and in the compressor, as well as the B-integral accumulation. The theoretical results show that the picosecond and the nanosecond temporal contrast in a CPA laser is mainly determined by the scattering pulses generated in the stretcher and the compressor, respectively. Both of these types of temporal contrasts degrade with increasing B-integral accumulation. In addition, the sensitivity of the picosecond temporal contrast to the stretcher scattering effect increases with the B-integral accumulation. In fact, this phenomenon can also be explained by the recent theory on the spectral modulation-induced temporal contrast degradation in a nonlinear CPA laser . For verification, a simple experimental demonstration was carried out that agreed well with the theoretical predictions. Finally, some suggestions for reducing the temporal contrast degradation caused by the scattering pulses were presented. We believe that this work is helpful for all CPA lasers, but especially for petawatt lasers, to further improve their temporal contrasts, and to provide a path for researching the scattering pulse problem in CPA laser systems.
A portion of this work was supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) (JP25247096).
The authors gratefully acknowledge Mr. T. Uesu, Mr. K. Teramoto and Mr. T. Terao for their contributions to upgrading the HALNA laser system.
References and links
1. C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, 1–14 (2015). [CrossRef]
2. M. D. Perry, D. Pennington, B. C. Stuart, G. Tietbohl, J. A. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H. T. Powell, M. Vergino, and V. Yanovsky, “Petawatt laser pulses,” Opt. Lett. 24(3), 160–162 (1999). [CrossRef] [PubMed]
4. N. Miyanaga, H. Azechi, K. A. Tanaka, T. Kanabe, T. Jitsuno, J. Kawanaka, Y. Fujimoto, R. Kodama, H. Shiraga, K. Knodo, K. Tsubakimoto, H. Habara, J. Lu, G. Xu, N. Morio, S. Matsuo, E. Miyaji, Y. Kawakami, Y. Izawa, and K. Mima, “10-kJ PW laser for the FIREX-I program,” J. Phys. 133, 81 (2006).
5. J. Kawanaka, “LFEX-Laser: A Multi-Kilojoule, Multi-Petawatt Heating Laser for Fast Ignition,” in 26th IAEA Fusion Energy Conference (2016).
6. Y. Chu, X. Liang, L. Yu, Y. Xu, L. Xu, L. Ma, X. Lu, Y. Liu, Y. Leng, R. Li, and Z. Xu, “High-contrast 2.0 Petawatt Ti:sapphire laser system,” Opt. Express 21(24), 29231–29239 (2013). [CrossRef] [PubMed]
8. D. N. Papadopoulos, C. L. Blanc, G. Chériaux, P. Georges, J. P. Zou, G. Mennerat, F. Druon, A. Pellegrina, P. Ramirez, F. Giambruno, A. Fréneaux, F. Leconte, D. Badarau, J. M. Boudenne, P. Audebert, D. Fournet, T. Valloton, C. Greverie, J. L. Paillard, J. L. Veray, M. Pina, P. Monot, P. Martin, F. Mathieu, J. P. Chambaret, and F. Amiranoff, “The Apollon-10P project: Design and current status,” in Advanced Solid-State Lasers Congress, OSA Technical Digest (Optical Society of America, 2013), paper ATu3A.43. [CrossRef]
9. R. Li, L. Yu, Z. Gan, C. Wang, S. Li, Y. Liu, X. Liang, Y. Leng, B. Shen, and Z. Xu, “Development of 10PW super intense laser facility at Shanghai,” in Extreme Light Scientific and Socio-economic Outlook (2016).
10. A. Lyachev, O. Chekhlov, J. Collier, R. Clarke, M. Galimberti, C. Hernandez-Gomez, P. Matousek, I. Musgrave, D. Neely, P. Norreys, I. Ross, Y. Tang, T. Winstone, and B. Wyborn, “The 10PW OPCPA Vulcan Laser Upgrade,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2011), paper HThE2.
11. G. A. Mourou, G. Korn, W. Sandner, and J. L. Collier, WHITEBOOK ELI-Extreme Light Infrastructure, Science and Technology with Ultra-Intense Lasers (Andreas Thoss, 2011).
12. The Institute of Applied Physics, the Russian Academy of Sciences, “Exawatt Center for Extreme Light Studies (XCELS),” http://www.xcels.iapras.ru/
13. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985). [CrossRef]
14. A. Dubietis, G. Jonušauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4), 437–440 (1992). [CrossRef]
15. J. Ren, W. Cheng, S. Li, and S. Suckewer, “A new method for generating ultraintense and ultrashort laser pulses,” Nat. Phys. 3(10), 732–736 (2007). [CrossRef]
16. M. D. Perry, R. D. Boyd, J. A. Britten, D. Decker, B. W. Shore, C. Shannon, and E. Shults, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20(8), 940–942 (1995). [CrossRef] [PubMed]
17. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5(9), 454–458 (1969). [CrossRef]
18. O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3-1.6 µm region,” IEEE J. Quantum Electron. 23(1), 59–64 (1987). [CrossRef]
19. C. Hooker, Y. Tang, O. Chekhlov, J. Collier, E. Divall, K. Ertel, S. Hawkes, B. Parry, and P. P. Rajeev, “Improving coherent contrast of petawatt laser pulses,” Opt. Express 19(3), 2193–2203 (2011). [CrossRef] [PubMed]
20. Y. Tang, C. Hooker, O. Chekhlov, S. Hawkes, J. Collier, and P. P. Rajeev, “Transmission grating stretcher for contrast enhancement of high power lasers,” Opt. Express 22(24), 29363–29374 (2014). [CrossRef] [PubMed]
21. X. Lu, Y. Peng, Y. Li, X. Guo, Y. Leng, Z. Sui, Y. Xu, and X. Wang, “High contrast amplification at 1053 nm limited by pulse stretching-compressing process,” Chin. Opt. Lett. 14(2), 023201 (2016). [CrossRef]
22. N. Stuart, T. Robinson, D. Hillier, N. Hopps, B. Parry, I. Musgrave, G. Nersisyan, A. Sharba, M. Zepf, and R. A. Smith, “Comparative study on the temporal contrast of femtosecond mode-locked laser oscillators,” Opt. Lett. 41(14), 3221–3224 (2016). [CrossRef] [PubMed]
23. S. Kane and J. Squier, “Fourth-order-dispersion limitations of aberration-free chirped-pulse amplification systems,” J. Opt. Soc. Am. B 14(5), 1237–1244 (1997). [CrossRef]
24. D. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “Decrease of pulse-contrast in nonlinear chirped-pulse amplification systems due to high-frequency spectral phase ripples,” Opt. Express 16(12), 8876–8886 (2008). [CrossRef] [PubMed]
25. D. N. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “The impact of spectral modulations on the contrast of pulses of nonlinear chirped-pulse amplification systems,” Opt. Express 16(14), 10664–10674 (2008). [CrossRef] [PubMed]
26. M. Iliev, A. K. Meier, B. Galloway, D. E. Adams, J. A. Squier, and C. G. Durfee, “Measurement of energy contrast of amplified ultrashort pulses using cross-polarized wave generation and spectral interferometry,” Opt. Express 22(15), 17968–17978 (2014). [CrossRef] [PubMed]
27. F. Tavella, A. Marcinkevičius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8(10), 219 (2006). [CrossRef]
28. K. Kondo, H. Maeda, Y. Hama, S. Morita, A. Zoubir, R. Kodama, K. A. Tanaka, Y. Kitagawa, and Y. Izawa, “Control of amplified optical parametric fluorescence for hybrid chirped-pulse amplification,” J. Opt. Soc. Am. B 23(2), 231–235 (2006). [CrossRef]
29. J. Moses, S.-W. Huang, K.-H. Hong, O. D. Mücke, E. L. Falcão-Filho, A. Benedick, F. Ö. Ilday, A. Dergachev, J. A. Bolger, B. J. Eggleton, and F. X. Kärtner, “Highly stable ultrabroadband mid-IR optical parametric chirped-pulse amplifier optimized for superfluorescence suppression,” Opt. Lett. 34(11), 1639–1641 (2009). [CrossRef] [PubMed]
30. C. Homann and E. Riedle, “Direct measurement of the effective input noise power of an optical parametric amplifier,” Laser Photonics Rev. 7(4), 580–588 (2013). [CrossRef]
31. J. Wang, P. Yuan, J. Ma, Y. Wang, G. Xie, and L. Qian, “Surface-reflection-initiated pulse-contrast degradation in an optical parametric chirped-pulse amplifier,” Opt. Express 21(13), 15580–15594 (2013). [CrossRef] [PubMed]
32. N. V. Didenko, A. V. Konyashchenko, A. P. Lutsenko, and S. Yu. Tenyakov, “Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses,” Opt. Express 16(5), 3178–3190 (2008). [CrossRef] [PubMed]
33. A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J. P. Rousseau, J. P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, “10-10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation,” Opt. Lett. 30(8), 920–922 (2005). [CrossRef] [PubMed]
34. R. C. Shah, R. P. Johnson, T. Shimada, K. A. Flippo, J. C. Fernandez, and B. M. Hegelich, “High-temporal contrast using low-gain optical parametric amplification,” Opt. Lett. 34(15), 2273–2275 (2009). [CrossRef] [PubMed]
35. P. Yuan, G. Xie, D. Zhang, H. Zhong, and L. Qian, “High-contrast near-IR short pulses generated by a mid-IR optical parametric chirped-pulse amplifier with frequency doubling,” Opt. Lett. 35(11), 1878–1880 (2010). [CrossRef] [PubMed]
36. J. Liu, K. Okamura, Y. Kida, and T. Kobayashi, “Temporal contrast enhancement of femtosecond pulses by a self-diffraction process in a bulk Kerr medium,” Opt. Express 18(21), 22245–22254 (2010). [CrossRef] [PubMed]
37. I. Musgrave, W. Shaikh, M. Galimberti, A. Boyle, C. Hernandez-Gomez, K. Lancaster, and R. Heathcote, “Picosecond optical parametric chirped pulse amplifier as a preamplifier to generate high-energy seed pulses for contrast enhancement,” Appl. Opt. 49(33), 6558–6562 (2010). [CrossRef] [PubMed]
38. Y. Huang, C. Zhang, Y. Xu, D. Li, Y. Leng, R. Li, and Z. Xu, “Ultrashort pulse temporal contrast enhancement based on noncollinear optical-parametric amplification,” Opt. Lett. 36(6), 781–783 (2011). [CrossRef] [PubMed]
39. H. Kiriyama, T. Shimomura, H. Sasao, Y. Nakai, M. Tanoue, S. Kondo, S. Kanazawa, A. S. Pirozhkov, M. Mori, Y. Fukuda, M. Nishiuchi, M. Kando, S. V. Bulanov, K. Nagashima, M. Yamagiwa, K. Kondo, A. Sugiyama, P. R. Bolton, T. Tajima, and N. Miyanaga, “Temporal contrast enhancement of petawatt-class laser pulses,” Opt. Lett. 37(16), 3363–3365 (2012). [CrossRef] [PubMed]
40. S. G. Liang, H. J. Liu, N. Huang, Q. B. Sun, Y. S. Wang, and W. Zhao, “Temporal contrast enhancement of picosecond pulses based on phase-conjugate wave generation,” Opt. Lett. 37(2), 241–243 (2012). [CrossRef] [PubMed]
41. D. Kaganovich, J. R. Peñano, M. H. Helle, D. F. Gordon, B. Hafizi, and A. Ting, “Origin and control of the subpicosecond pedestal in femtosecond laser systems,” Opt. Lett. 38(18), 3635–3638 (2013). [CrossRef] [PubMed]
42. A. Yogo, K. Kondo, M. Mori, H. Kiriyama, K. Ogura, T. Shimomura, N. Inoue, Y. Fukuda, H. Sakaki, S. Jinno, M. Kanasaki, and P. R. Bolton, “Insertable pulse cleaning module with a saturable absorber pair and a compensating amplifier for high-intensity ultrashort-pulse lasers,” Opt. Express 22(2), 2060–2069 (2014). [CrossRef] [PubMed]
43. J. Wang, J. Ma, Y. Wang, P. Yuan, G. Xie, and L. Qian, “Noise filtering in parametric amplification by dressing the seed beam with spatial chirp,” Opt. Lett. 39(8), 2439–2442 (2014). [CrossRef] [PubMed]
44. H. Liebetrau, M. Hornung, A. Seidel, M. Hellwing, A. Kessler, S. Keppler, F. Schorcht, J. Hein, and M. C. Kaluza, “Ultra-high contrast frontend for high peak power fs-lasers at 1030 nm,” Opt. Express 22(20), 24776–24786 (2014). [CrossRef] [PubMed]
45. H. Liebetrau, M. Hornung, S. Keppler, M. Hellwing, A. Kessler, F. Schorcht, J. Hein, and M. C. Kaluza, “High contrast, 86 fs, 35 mJ pulses from a diode-pumped, Yb:glass, double-chirped-pulse amplification laser system,” Opt. Lett. 41(13), 3006–3009 (2016). [CrossRef] [PubMed]
47. T. Kawashima, T. Kanabe, O. Matsumoto, R. Yasuhara, H. Furukawa, M. Miyamoto, T. Sekine, T. Kurita, H. Kan, M. Yamanaka, M. Nakatsuka, and Y. Izawa, “Development of diode-pumped solid-state laser HALNA for fusion reactor driver,” Electr. Eng. Jpn. 155(2), 27–35 (2006). [CrossRef]