1 Introduction
With the great advances in chirped-pulse amplification (CPA)[ Reference Strickland and Mourou 1 ], the development of high-intensity femtosecond laser systems has been dramatically accelerated. The peak power of femtosecond lasers has advanced from the terawatt (TW)[ Reference Xu, Lu, Li, Wu, Li, Wang, Li, Lu, Liu, Leng, Li and Xu 2 ] to the petawatt (PW)[ Reference Li, Gan, Yu, Wang, Liu, Guo, Xu, Xu, Hang, Xu, Wang, Huang, Cao, Yao, Zhang, Chen, Tang, Li, Liu, Li, He, Yin, Liang, Leng, Li and Xu 3 – Reference Zhang, Wu, Hu, Yang, Gui, Liu, Wang, Liu, Lu, Xu, Leng, Li and Xu 5 ] level, and high focused intensities of 1022 W/cm2 or more have become available at laboratories around the world. Under such extreme intensities, the temporal contrast ratio (TCR) emerges as a critical parameter, as dictated by strong-field physics requirements. When pre-pulses or pedestal noises exceed 10–12 relative to the peak intensity, these temporal noises can interact with the target material prematurely (on ps-to-ns timescales), inducing significant pre-ionization. This alters the initial target conditions (e.g., density, ionization degree), thereby perturbing the ultrafast dynamics between the main pulse and the target.
Temporal contrast degradation arises from three dominant noise sources: the amplified spontaneous emission (ASE), pre-pulse and coherent pedestals. Over the past decade, significant progress in temporal contrast enhancement techniques – including double-chirped-pulse amplification (double-CPA)[ Reference Kalashnikov, Risse, Schonnagel and Sandner 6 ], saturable absorbers (SAs)[ Reference Kiriyama, Pirozhkov, Nishiuchi, Fukuda, Ogura, Sagisaka, Miyasaka, Mori, Sakaki, Dover, Kondo, Koga, Esirkepov, Kando and Kondo 7 , Reference Fourmaux, Payeur, Buffechoux, Lassonde, Pierre, Martin and Kieffer 8 ], optical parametric amplification (OPA)[ Reference Dorrer, Begishev, Okishev and Zuegel 9 , Reference Liu, Wang, Li, Zhang, Han, Teng and Wei 10 ] and cross-polarized wave generation (XPWG)[ Reference Yu, Xu, Liu, Li, Li, Liu, Li, Wu, Yang, Yang, Wang, Lu, Leng, Li and Xu 11 – Reference Jullien, Albert, Burgy, Hamoniaux, Rousseau, Chambaret, Rochereau, Chériaux, Etchepare, Minkovski and Saltiel 13 ] – has enabled effective suppression of ASE in femtosecond lasers. Pre-pulses can be categorized into linear-origin pre-pulses and those converted via nonlinear effects. The former primarily originate from multiple reflections in optical components[ Reference Bai, Zhang, Wang, Wu, Hu, Yang, Qian, Gui, Lu, Liu, Xu, Liang, Leng and Li 14 ] or scattering noise induced by diffraction gratings in the stretcher[ Reference Wang, Liu, Lu, Chen, Long, Li, Chen, Chen, Bai, Li, Peng, Liu, Wu, Wang, Li, Xu, Liang, Leng and Li 15 , Reference Hooker, Tang, Chekhlov, Collier, Divall, Ertel, Hawkes, Parry and Rajeev 16 ]. The latter are mainly generated by post-pulses from the multiple reflection in optical components, due to the nonlinear coupling associated with the B-integral accumulation in CPA[ Reference Didenko, Konyashchenko, Lutsenko and Tenyakov 17 ] or the instantaneous gain effect in OPA[ Reference Wang, Yuan, Ma, Wang, Xie and Qian 18 , Reference Wang, Lu, Guo, Xu and Leng 19 ]. The origin mechanisms of such pre-pulses have been extensively investigated through both theoretical and experimental studies[ Reference Chen, Wang, Chen, Yang, Hu, Bai, Zhao, Pan, Wu, Zhang, Xu and Leng 20 – Reference Kiriyama, Miyasaka, Sagisaka, Ogura, Nishiuchi, Pirozhkov, Fukuda, Kando and Kondo 22 ]. In addition, these studies demonstrate that optimizing the laser optical path configuration[ Reference Bai, Zhang, Wang, Wu, Hu, Yang, Qian, Gui, Lu, Liu, Xu, Liang, Leng and Li 14 , Reference Kiriyama, Miyasaka, Kon, Nishiuchi, Sagisaka, Sasao, Pirozhkov, Fukuda, Ogura, Kondo, Nakanii, Mashiba, Dover, Liu, Kando, Bock, Ziegler, Püschel, Schlenvoigt, Zeil and Schramm 23 ] or employing wedge-angle optical elements[ Reference Wang, Liu, Lu, Chen, Long, Li, Chen, Chen, Bai, Li, Peng, Liu, Wu, Wang, Li, Xu, Liang, Leng and Li 15 , Reference Kiriyama, Miyasaka, Kon, Nishiuchi, Sagisaka, Sasao, Pirozhkov, Fukuda, Ogura, Kondo, Dover and Kando 24 ] can effectively eliminate pre- and post-pulses.
Coherent pedestals appearing within hundreds of picoseconds of the main pulse are attributed to two dominant mechanisms: surface roughness in the stretcher optics induces random spatio-phase noise (RSPN), degrading the temporal coherence of the main pulse and generating a noisy temporal pedestal (stretcher-generated coherent noise); the formation of the post-pedestal during pulse amplification introduces structural asymmetry in the coherent pedestal profile. Subsequent nonlinear processes drive the conversion of this post-pedestal into a pre-pedestal as amplification proceeds (amplifier-induced coherent noise). For the former case, computational modeling and experiments[ Reference Dorrer and Bromage 25 ] confirm that the surface quality of the convex mirror in Öffner stretchers directly degrades the TCR. Recent experimental studies[ Reference Ranc, Le Blanc, Lebas, Martin, Zou, Mathieu, Radier, Ricaud, Druon and Papadopoulos 26 ] have quantitatively characterized the impact of RSPN on pulse contrast, demonstrating a strong correlation between the temporal pedestal and the roughness of the convex mirror in Öffner stretchers. Experimental measurements performed on the J-KAREN-P laser system[ Reference Kiriyama, Miyasaka, Kon, Nishiuchi, Sagisaka, Sasao, Pirozhkov, Fukuda, Ogura, Kondo, Nakanii, Mashiba, Dover, Liu, Kando, Bock, Ziegler, Püschel, Schlenvoigt, Zeil and Schramm 23 ] further confirm that replacing the conventional mirror (root-mean-square (RMS) roughness: ~10 nm) with a high-quality convex mirror (RMS roughness: 0.2–0.3 nm) leads to significant suppression of coherent noise in the pulse temporal profile. Regarding the latter, systematic studies reveal that the post-pedestal induces structural asymmetry in the coherent pedestal profile, arising from the gain medium in CPA systems. Furthermore, the post-pedestal-to-pre-pedestal conversion efficiency exhibits a clear scaling dependence on the accumulated B-integral[ Reference Khodakovskiy, Kalashnikov, Gontier, Falcoz and Paul 27 ]. Furthermore, numerical and experimental investigations also reveal post-pedestal-to-pre-pedestal conversion dynamics in optical parametric chirped-pulse amplification (OPCPA) systems[ Reference Webb, Feng, Dorrer, Jeon, Roides, Bucht and Bromage 28 ]. While both generation mechanisms have been well-studied individually, their relative contributions to the final pedestal after high-power amplification in CPA systems remain debated. Here, we investigate the distinct evolution characteristics of these two dominant coherent noise sources (stretcher-generated and amplifier-induced) during high-power amplification and quantify their relative impacts on the temporal contrast of output pulses.
This study provides systematic experimental and numerical evidence revealing distinct evolutionary characteristics between stretcher-generated and amplifier-induced pedestals in high-power amplification. Crucially, we demonstrate their independent development dynamics through practical laser-system contrast degradation analysis, and further identify the pre-pedestal – resulting from post-pedestal conversion in high-power CPA – as the primary determinant of ultrashort pulse TCR degradation. The study is organized as follows. Firstly, we present the home-made 200-TW CPA system and experimentally measure the TCR of pulses at different amplification conditions after adopting an ultra-low-roughness convex mirror (RMS <0.2 nm), revealing the anomalous growth of asymmetric coherent noise (Section 2). Secondly, our numerical model systematically analyzes the distinct evolution mechanisms of both critical coherent noise sources (Section 3). Thirdly, using our numerical model, we investigate the evolution of pre-pedestal structures under higher B-integral conditions relevant to PW-class laser systems (Section 4). Finally, by analyzing experimental data and simulation results, we identify that the nonlinear effect of trailing-to-leading-edge coherent noise conversion during high-power amplification in the CPA system plays a decisive role in limiting the ultimate TCR of ultrashort laser pulses.
2 System performance and noise dynamics in a 200-TW chirped-pulse amplification laser
The home-made Ti:sapphire (Ti:sa) laser at the Shanghai Institute of Optics and Fine Mechanics (SIOM) facility was constructed in 2015 and has been further upgraded to improve the pulse contrast[ Reference Xu, Lu, Li, Wu, Li, Wang, Li, Lu, Liu, Leng, Li and Xu 2 , Reference Wu, Zhang, Yang, Hu, Ji, Gui, Wang, Chen, Peng, Liu, Liu, Lu, Xu, Leng, Li and Xu 29 ]. A simplified layout of the 200 TW/1 Hz Ti:sa laser is shown in Figure 1. The first CPA stage (Coherent, Astrella) provides a 40 fs seed pulse with energy of 6 mJ at a 1 kHz repetition rate, which is transmitted through a compact nonlinear temporal filter. The nonlinear temporal filter combining XPWG and fs-OPA can deliver cleaned pulses at a 1 kHz repetition rate with energy of 100 μJ and the TCR of the seed pulse can be optimized up to 10–11 with a significantly suppressed pedestal, as shown in Figure 2 [ Reference Yu, Xu, Liu, Li, Li, Liu, Li, Wu, Yang, Yang, Wang, Lu, Leng, Li and Xu 11 , Reference Hu, Wang, Yang, Bai, Wu, Zhang, Chen, Yang, Qian, Gui, Li, Liu, Lu, Xu and Leng 12 ]. The trailing- and leading-edge coherent noises exhibit comparable magnitudes. The picosecond temporal contrast measurement was performed using a scanning third-order cross-correlator (TOCC; Sequoia, Amplitude Laser), which provides an intrinsic dynamic range of up to 11 orders of magnitude.
Layout of the 200 TW/1 Hz Ti:sapphire laser system.
Figure 1 Long description
The flowchart consists of two rows of black-bordered boxes connected by red arrows indicating the main beam path and green boxes/arrows indicating pump sources.
Top Row (Left to Right):
* First C P A Stage: Connects via a red arrow labeled 6 m J to the next box.
* Nonlinear Temporal Filter: Connects via a red arrow labeled 100 u J to the next box.
* Offner stretcher: Connects via a red arrow labeled 25 u J to the next box.
* Regeneration Amplifier: Connects via a red arrow labeled 1.5 m J downward to the second row.
Bottom Row (Right to Left):
* Multi-pass Amplifier M P A-1: Receives the 1.5 m J beam from above. It is pumped by an Nd YAG laser (220 m J 10 H z) providing 180 m J. A green feedback arrow labeled 35 m J returns to the Regeneration Amplifier. It connects via a red arrow labeled 48 m J to the left.
* Power Amplifier M P A-2: Receives the 48 m J beam. It is pumped by an Nd YAG laser (5 J 1 H z) providing 5 J. It connects via a red arrow labeled 2 J to the left.
* Final Amplifier M P A-3: Receives the 2 J beam. It is pumped by 4 Nd YAG lasers (5 J 1 H z) providing 20 J. It connects via a red arrow labeled 8 J to the left.
* Vacuum Compressor: Receives the 8 J beam. A final red arrow points downward to the system output text: 5.5 J 27 f s, approximately 200 T W 1 H z.
Measured temporal contrast before (blue line) and after (red line) the nonlinear temporal filter.
Figure 2 Long description
The line graph uses a logarithmic Y-axis labeled Normalized Intensity ranging from 10 super -12 to 10 super 0. The X-axis is labeled Time in p s, ranging from -300 to 150.
* The blue line represents the signal before filtering. It maintains a noisy baseline at approximately 10 super -7 from -300 to -50 p s. It rises to a peak of 10 super 0 at 0 p s and then settles into a post-pulse noise floor around 10 super -6 with several distinct secondary peaks between 25 and 150 p s.
* The red line represents the signal after the nonlinear temporal filter. It shows a significantly lower noise floor, starting at approximately 10 super -11 from -300 to -25 p s. It rises sharply to the same peak of 10 super 0 at 0 p s. Following the main pulse, the red line drops much faster than the blue line, reaching a post-pulse floor near 10 super -11, effectively suppressing the background noise by four to five orders of magnitude compared to the blue line.
The seed pulse is then re-stretched using a grating-based all-reflective Öffner stretcher for the second CPA stage, and an acousto-optic programmable dispersive filter (AOPDF; Dazzler, Fastlite) is implemented to compensate for high-order dispersion terms resulting from beam propagation. Before entering the regenerative amplifier, a single pulse at a 10 Hz repetition rate is selected by a Pockels cell (PC) assembly that consists of two high extinction ratio Glan laser polarizers and a KD*P PC. The 10 Hz laser pulse is amplified to 1.5 mJ in the regenerative amplifier with pump energy of 35 mJ. After passing through another two PC assemblies, the repetition rate of the laser pulse is changed from 10 to 1 Hz. Subsequently, the pulse is amplified to 8 J through a multi-pass pre-amplifier (MPA-1), a power amplifier (MPA-2) and a final amplifier (MPA-3). The amplified laser pulse is delivered into a vacuum compressor, and the pulse duration of 27 fs is achieved.
To ensure a consistent dynamic range in our measurements while characterizing coherent noise evolution throughout the amplification stages, we conducted comparative TCR analysis using a TOCC under two amplification conditions: low-energy amplification (only the regenerative amplifier and MPA-1 work) and high-energy amplification (all amplifiers work). For both amplification conditions, the chirped pulses traveled through nearly identical optical paths in the laser system. The resulting compressed femtosecond pulses were sampled by a pick-off mirror inside the compressor and subsequently directed into the TOCC for TCR characterization. Active spectral control via the AOPDF ensured a consistent output spectral width and profile under the different amplification conditions. Furthermore, to maintain constant energy levels at the TOCC under the different amplification conditions, an adjustable attenuator – consisting of uncoated wedges and pick-off mirrors with different splitting ratios – was implemented in the measurement beam path.
According to the experimental results reported in Ref. [Reference Kiriyama, Miyasaka, Kon, Nishiuchi, Sagisaka, Sasao, Pirozhkov, Fukuda, Ogura, Kondo, Nakanii, Mashiba, Dover, Liu, Kando, Bock, Ziegler, Püschel, Schlenvoigt, Zeil and Schramm23], integrating optical components with superior surface roughness in the laser system, we can effectively suppress stretcher-generated coherent noise. This approach enables clearer observation of amplifier-induced noise evolution and facilitates investigation into potential interactions between the two noise sources. In this work, we replaced the original convex mirror (RMS roughness: 1–2 nm) with newly fabricated high-precision optics with less than 0.2 nm RMS roughness. The surface roughness measured by the ZYGO laser interferometer is shown in Figure 3. The old convex mirror (Figure 3(a)) exhibits an RMS roughness of approximately 1.18 nm, whereas the new convex mirror (Figure 3(b)) yields an RMS value of approximately 0.14 nm. The reduction in surface roughness effectively suppresses stretcher-generated noise, thereby enabling more precise observation and comparative analysis of contrast degradation attributable to amplification dynamics.
Surface roughness of the convex mirrors measured using laser interferometry.
After replacing the convex mirror, we measured the temporal contrast and optical spectrum (Figure 4) under two amplification conditions: low-energy (27 mJ) and high-energy (5.2 J) operation, as illustrated in Figure 4. The output pulses from both amplification conditions undergo identical compression, yielding a measured pulse width of approximately 27 fs (Fastlite Wizzler). The red and blue curves correspond to the temporal contrast and spectral profiles for the low- and high-energy cases, respectively. The comparison reveals that under high-energy amplification conditions, the pre-pedestal emerges earlier (from −130 ps) and within the leading-edge temporal window (−80 to −10 ps) the coherent noise intensity exhibits a pronounced amplification of approximately one to two orders of magnitude, while the trailing-edge noise retains nearly invariant intensity and structure. Intriguingly, optimizing the stretcher’s optical surface quality yields negligible suppression of coherent noise in high-energy amplification regimes. Instead, experimental measurements reveal significant enhancement of the pre-pedestal. Consequently, our experiments reveal the amplification characteristics of the pre-pedestal in high-power CPA systems, although its underlying physical mechanisms and temporal dynamics remain unclear.
Measured temporal contrast (a) and spectrum (b) under two amplification conditions.
Figure 4 Long description
Panel a is a line graph of Normalized Intensity on a logarithmic Y axis from 10 super minus 11 to 10 super 0 versus Time in p s on an X axis from minus 300 to 150. A sharp central peak occurs at 0 p s. The blue line shows higher noise levels and a broader pedestal between minus 150 and 0 p s compared to the red line. Both lines decay asymmetrically, with a steeper drop-off on the negative time side and a more gradual, noisy slope on the positive time side.
Panel b is a line graph of Normalized Intensity on a linear Y axis from 0.0 to 1.0 versus Spectrum in n m on an X axis from 700 to 900. The data shows a broad double-peaked structure between 760 and 840 n m. The first peak is at approximately 780 n m and the second at 815 n m. The blue line has a higher intensity in the central valley around 800 n m and slightly higher secondary peaks compared to the red line, which shows a deeper dip between the two main peaks.
3 Numerical modeling of temporal coherent noise evolution in chirped-pulse amplification systems
Using the established CPA model[ Reference Chen, Wang, Chen, Yang, Hu, Bai, Zhao, Pan, Wu, Zhang, Xu and Leng 20 , Reference Chen, Wang, Liu, Chen, Bai, Pan, Hu, Hu, Wu, Zhang, Liu, Xu and Leng 21 ], we systematically simulate and analyze the dynamic evolution of two dominant coherent noise sources during high-power amplification. Given the high temporal contrast provided by our nonlinear temporal filter – particularly in suppressing pre-/post-pedestal noise within the coherent noise region (covering 100 ps around the main pulse) – the purified temporal contrast (red line in Figure 2) clearly demonstrates complete suppression of CPA-1-stage coherent noise. Thus, the seed light in simulations is modeled as an ideal super-Gaussian pulse (spectrum with a 10th-order super-Gaussian profile, 50-nm full width at half maximum (FWHM) bandwidth centered at 800 nm). Firstly, we investigate the coherent noise introduced by surface roughness of near-/far-field optics in the stretcher. Building on the universal theoretical and experimental framework established in Ref. [Reference Dorrer and Bromage25], we adopt a similar noise modeling approach, in which the spectrum E(ω) of the optical pulse is analytically expressed as follows:
where I(ω) and φ(ω) are the spectral intensity and phase of the field, respectively.
The spectral phase of the pulse is decomposed as φ(ω) = φ0(ω) + δφ(ω), where φ 0(ω) represents a slowly varying spectral phase (e.g., linear or nonlinear chirp) and δφ(ω) represents a high-frequency spectral phase modulation of small amplitude. Assuming that the amplitude of δφ(ω) is small relative to unity, one can write exp[iδφ(ω)] ≈ 1 + iδφ(ω). Equation (1) can be rewritten as follows:
We first investigate the coherent noise evolution induced solely by the stretcher-generated pedestal during high-power amplification. As demonstrated in Ref. [Reference Dorrer and Bromage25], the temporal pedestal produced via high-frequency phase modulation in the stretcher exhibits inherent symmetry. To ensure direct comparison with experimental results while eliminating post-pedestal effects from amplifiers, the numerical model employs a stretcher-generated pedestal whose leading-edge pre-pedestal matches the experimentally measured pre-pedestal (red curve) in Figure 4(a), while maintaining a symmetric post-pedestal profile. The pulse function, including coherent noise contributions from optical surface roughness in the stretcher, was then used in simulations to study two different amplification conditions, corresponding to the experimental cases. The simulation results are shown in Figure 5(a), where the red curve represents the simulated temporal contrast of the compressed pulse under the low-energy amplification case, with a total accumulated B-integral of approximately 0.04 rad during propagation in the crystal. The blue curve corresponds to the high-energy amplification case, exhibiting a higher accumulated nonlinear phase (~0.47 rad). Comparative analysis shows that, during high-power amplification in the CPA system, the coherent noise induced by optical surface roughness does not exhibit significant asymmetric distortion. Moreover, the pedestal of this symmetric structure shows no notable intensity enhancement.
Simulation results of pedestal (stretcher-generated (a) and amplifier-induced (b)) evolution in high-power amplification.
Figure 5 Long description
A two-panel attribute space diagram. Both panels share a Y-axis of Normalized Intensity on a logarithmic scale from 10 super minus 11 to 10 super 0 and an X-axis of Time in p s from minus 150 to 150.
Panel a, located on the left, displays a symmetric pedestal. A sharp central peak at 0 p s reaches 10 super 0. The intensity decays symmetrically on both sides, forming a triangular pedestal shape that reaches approximately 10 super minus 10 at plus or minus 100 p s. Red and blue data lines are overlaid, showing nearly identical overlapping trends.
Panel b, located on the right, displays an asymmetric pedestal. While the central peak remains at 0 p s, the intensity distribution is skewed. The blue data line shows a higher intensity floor on the negative time side (leading edge) compared to the red line. On the positive time side (trailing edge), the red data shows a plateau-like structure with significant noise or fluctuations, maintaining an intensity between 10 super minus 7 and 10 super minus 9 out to 150 p s, whereas the blue data drops off more sharply.
Next, we investigate the nonlinear conversion (via self-phase modulation, SPM) of an asymmetric post-pedestal into a pre-pedestal and its evolution during high-power amplification in CPA systems. Following the post-pedestal modeling approach described in Ref. [Reference Webb, Feng, Dorrer, Jeon, Roides, Bucht and Bromage28], we synthesize an asymmetric post-pedestal consisting of 200 replicas of the main pulse. Each replica is temporally displaced with a random delay, assigned a random phase (0–2π), and scaled in amplitude according to the post-pedestal experimental data corresponding to the red curve in Figure 4(a). The seed pulse embedded with an asymmetric coherent noise structure is propagated through our amplification model, with simulations conducted under both experimental amplification conditions (matching the parameters in Figure 4). The simulation results are shown in Figure 5(b), where the red and blue curves represent the temporal contrast of the compressed pulse under the low-energy and high-energy amplification case, with accumulated B-integrals of approximately 0.04 rad and approximately 0.47 rad during laser propagation, respectively. Notably, the simulated coherent noise exhibits an evolution trend (with a 1–2 orders-of-magnitude growth of pre-pedestal within the leading 100-ps range) closely matching our experimental measurements during high-power CPA.
A detailed comparison between simulations and experimental measurements shows that the simulated pre-pedestal in the range of −75 ps to 0 ps is within 0.5 orders of magnitude lower than the experimentally observed. Given that the numerical model does not account for transmission elements (e.g., beam expanders and electro-optic crystals) in the actual system, we consider this difference to be justified. Furthermore, when simulating the combined effect of both dominant noise sources, the calculated noise intensity and temporal distribution at high-energy amplification condition exhibit negligible deviation from the case where only the latter source is considered, suggesting no significant interaction between the two noise mechanisms. This also explains why replacing with convex mirrors of high-precision surface roughness failed to achieve noticeable TCR improvement under high-energy amplification condition. A qualitative physical explanation aligns with the observed phenomenon. The stretcher-generated pedestal originates from high-frequency spectral phase modulation within the main pulse’s spectral bandwidth, primarily caused by surface roughness of far-field optical elements in the stretcher. After stretching, such high-frequency spectral phase modulation converts into temporal intensity modulation through the time-frequency coupling of the chirped pulse. However, its modulation amplitude remains negligible and cannot be effectively amplified by the accumulated B-integral in the laser system. Conversely, the main pulse can temporally overlap with the post-pulses forming the post-pedestal, directly inducing intensity modulation. This intensity modulation is sufficiently strong to be converted into spectral phase modulation via SPM during amplification. Ultimately, the effect replicates from the trailing to leading edge, resulting in significant pre-pedestal growth.
4 B-integral dependent coherent noise dynamics during TW-to-PW power scaling
When scaling the output power of CPA laser systems from TW to PW class, the accumulated B-integral during amplification and propagation increases significantly. This enhanced B-integral necessitates careful consideration of the subsequent evolution characteristics of the leading-edge coherent noise. Building upon the established numerical model, we further simulation the nonlinear dynamics in high-power CPA laser systems. Figure 6 systematically investigates the evolution of coherent noise with increasing B-integral accumulation. The simulations retained the same initial laser parameters as the previously modeled 200 TW system. Based on our home-made SULF-10 PW facility[ Reference Li, Gan, Yu, Wang, Liu, Guo, Xu, Xu, Hang, Xu, Wang, Huang, Cao, Yao, Zhang, Chen, Tang, Li, Liu, Li, He, Yin, Liang, Leng, Li and Xu 3 ], the accumulated B-integral in the amplifier system was approximately 1 rad at the 1 PW peak power level, increasing to approximately 2 rad at 10 PW. Under the same amplifier design, further scaling the peak power beyond 10 PW would drive the B-integral to 3 rad or higher. Figure 6(a) quantifies the degradation of temporal contrast as the B-integral rises from 0.1 rad to 3.0 rad, while Figure 6(b) emphasizes the dynamic structural variations of pre-pedestal noise within a 150-ps temporal window preceding the main pulse.
Simulated evolution of coherent noise with increasing B-integral values in TW-to-PW-class laser systems.
Figure 6 Long description
A two-panel multiplot labeled a and b.
Panel a: A line graph with a horizontal x-axis representing Time in p s from minus 150 to 150 and a vertical y-axis representing Normalized Intensity on a logarithmic scale from 10 super minus 11 to 10 super 0. The data shows a central peak at 0 p s. Four colored datasets represent B-integral values: black for B equals 0.1, red for B equals 1.0, green for B equals 2.0, and blue for B equals 3.0. As the B-integral value increases, the noise floor surrounding the central peak rises significantly, particularly in the range of minus 50 to 50 p s.
Panel b: A line graph focusing on the pre-pulse region with an x-axis from minus 150 to 0 p s and a y-axis from 10 super minus 12 to 10 super minus 3. It uses the same color-coded B-integral values as panel a. The graph illustrates that higher B-integral values lead to a higher and more structured coherent noise pedestal. The blue line (B equals 3.0) maintains the highest intensity across the entire time range, while the black line (B equals 0.1) represents the lowest noise floor.
Comparative analysis reveals that as the accumulated B-integral increases during CPA and propagation, the pre-pedestal converted from the trailing-edge coherent noise exhibits growing intensity, demonstrating a strong positive correlation with the B-integral magnitude. Further analysis demonstrates inhomogeneous structural evolution of pre-pedestal. When B-integral < 1 rad, the strongest amplification occurs within the −50 ps to 0 ps temporal window, while no significant enhancement is observed beyond this interval. When B-integral > 1 rad, the growth rate of pre-pedestal within the −50 ps to 0 ps range decelerates, whereas a pronounced enhancement emerges in the region beyond −50 ps (temporally isolated from the main pulse). Concurrently, the trailing-edge coherent noise no longer remains constant but exhibits synchronized degradation with the pre-pedestal. The inhomogeneous structural growth of the pre-pedestal may be qualitatively explained by a mechanism analogous to pre-pulse generation from post-pulses in chirped-pulse amplifiers[ Reference Chen, Wang, Chen, Yang, Hu, Bai, Zhao, Pan, Wu, Zhang, Xu and Leng 20 , Reference Kiriyama, Miyasaka, Sagisaka, Ogura, Nishiuchi, Pirozhkov, Fukuda, Kando and Kondo 22 ]. Similar to post-pulse interactions with the main pulse, the post-pedestal temporally overlaps with the main pulse during high-power amplification, resulting in mutual intensity modulation. Through the self-phase modulation (SPM) effect in CPA systems, this intensity modulation is converted into a nonlinear phase. After compression, these nonlinear phase shifts manifest temporally as a pre-pedestal whose intensity correlates directly with the B-integral value.
Our findings demonstrate that the accumulated B-integral nonlinear phase in CPA laser systems significantly influences the evolution dynamics of coherent noise. When the B-integral exceeds 1 rad, the nonlinear effects induce not only strong amplification of the pre-pedestal but also energy coupling toward the trailing edge. These processes degrade the temporal contrast by two to three orders of magnitude, thereby fundamentally limiting the performance enhancement achievable through higher peak power in ultra-intense ultrafast laser systems.
5 Conclusion
Experimental and numerical studies demonstrate the distinct evolution dynamics of ps-scale coherent noise in high-power CPA laser systems, governed by its origin: stretcher-generated noise maintains symmetric pedestals with negligible distortion during energetic amplification; in contrast, amplifier-induced noise develops asymmetric pedestals, exhibiting pre-pedestal growth proportional to the accumulated B-integral. Through combined simulations and experiments, we confirm that these two coherent noises independently affect the final temporal contrast of the output pulses. Even with stretcher-generated coherent noise suppressed via sub-nanometer optics polishing, its mitigation proves ineffective under high B-integral conditions, where amplifier-induced noise dominates, and ultimately limits the TCR. This effect becomes critical toward the 10 and 100 PW regimes, where contrast control is essential not only for peak intensity but also for enabling next-generation strong-field physics experiments.
Our findings establish the B-integral as a decisive metric for contrast optimization in PW-class CPA lasers, shifting the optimization focus from stretcher design to active management of nonlinear phase accumulation. These results provide guidelines for coherent noise characterization and mitigation, advancing the development of ultra-high-intensity CPA lasers.
Acknowledgements
This work was supported by the National Key R&D Program of China (Grant No. 2025YFF0515102), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB0890100), the National Natural Science Foundation of China (Grant No. 12388102) and the Top-notch Project of Shanghai Oriental Talents Program (Comprehensive Platform).
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