基于相位板旋转排布的超快束匀滑方案 
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In the inertial confinement nuclear fusion (ICF) facility, the non-uniformity of the target plane irradiation aggravates the instability of various laser plasmas such as magnification into filaments, stimulated Raman scattering, and stimulated Brillouin scattering, and destroys the target pellet symmetry of compression. In order to improve the irradiation uniformity of the target plane, researchers have successively developed a variety of beam smoothing schemes, such as radial smoothing (RS), azimuthal smoothing (AS), dynamic interference smoothing, and the combination of induced spatial incoherence(ISI) and lens array(LA) based on broadband light proposed by Shanghai Institute of Laser Plasma. However, these schemes have some shortcomings. Therefore, there is an urgent need to further develop a more feasible ultrafast beam smoothing scheme with a picosecond time scale.
Taking the 2×2 beam as an example, by establishing a physical model of the ultrafast beam smoothing scheme based on the rotation arrangement of phase plates, the effects of parameters of phase plates, beam arrangement, spatial wavefront distortion, and spatial deviation of laser beams on beam smoothing are analyzed.
Through calculation and simulation, the effects of parameters of phase plates, beam arrangement, spatial wavefront distortion, and spatial deviation of laser beams on beam smoothing are first investigated, the smoothing effect when the scheme is combined with the traditional beam smoothing scheme is then analyzed, and finally the influence of spatial deviation in the actual system on beam smoothing is studied. The simulation results show that when the peak valley (PV) value of the phase plate is 2λ3λ, it can not only ensure the beam smoothing effect of the scheme, but also avoid the excessive energy loss caused by wavefront distortion (Fig. 4). In addition, changing the arrangement of phase plates has little effect on the smoothing effect of the scheme (Fig. 5). When the PV value of phase distortion does not exceed 3λ, the scheme can show a better smoothing effect, and at the same time, the energy utilization rate of continuous phase plate (CPP) is less reduced (Fig. 6). Moreover, the combination of beam smoothing schemes based on the rotation arrangement of phase plates and smoothing by two-dimension spectral dispersion(2D-SSD) can further improve the smoothing effect of the target plane (Fig. 7). Finally, this scheme also has a large tolerance for spatial deviation (Fig. 8).
This paper proposes an ultrafast beam smoothing scheme based on the rotation arrangement of phase plates. By rotationally arranging the phase plates with a rotational asymmetric distribution in the laser quad, different spatial phase modulations are first provided for each sub-beam in the laser quad. Then the dynamic interference of the sub-beams with a certain wavelength difference on the target plane makes the speckles within the focal spot sweep rapidly in multiple directions and multiple dimensions, so as to achieve the goal of improving the uniformity of the focal spot in the picosecond time scale. On this basis, the effects of parameters of phase plates, beam arrangement, spatial wavefront distortion, and spatial deviation of laser beams on beam smoothing are analyzed. The results show that in the ultrafast beam smoothing scheme based on the rotation arrangement of phase plates, only the same phase plates with a rotational asymmetric distribution are required to be processed at the same time, which can lower the design and processing difficulty of phase plates. In addition, this scheme is little affected by spatial wavefront distortion, beam arrangement, and spatial deviation of laser beams. Combining the beam smoothing scheme based on the rotation arrangement of phase plates proposed in this paper with the traditional beam smoothing schemes can significantly improve the uniformity of focal spots within a few picoseconds, which can be an effective supplement to the traditional beam smoothing schemes.
1 引言
在惯性约束核聚变(Inertial Confinement Fusion，ICF)装置中，靶面辐照非均匀性会加剧放大成丝、受激拉曼散射、受激布里渊散射等多种激光等离子体的不稳定性，并破坏靶丸的压缩对称性[1-3]。为了提高靶面的辐照均匀性，人们相继发展了多种束匀滑方案，如随机相位板(Random Phase Plate，RPP)、连续相位板(Continuous Phase Plate，CPP)、透镜列阵(Lens Array，LA)等空域匀滑技术[4-6]，诱导空间非相干(Induced Spatial Incoherence，ISI)、光谱色散平滑(Smoothing by Spectral Dispersion, SSD)等时域匀滑技术[7-8]以及偏振匀滑[9-10](Polarization Smoothing，PS)技术。其中，连续相位板(CPP)作为一种纯相位元件，理论上具有接近100%的衍射效率，可以有效地控制远场强度包络，从而达到平滑远场大尺度不均匀性的目的[11-12]。然而，激光束的高相干性会使焦斑内部产生大量散斑，从而引起小尺度不均匀性，进而引发激光与等离子体相互作用过程中各种非线性效应的产生[13]。为了抑制散斑的影响，需要采用时域匀滑技术实现靶面光场分布的快速变化，进而从时间平均的意义上改善激光束光斑品质。光谱色散平滑(SSD)是目前国际上主流的时域束匀滑技术，其原理是借助电光调制晶体对激光束进行相位调制，再使相位调制脉冲通过光栅衍射，从而引入时空耦合的正弦型相位调制，最终实现焦斑内部散斑的快速扫动[14]。在SSD技术中，由于受电光调制晶体调制频率的限制，靶面焦斑的均匀性需要几十皮秒才能达到稳定状态，这个时间远大于流体动力学和激光等离子体不稳定性的特征时间[15]。为了更快速地改善焦斑的均匀性，研究人员提出了多种超快束匀滑方案[16-19]，如径向匀滑[20](Radial Smoothing，RS)、角向匀滑[21](Azimuthal Smoothing，AS)和动态干涉匀滑[22]等皮秒量级的超快束匀滑方案，以及基于宽带光的诱导空间非相干(Induced Spatial Incoherence，ISI)与透镜阵列(Lens Array，LA)联用方案[23]。这些超快束匀滑方案均可实现靶面光场皮秒或亚皮秒量级的快速变化，从而在极短时间内改善激光束光斑品质。然而，RS方案需要高能量周期性皮秒脉冲串作为泵浦光[24]，AS方案的束匀滑效果有限[22]，而动态干涉匀滑方案对共轭相位板的加工要求比较高[25]。因此，亟须进一步发展更具可行性的皮秒量级时间尺度的超快速束匀滑方案。
本文提出了一种基于相位板旋转(Phase Plate Rotation，PPR)排布的超快束匀滑方案。该方案使用4块完全相同且具有旋转非对称性的相位板，针对激光集束中的不同子束，将相位板以不同角度旋转排布，进而借助其旋转非对称性为各个子束附加不同的相位调制，在各子束之间存在一定波长差的前提下，利用不同子束的动态干涉使得焦斑内部的散斑快速扫动，从而在皮秒量级时间尺度内改善靶面的辐照均匀性。本文以典型惯性约束聚变装置中的2×2激光集束为例，通过建立相关物理模型，计算模拟了该方案的束匀滑特性，进而分析了相位板参数、相位板排布方式、激光束相位畸变以及空间偏差等对束匀滑效果的影响。
2 理论模型
在
图 1. 基于相位板旋转排布的超快束匀滑方案
Fig. 1. Ultrafast beam smoothing scheme based on rotation arrangement of phase plates
假设激光集束中的子束为具有振幅调制和相位畸变的超高斯光束[26]，其近场光场分布可表示为
于是，各子束在靶面的光场分布可以用Collins公式进行计算：
由于各子束之间存在一定的波长差且相位分布存在差异，不同子束在焦面的光强分布通过拍频效应随时间发生快速变化，其变化周期可以表示为
子光束对的动态干涉将引起靶面光斑内部散斑在不同方向发生快速扫动，从而达到在皮秒时间内改善激光束光斑品质的目的。因此，Δt积分时间内的焦面时间平均光强可表示为
3 束匀滑效果分析
在计算模拟时，主激光束参数为：1、2子束倍频后的波长
3.2 焦斑特性分析
以倾斜相位板、离轴椭球面相位板和离轴螺旋相位板为例，
图 2. 不同相位板旋转后的焦面动态干涉图样
Fig. 2. Dynamic interference patterns on focal plane after rotation of different phase plates
从
图 3. 不同匀滑方案的焦斑光强分布。(a)2D-SSD ＋ CPP；(b)PPR ＋ CPP；(c)2D-SSD ＋ PPR ＋ CPP
Fig. 3. Focal spot light intensity distributions by different smoothing schemes. (a) 2D-SSD ＋ CPP; (b) PPR＋ CPP; (c) 2D-SSD ＋ PPR ＋ CPP
从
3.3 基于相位板旋转排布的超快束匀滑特性分析
本小节我们讨论相位板参数、相位板排布方式、激光束相位畸变对束匀滑效果的影响，以及本方案与传统束匀滑方案联用时的匀滑效果，最后计算实际系统中的空间偏差对束匀滑效果的影响。
3.3.2 相位板参数的影响
图 4. 相位板的参数对束匀滑效果的影响。(a)不同类型相位板阵列的光通量对比度随相位板PV值的变化曲线；在不同相位板PV值下，(b)离轴椭球面相位板和(c)离轴螺旋相位板的匀滑效果与偏移量的关系曲线；(d)离轴椭球面相位板的桶中功率曲线
Fig. 4. Influences of parameters of phase plate on beam smoothing effect. (a) Contrast of every type of phase plate array versus PV value of phase plate; smoothing effects of (b) off-axis ellipsoidal phase plate and (c) off-axis spiral phase plate versus deviation under different PV values; (d) power in bucket of off-axis ellipsoidal phase plate
从
3.3.3 相位板排布方式的影响
图 5. 不同类型相位板阵列在不同排布方式下的光通量对比度曲线。(a)倾斜相位板；(b)离轴椭球面相位板；(c)离轴螺旋相位板
Fig. 5. Contrasts of every type of phase plate array under different arrangement patterns. (a) Tilted phase plate; (b) off-axis ellipsoidal phase plate; (c) off-axis spiral phase plate
从
3.3.4 激光相位畸变的影响
图 6. 激光束相位畸变对束匀滑效果的影响。(a)光通量对比度随波前相位畸变PV值的变化曲线(积分时间为10 ps)；(b)不同相位畸变PV值下光通量对比度随时间的变化曲线；(c)桶中功率的变化曲线
Fig. 6. Influence of phase distortion of laser beam on beam smoothing effect. (a) Contrast versus PV value of wavefront phase distortion(integration time of 10 ps); (b) contrast versus time under different phase distortion PV values of phase distortion; (c) power in bucket
从
3.3.5 与传统束匀滑方案的联用
以倾斜相位板为例，
图 7. 不同方案的束匀滑效果。(a)光通量对比度曲线；(b)FOPAI曲线
Fig. 7. Beam smoothing effects of different schemes. (a) Contrast curves; (b) FOPAI curves
从
3.3.6 空间偏差的影响
为了研究相位板旋转排布方案对子束近、远场的空间偏差的容限，本节讨论了激光束入射到相位元件时的空间偏差以及子光束焦斑在靶面的重合程度对束匀滑效果的影响。
图 8. 空间偏差对束匀滑效果的影响。(a)激光束入射到相位元件时的空间偏差对束匀滑效果的影响；(b)子光束焦斑重合程度对束匀滑效果的影响
Fig. 8. Influences of spatial deviation on beam smoothing effect. (a) Influence of spatial deviation on beam smoothing effect for laser beam incident on phase element; (b) influence of coincidence degree of sub-beam focal spots on beam smoothing effect
从
4 结论
提出了一种基于相位板旋转排布的超快束匀滑方案。该方案通过在激光集束中针对不同子束以不同角度旋转具有旋转非对称性的相位板，对存在一定波长差的子束进行不同的空间相位调制，进而利用各子光束在靶面的动态干涉，使得焦斑内部散斑在多方向、多维度快速扫动，从而达到在皮秒时间尺度内改善焦斑均匀性的目的。在此基础上，讨论了相位板参数、排布方式、激光束相位畸变以及空间偏差等对束匀滑效果的影响。结果表明，该方案仅需同时加工多套参数相同且具有旋转非对称性的相位板，对相位板面形分布无特殊要求，从而极大地降低了相位板的设计、加工难度。此外，该方案对相位板排布方式、激光波前相位畸变以及空间偏差具有一定的容限，进一步降低了对相位板的加工精度和一致性的要求。将所提相位板旋转排布束匀滑方案与传统束匀滑方案联用，能够在数皮秒时间范围内明显改善焦斑均匀性，可以作为传统束匀滑方案的有效补充。
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Article Outline
邹冬岩, 熊皓, 钟哲强, 张彬. 基于相位板旋转排布的超快束匀滑方案[J]. 中国激光, 2022, 49(4): 0405003. Dongyan Zou, Hao Xiong, Zheqiang Zhong, Bin Zhang. Ultrafast Beam Smoothing Scheme Based on Rotation Arrangement of Phase Plates[J]. Chinese Journal of Lasers, 2022, 49(4): 0405003.
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