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弱相对论涡旋光在等离子体中传播的波前畸变及补偿

刘伟 贾青 郑坚

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弱相对论涡旋光在等离子体中传播的波前畸变及补偿

刘伟, 贾青, 郑坚

Wavefront distortion and compensation for weakly relativistic vortex beams propagating in plasma

Liu Wei, Jia Qing, Zheng Jian
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  • 涡旋光与等离子体相互作用近年来在激光等离子体领域引起了广泛的关注. 深入研究涡旋光在等离子体中的传播对粒子加速和辐射源产生等工作具有重要意义. 本文着重探讨了弱相对论涡旋光在等离子中传播时, 传播过程对电磁波结构的影响. 基于三维粒子模拟, 发现弱相对论涡旋光在等离子体中传播时会产生波前畸变. 在给定等离子体密度时, 畸变程度与电磁波强度及传播距离密切相关. 基于相位修正模型, 通过考虑电子相对论质量修正, 在理论上对该现象进行了解释. 此外, 研究还发现可以通过设置适当的初始密度调制对波前畸变进行补偿抑制, 并通过三维粒子模拟进行了验证. 本工作加强了对涡旋光在等离子体中传播过程的理解, 并为设计应用于相对论涡旋光的等离子体器件提供了参考.
    The propagation of electromagnetic wave in plasma is one of the long-standing concerns in the field of laser plasma, and it is closely related to the researches of radiation source generation, particle acceleration, and inertial confinement fusion. Recently, the proposal of various schemes for generating intense vortex beams has led to an increasing number of researchers focusing on the interaction between intense vortex beams and plasmas, resulting in significant research progress in various areas, such as particle acceleration, high-order harmonic generation, quasi-static self-generated magnetic fields, and parametric instability. Compared with traditional Gaussian beams, vortex beams, featuring their hollow amplitudes and helical phases, can exhibit novel phenomena during propagating through plasma. In this work, we primarily focus on studying the influence of the propagation process on the wave structure of vortex beams before filamentation occurs. The three-dimensional particle-in-cell simulations show that weakly relativistic vortex beams exhibit wavefront distortion during their propagation in plasma. The distortion degree is closely related to the intensity of the electromagnetic wave and the propagation distance for a given plasma density. This phenomenon is theoretically explained by using a phase correction model that considers the relativistic mass correction of electrons. Additionally, we demonstrate that the wavefront distortion can be compensated for and suppressed by appropriately modulating the initial plasma density, as confirmed by three-dimensional particle simulations. The results of decomposing the wavefront into Laguerre-Gaussian (LG) mode components indicate that the wavefront distortion is primarily caused by high-order p LG modes, and it is independent of other l LG modes. Additionally, we extend the present investigation to the propagation of vortex beams in axially magnetized plasma, where the phase correction model can also effectively explain the occurrence of wavefront distortion. Our work can deepen the understanding of the interaction between plasma and strong vortex beams, and provide some valuable references for designing plasma devices serving as the manipulation of intense vortex beams in future research.
      通信作者: 贾青, qjia@ustc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11975014)和中国科学院战略性先导科技专项(批准号: XDA25050400, XDA25010200)资助的课题.
      Corresponding author: Jia Qing, qjia@ustc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11975014) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDA25050400, XDA25010200).
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  • 图 1  三维粒子模拟中, 在不同光强(a)—(d) $ a = 0.01 $, (e)—(h) $ a = 0.1 $, (i)—(l) $ a = 0.2 $下, 模式为$ l = 1,\; {\sigma_x} = 1 $的圆偏振涡旋光在等离子中传播至不同距离(a)(e)(i) $ x = 5\; {\text{μm}} $, (b)(f)(j) $ x = 10\; {\text{μm}} $, (c)(g)(k) $ x = 15\; {\text{μm}} $, (d)(h)(l) $ x = 20\; {\text{μm}} $处, 对应的电场$ E_y $分布

    Fig. 1.  Transverse distributions of electric fields $ E_y $ obtained by three-dimensional (3D) particle-in-cell (PIC) simulations for different laser intensities (a)–(d) $ a = 0.01 $, (e)–(h) $ a = 0.1 $, (i)–(l) $ a = 0.2 $, when a circularly polarized vortex light beam with $ l = 1,\; {\sigma_x} = 1 $ propagates in the plasma over different distances (a)(e)(i) $ x = 5\; {\text{μm}} $, (b)(f)(j) $ x = 10\; {\text{μm}} $, (c)(g)(k) $ x = 15\; {\text{μm}} $, (d)(h)(l) $ x = 20\; {\text{μm}} $

    图 2  在粒子模拟中, 强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $模式的圆偏振涡旋光在密度为$ {{n}_{{\mathrm{e}}}} = 0.56{{n}_{{\mathrm{c}}}} $的等离子体中传播时, 电场$ E_y $在沿传播方向上k空间的频谱分布

    Fig. 2.  Distribution of electric field $ E_y $ in k-space along the propagation direction obtained by 3D PIC simulations when a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagates in a plasma with a density of $ {n_{\mathrm{e}}} = 0.56 {n_{\mathrm{c}}} $

    图 3  基于相位修正模型, 考虑相对论电子质量修正效应时, 强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $模式的圆偏振涡旋光在等离子体中传播至不同距离处的电场$ E_y $分布 (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $

    Fig. 3.  Transverse distributions of electric fields $ E_y $ obtained by the phase-correction model taking into account the relativistic electron mass effect when a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagating in the plasma over different distances: (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $

    图 4  基于相位修正模型, 考虑激光有质动力效应时, 强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $模式的圆偏振涡旋光在等离子体中传播至不同距离处的电场$ E_y $分布 (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $

    Fig. 4.  Transverse distributions of electric fields $ E_y $ obtained by the phase-correction model considering the laser ponderomotive force effect when a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagating in the plasma over different distances: (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $

    图 5  在三维粒子模拟中, 强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $的圆偏振涡旋光在预设密度分布为$ n(r) = {n_{{\mathrm{ini}}}}\sqrt{1+{{{| \boldsymbol{E}|}^{2}}}/{2{{E}_{0}^{2}}}} $ ($ n_{{\mathrm{ini}}} = 0.56 {n_{\mathrm{c}}} $)的等离子体中传播至不同距离处, 电场$ E_y $分布 (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $

    Fig. 5.  Transverse distributions of electric fields $ E_y $ obtained by 3D PIC simulation when a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagating in a plasma with a predetermined density distribution of $ n(r) = {n_{{\mathrm{ini}}}}\sqrt{1+{{{| \boldsymbol{E}|}^{2}}}/{2{{E}_{0}^{2}}}} $ over different distances: (a) $ x = 5\; {\text{μm}} $; (b) $ x = 10\; {\text{μm}} $; (c) $ x = 15\; {\text{μm}} $; (d) $ x = 20\; {\text{μm}} $, where $ n_{{\mathrm{ini}}} = 0.56 {n_{\mathrm{c}}} $

    图 6  强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $的圆偏振涡旋光在等离子体中传播至$ x = 20\; {\text{μm}} $处, 对波前复振幅进行LG模式分解的结果 (a)不同l模式$ ({a}_{l} = \displaystyle\sum\nolimits_{p}{a}_{l, p}) $的能量占比分布; (b) $ l = 1 $的不同p模式的能量占比分布. 图中橙色表示与图1(l)对应的粒子模拟结果, 蓝色表示与图3(d)对应的理论结果

    Fig. 6.  The results of LG mode decomposition of wavefront for a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagating in a plasma to a distance of $ x = 20\; {\text{μm}} $: (a) Dstribution of $ {a}_{l} = \displaystyle\sum\nolimits_{p}{a}_{l, p} $; (b) distribution of different p modes for $ l = 1 $. The orange and blue colors in the figure indicate the results corresponding to Fig. 1(l) and Fig. 3(d), respectively

    图 7  在三维粒子模拟中, 强度为$ a/\sqrt{2} = 0.2 $的$ l = 1,\; p = 0 $的线偏振涡旋光在(a)—(d)均匀密度等离子体及(e)—(h)预设密度分布$ n(r) $等离子中传播至不同距离处的电场$ E_y $分布 (a)(e) $ x = 5\; {\text{μm}} $; (b)(f) $ x = 10\; {\text{μm}} $; (c)(g) $ x = 15\; {\text{μm}} $; (d)(h) $ x = 20\; {\text{μm}} $

    Fig. 7.  Transverse distributions of electric fields $ E_y $ obtained by 3D PIC simulations when a $ l = 1,\; p = 0 $ linearly polarized vortex light beam with $ a/\sqrt{2} = 0.2 $ propagating in (a)–(d) uniform plasmas and (e)–(h) plasmas with a predetermined density distribution $ n(r) $ over different distances: (a)(e) $ x = 5\; {\text{μm}} $; (b)(f) $ x = 10\; {\text{μm}} $; (c)(g) $ x = 15\; {\text{μm}} $; (d)(h) $ x = 20\; {\text{μm}} $

    图 8  在三维粒子模拟中, 强度为$ a = 0.2 $的$ l = 1,\; {\sigma_x} = 1 $的圆偏振涡旋光在(a)—(d)均匀轴向磁化等离子体及(e)—(h)预设密度及轴向磁化的等离子中传播至不同距离处的电场$ E_y $分布 (a)(e) $ x = 5\; {\text{μm}} $; (b)(f) $ x = 10\; {\text{μm}} $; (c)(g) $ x = 15\; {\text{μm}} $; (d)(h) $ x = 20\; {\text{μm}} $

    Fig. 8.  Transverse distributions of electric fields $ E_y $ obtained by 3D PIC simulations when a $ l = 1,\; {\sigma_x} = 1 $ circularly polarized vortex light beam with $ a = 0.2 $ propagating in (a)–(d) uniformly axially magnetized plasmas and (e)–(h) plasmas with a predetermined density and axial magnetization over different distances: (a)(e) $ x = 5\; {\text{μm}} $; (b)(f) $ x = 10\; {\text{μm}} $, (c)(g) $ x = 15\; {\text{μm}} $; (d)(h) $ x = 20\; {\text{μm}} $

    图 A1  三维粒子模拟中, 在不同密度(a)—(d) $ n_{\mathrm{e}} = 0.36 n_{\mathrm{c}} $, (e)—(h) $ n_{\mathrm{e}} = 0.56 n_{\mathrm{c}} $, (i)—(l) $ n_{\mathrm{e}} = 0.64 n_{\mathrm{c}} $下, 强度为$ a = 0.2 $, 模式为$ l = 1, {\sigma_x} = 1 $的圆偏振涡旋光在等离子中传播至不同距离(a)(e)(i) $ x = 5\; {\text{μm}} $, (b)(f)(j) $ x = 10\; {\text{μm}} $, (c)(g)(k) $ x = 15\; {\text{μm}} $, (d)(h)(l) $ x = 20\; {\text{μm}} $处, 对应的电场$ E_y $分布

    Fig. A1.  Transverse distributions of electric fields $ E_y $ obtained by 3D PIC simulations for different plasma densities (a)–(d) $ n_{\mathrm{e}} = 0.36 n_{\mathrm{c}} $, (e)–(h) $ n_{\mathrm{e}} = 0.56 n_{\mathrm{c}} $, (i)–(l) $ n_{\mathrm{e}} = 0.64 n_{\mathrm{c}} $, when a $ a = 0.2 $ circularly polarized vortex light beam with $ l = 1, {\sigma_x} = 1 $ propagates in the plasma over different distances (a)(e)(i) $ x = 5\; {\text{μm}} $, (b)(f)(j) $ x = 10\; {\text{μm}} $, (c)(g)(k) $ x = 15\; {\text{μm}} $, (d)(h)(l) $ x = 20\; {\text{μm}} $

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    Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185Google Scholar

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    He H, Friese M E J, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826Google Scholar

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    Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y, Yue Y, Dolinar S, Tur M, Willner A E 2012 Nat. Photonics 6 488Google Scholar

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    Bozinovic N, Yue Y, Ren Y, Tur M, Kristensen P, Huang H, Willner A E, Ramachandran S 2013 Science 340 1545Google Scholar

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    Tamburini F, Anzolin G, Umbriaco G, Bianchini A, Barbieri C 2006 Phys. Rev. Lett. 97 163903Google Scholar

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    Harwit M 2003 The Astrophysical Journal 597 1266Google Scholar

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    Tamburini F, Thidé B, Molina-Terriza G, Anzolin G 2011 Nat. Phys. 7 195Google Scholar

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    Tamburini F, Thidé B, Della Valle M 2019 Mon. Not. R. Astron. Soc. 492 L22

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    Shi Y, Shen B, Zhang L, Zhang X, Wang W, Xu Z 2014 Phys. Rev. Lett. 112 235001Google Scholar

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    Vieira J, Trines R M G M, Alves E P, Fonseca R A, Mendonca J T, Bingham R, Norreys P, Silva L O 2016 Nat. Commun. 7 10371Google Scholar

    [12]

    Leblanc A, Denoeud A, Chopineau L, Mennerat G, Martin P, Quéré F 2017 Nat. Phys. 13 440Google Scholar

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    Qu K, Jia Q, Fisch N J 2017 Phys. Rev. E 96 053207Google Scholar

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    Shi Y, Blackman D, Stutman D, Arefiev A 2021 Phys. Rev. Lett. 126 234801Google Scholar

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    Vieira J, Mendonca J T 2014 Phys. Rev. Lett. 112 215001Google Scholar

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    Brabetz C, Busold S, Cowan T, Deppert O, Jahn D, Kester O, Roth M, Schumacher D, Bagnoud V 2015 Phys. Plasmas 22 013105Google Scholar

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    Willim C, Vieira J, Malka V, Silva L O 2023 Phys. Rev. Res. 5 023083Google Scholar

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    Zhang X, Shen B, Shi Y, Wang X, Zhang L, Wang W, Xu J, Yi L, Xu Z 2015 Phys. Rev. Lett. 114 173901Google Scholar

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    Denoeud A, Chopineau L, Leblanc A, Quéré F 2017 Phys. Rev. Lett. 118 033902Google Scholar

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    Shi Y, Vieira J, Trines R M G M, Bingham R, Shen B F, Kingham R J 2018 Phys. Rev. Lett. 121 145002Google Scholar

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    Longman A, Fedosejevs R 2021 Phys. Rev. Res. 3 043180Google Scholar

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    Liu W, Jia Q, Zheng J 2023 Matter Radiat. Extremes 8 014405Google Scholar

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    Wang W P, Jiang C, Shen B F, Yuan F, Gan Z M, Zhang H, Zhai S H, Xu Z Z 2019 Phys. Rev. Lett. 122 024801Google Scholar

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    Baumann C, Pukhov A 2018 Phys. Plasmas 25 083114Google Scholar

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    Mendonca J T, Thidé B, Then H 2009 Phys. Rev. Lett. 102 185005Google Scholar

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    Nuter R, Korneev P, Tikhonchuk V T 2022 Phys. Plasmas 29 062101Google Scholar

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    Arber T D, Bennett K, Brady C S, Lawrence-Douglas A, Ramsay M G, Sircombe N J, Gillies P, Evans R G, Schmitz H, Bell A R, Ridgers C P 2015 Plasma Phys. Control. Fusion 57 113001Google Scholar

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    盛政明 2014 强场激光物理研究前沿(上海: 上海交通大学出版社) 第21页

    Sheng Z M 2014 Advances in High Field Laser Physics (Shanghai: Shanghai Jiao Tong University Press) pp21

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  • 被引次数: 0
出版历程
  • 收稿日期:  2023-10-11
  • 修回日期:  2023-11-02
  • 上网日期:  2023-11-29
  • 刊出日期:  2024-03-05

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