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Elliptically polarized attosecond pulse has significant applications in studying the ultrafast chiral dynamics and X-ray magnetic circular dichroism (XMCD) due to its ultrashort time-scale (attosecond) and elliptical polarization characteristics. In this work, the interaction between the non-uniform linearly polarized laser field and the Ne atoms is simulated by numerically solving the time-dependent Schrödinger equation. Specifically, the influences of the non-uniformity of the driving field and the orbital angular momentum (OAM) of the initial orbital on high-order harmonics (HHs) and attosecond pulses are revealed. HHs generated by the linearly polarized laser fields with different non-uniformities are calculated. The results indicate that the non-uniformity significantly influences the smoothness and spectral broadening of the harmonic spectra, consequently affecting the properties of the attosecond pulses. Moreover, our findings also reveal that the OAM of the initial orbital plays a significant role in the polarization state of the attosecond pulses. When the OAM is zero (e.g., 1s orbital), the radiated attosecond pulses are linearly polarized, whereas non-zero OAM (e.g., current carrying state 2p– orbital) leads to elliptically polarized emission. This study provides a theoretical foundation for generating and controlling elliptically polarized isolated attosecond pulses by using non-uniform linearly polarized laser fields, and offers new possibilities for ultrafast spectroscopy and magnetic material characterization.
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Keywords:
- high order harmonic /
- elliptically polarized isolated attosecond pulse /
- current carrying state /
- non-unifom laser field
[1] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
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[38] 罗江华 2014 博士学位论文(武汉: 华中科技大学)
Luo J H 2014 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology
[39] Zhang X F, Zhu X S, Liu X, Wang D, Zhang Q B, Lan P F, Lu P X 2017 Opt. Lett. 42 1027
Google Scholar
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图 1 (a) 1s轨道概率密度空间分布图; (b) 1s轨道相位空间分布图; (c) 2p–轨道概率密度空间分布图; (d) 2p–轨道相位空间分布图
Figure 1. (a) Probability density space distribution graph of the 1s orbital; (b) phase space distribution diagram of the 1s orbital; (c) probability density space distribution graph of the 2p– orbital; (d) phase space distribution diagram of the 2p– orbital.
图 2 不同$ \kappa $值驱动场下1s轨道和2p–轨道产生的高次谐波谱 (a) $ \kappa $ = 0, 1s轨道; (b) $ \kappa $ = 0.001, 1s轨道; (c) $ \kappa $ = 0.002, 1s轨道; (d) $ \kappa $ = 0.003, 1s轨道; (e) $ \kappa $ = 0, 2p–轨道; (f) $ \kappa $ = 0.001, 2p–轨道; (g) $ \kappa $ = 0.002, 2p–轨道; (h) $ \kappa $ = 0.003, 2p–轨道 (蓝色实线和红色虚线分别表示高次谐波的右、左旋分量)
Figure 2. High-order harmonic spectra generated by 1s and 2p– orbitals under different $ \kappa $ value of driving fields: (a) $ \kappa $ = 0, 1s orbital; (b) $ \kappa $ = 0.001, 1s orbital; (c) $ \kappa $ = 0.002, 1s orbital; (d) $ \kappa $ = 0.003, 1s orbital; (e) $ \kappa $ = 0, 2p– orbital; (f) $ \kappa $ = 0.001, 2p– orbital; (g) $ \kappa $ = 0.002, 2p– orbital; (h) $ \kappa $ = 0.003, 2p– orbital (Blue solid line and the red dashed line, respectively, represent the left- and right-handed circular components of the higher-order harmonics).
图 3 高次谐波的时频分析图 (a) $ \kappa $ = 0, 1s轨道; (b) $ \kappa $ = 0.001, 1s轨道; (c) $ \kappa $ = 0.002, 1s轨道; (d) $ \kappa $ = 0.003, 1s轨道; (e) $ \kappa $ = 0, 2p–轨道; (f) $ \kappa $ = 0.001, 2p–轨道; (g) $ \kappa $ = 0.002, 2p–轨道; (h) $ \kappa $ = 0.003, 2p–轨道
Figure 3. Time-frequency analysis diagram of high-order harmonics: (a) $ \kappa $ = 0, 1s orbital; (b) $ \kappa $ = 0.001, 1s orbital; (c) $ \kappa $ = 0.002, 1s orbital; (d) $ \kappa $ = 0.003, 1s orbital; (e) $ \kappa $ = 0, 2p– orbital; (f) $ \kappa $ = 0.001, 2p– orbital; (g) $ \kappa $ = 0.002, 2p– orbital; (h) $ \kappa $ = 0.003, 2p– orbital.
图 4 高次谐波椭偏率 (a) $ \kappa $ = 0, 1s轨道; (b) $ \kappa $ = 0.001, 1s轨道; (c) $ \kappa $ = 0.002, 1s轨道; (d) $ \kappa $ = 0.003, 1s轨道; (e) $ \kappa $ = 0, 2p–轨道; (f) $ \kappa $ = 0.001, 2p–轨道; (g) $ \kappa $ = 0.002, 2p–轨道; (h) $ \kappa $ = 0.003, 2p–轨道
Figure 4. Ellipticity of high harmonics: (a) $ \kappa $ = 0, 1s orbital; (b) $ \kappa $ = 0.001, 1s orbital; (c) $ \kappa $ = 0.002, 1s orbital; (d) $ \kappa $ = 0.003, 1s orbital; (e) $ \kappa $ = 0, 2p– orbital; (f) $ \kappa $ = 0.001, 2p– orbital; (g) $ \kappa $ = 0.002, 2p– orbital; (h) $ \kappa $ = 0.003, 2p– orbital.
图 5 高次谐波的时频分析图 (a) $ \kappa $ = 0.001, 1s轨道x分量; (b) $ \kappa $ = 0.001, 2p–轨道x分量; (c) $ \kappa $ = 0.001, 1s轨道y分量; (d) $ \kappa $ = 0.001, 2p–轨道y分量
Figure 5. Time-frequency analysis diagram of high-order harmonics: (a) $ \kappa $ = 0.001, x component of 1s orbital; (b) $ \kappa $ = 0.001, x component of 2p– orbital; (c) $ \kappa $ = 0.001, y component of 1s orbital; (d) $ \kappa $ = 0.001, y component of 2p– orbital.
图 6 阿秒脉冲时域包络 (a) $ \kappa $ = 0, 1s轨道; (b) $ \kappa $ = 0.001, 1s轨道; (c) $ \kappa $ = 0.002, 1s轨道; (d) $ \kappa $ = 0.003, 1s轨道; (e) $ \kappa $ = 0, 2p–轨道; (f) $ \kappa $ = 0.001, 2p–轨道; (g) $ \kappa $ = 0.002, 2p–轨道; (h) $ \kappa $ = 0.003, 2p–轨道
Figure 6. Time-domain envelope of attosecond pulses: (a) $ \kappa $ = 0, 1s orbital; (b) $ \kappa $ = 0.001, 1s orbital; (c) $ \kappa $ = 0.002, 1s orbital; (d) $ \kappa $ = 0.003, 1s orbital; (e) $ \kappa $ = 0, 2p– orbital; (f) $ \kappa $ = 0.001, 2p– orbital; (g) $ \kappa $ = 0.002, 2p– orbital; (h) $ \kappa $ = 0.003, 2p– orbital
图 7 阿秒脉冲时域电场形式 (a) $ \kappa $ = 0, 1s轨道; (b) $ \kappa $ = 0.001, 1s轨道; (c) $ \kappa $ = 0.002, 1s轨道; (d) $ \kappa $ = 0.003, 1s轨道; (e) $ \kappa $ = 0, 2p–轨道; (f) $ \kappa $ = 0.001, 2p–轨道; (g) $ \kappa $ = 0.002, 2p–轨道; (h) $ \kappa $ = 0.003, 2p–轨道
Figure 7. Time-domain electric field forms of attosecond pulses: (a) $ \kappa $ = 0, 1s orbital; (b) $ \kappa $ = 0.001, 1s orbital; (c) $ \kappa $ = 0.002, 1s orbital; (d) $ \kappa $ = 0.003, 1s orbital; (e) $ \kappa $ = 0, 2p– orbital; (f) $ \kappa $ = 0.001, 2p– orbital; (g) $ \kappa $ = 0.002, 2p– orbital; (h) $ \kappa $ = 0.003, 2p– orbital.
图 8 (a)—(c) 2p-轨道高次谐波截止区能量、合成的阿秒脉冲脉宽以及椭偏率随驱动激光场波长的变化; (d)—(f) 驱动激光场光周期为$ {2 T}_{0} $时的高次谐波谱、合成的阿秒脉冲以及时域电场(红色实线表示光周期为$ {3 T}_{0} $的结果), 合成的高次谐波谱段均为35阶—50阶. 其余参数与图2(h)相同
Figure 8. (a)–(c) Cut-off energy of high harmonic spectra of the 2p- orbital, pulse duration and ellipticity versus the wavelength; (d)–(f) the high harmonic spectra, attosecond pulses and time-domain electric field for the driving field with $ {2 T}_{0} $ (The red solid lines represent the results for the driving field with $ {3 T}_{0} $). The attosecond pulses synthesized by the harmonics of 35th–40th. Other parameters are the same as those in Fig. 2(h).
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[1] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
Google Scholar
[2] Paul P M, Toma E S, Breger P, Mullot G, Augé F, Balcou Ph, Muller H G, Agostini P 2001 Science 292 1689
Google Scholar
[3] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F, Wörner H J 2017 Opt. Express 25 27506
Google Scholar
[4] Sansone G, Benedetti E, Calegari F, et al. 2006 Science 314 443
Google Scholar
[5] Seres J, Yakovlev S V, Seres E, Streli CH, Wobrauschek P, Spielmann C H, Krausz F 2007 Nat. Phys. 3 878
Google Scholar
[6] Goulielmakis E, Schultze M, Hofstetter M 2008 Science 320 1614
Google Scholar
[7] Mairesse Y, Bohan D A, Frasinski J K, et al. 2003 Science 302 1540
Google Scholar
[8] Li J, Ren X, Yin Y, et al. 2017 Nat. Commun. 8 186
[9] Kukk E, Myllynen H, Nagaya K, et al. 2019 Phys. Rev. A 99 023411
Google Scholar
[10] Mairesse Y, Higuet J, Dudovich N, et al. 2010 Phys. Rev. Lett. 104 229901
Google Scholar
[11] Chen Z J, Wang Y, Morishita T 2019 Phys. Rev. A 100 023405
Google Scholar
[12] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[13] Ferré A, Handschin C, Dumergue M, et al. 2015 Nat. Photonics 9 93
[14] Kfir O, Grychto P, Turgut E, et al. 2015 Nat. Photonics 9 99
[15] Sinev I, Richter U F, Toftul I, Glebov N, Koshelev K, Hwang Y, Lancaster G D, Kivshar Y, Altug H 2025 Nat. Commun. 16 6091
Google Scholar
[16] Valev K V, Engheta N, Pendry B J 2023 Adv. Mater. 35 e2306073
Google Scholar
[17] Shao R, Zhai C, Zhang Y, Sun N, Cao W, Lan P, Lu P 2020 Opt. Express 28 15874
Google Scholar
[18] Lambert G, Vodungbo B, Gautier J, et al. 2015 Nat. Commun. 6 6167
Google Scholar
[19] Yuan J K, Bandrauk D A 2013 Phys. Rev. Lett. 110 023003
Google Scholar
[20] Fleischer A, Kfir O, Diskin T, Sidorenko P, Cohen O 2014 Nat. Photonics 8 543
[21] Medišauskas L, Wragg J, van der Hart H, Yu. Ivanov M 2015 Phys. Rev. Lett. 115 153001
Google Scholar
[22] Zhou X, Lock R, Wagner N, Li W, Kapteyn C H, Murnane M M 2009 Phys. Rev. Lett. 102 073902
Google Scholar
[23] Niikura H, Dudovich N, Villeneuve M D, Corkum B P 2010 Phys Rev. Lett. 105 053003
Google Scholar
[24] Xie X, Scrinzi A, Wickenhauser M, Baltuška A, Barth I, Kitzler M 2008 Phys. Rev. Lett. 101 033901
Google Scholar
[25] Weber A, Böning B, Minneker B, Fritzsche S 2021 Phys. Rev. A 104 063118
Google Scholar
[26] Liu X, Zhu X, Li L, Li Y, Zhang Q, Lan P, Lu P 2016 Phys. Rev. A 94 033410
Google Scholar
[27] Miloševic B D 2015 Phys. Rev. A 92 043827
Google Scholar
[28] Mauger F, Bandrauk D A, Uzer T 2016 J. Phys. B 49 10LT01
Google Scholar
[29] Hickstein D D, Dollar J F, Grychtol P, et al. 2015 Nat. Photonics 9 743
Google Scholar
[30] Dorney M K, Ellis L J, Hernández-García C, et al. 2017 Phys. Rev. Lett. 119 063201
Google Scholar
[31] Zhang X, Li L, Zhu X, Liu K, Liu X, Wang D, Lan P, Barth I, Lu P 2018 Phys. Rev. A 98 023418
Google Scholar
[32] Le A T, Lucchese R R, Lin C D 2010 Phys. Rev. A 82 023814
Google Scholar
[33] Zhang X F, Zhu X S, Liu X, Wang F, Qin M Y, Liao Q, Lu P X 2020 Phys. Rev. A 102 033103
Google Scholar
[34] Ou T, Wang F, Yuan H, Yang C, Song J, Liao Q 2025 Opt. Commun. 574 131183
Google Scholar
[35] Mandal A, Singh P K 2023 Laser Phys. 33 015301
Google Scholar
[36] Ammosov M V, Delone N B, Krainov V P 1986 Sov. Phys. JETP 64 1191
[37] Ding Y, Wang K, Zhang X 2025 Opt. Laser Technol. 184 112561
Google Scholar
[38] 罗江华 2014 博士学位论文(武汉: 华中科技大学)
Luo J H 2014 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology
[39] Zhang X F, Zhu X S, Liu X, Wang D, Zhang Q B, Lan P F, Lu P X 2017 Opt. Lett. 42 1027
Google Scholar
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