Theoretical study of high-order harmonics and single ultrashort attosecond pulse generated by optimized combination of laser field

Han Lin; Miao Shu-Li; Li Peng-Cheng

doi:10.7498/aps.71.20221298

Abstract

High-order harmonic generation, which is a hot topic of strong ultrafast fields, is one of the most important ways for obtaining the ultraviolet attosecond sources, and has a very wide application prospect. This work focuses on the challenges of the generation of either short or high attosecond pulses. We present the research progress of the high-order harmonics and attosecond pulse generation, and propose an effective and feasible method, and show some results. Specifically, combining the time-dependent Schrödinger equation and new unconstrained optimization algorithm, the objective function with the aim of the widest supercontinuum plateau of He atom is designed and the optimized two-color and three-color laser fields are obtained. The supercontinuum spectra extend up to 100 harmonic orders for the case of the optimized two-color laser field. As a result, a single ultrashort attosecond pulse of 25 as is produced. For the three-color case, the supercontinuum spectra reach up to 170 harmonic orders, and the width of single shortest attosecond pulse obtained by superposing pulses from low order (110 order) to high order (280 order) is obtained to be 17 as . Taking the optimized two-color laser field for example, the macroscopic medium propagation is discussed by solving the Maxwell equation. The results show that the selectivity of quantum trajectories from far-field space distribution can obtain the single ultra-short attosecond pulse.

Keywords:

Authors and contacts

1.
Research Center for Advanced Optics and Photoelectronics, Department of Physics, College of Science, Shantou University, Shantou 515063, China
2.
Key Laboratory of Theoretical Physics of Gansu Province, Theoretical Physics Center of Lanzhou, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

Corresponding author: Li Peng-Cheng, pchli@stu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 91850209, 12074239, 12047501), the Natural Science Foundation of Guangdong Province, China (Grant No. 2020A1515010927), the Science and Technology Project of Guangdong Province, China (Grant No. 2020ST084), the Special Innovation Program of Universities of Guangdong Province (Grant Nos. 2019KTSCX038, 2020KCXTD012), and the Shantou University, China (Grant No. NTF18030)

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References

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Cited By

图 1 (a) 优化前和优化后的双色组合激光场; (b)优化前和优化后的双色组合激光场驱动He原子产生的高次谐波谱

Figure 1. (a) Initial laser field and the optimized two-color laser field; (b) corresponding HHG power spectra

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图 2 (a) 优化前高次谐波时频分析图; (b)优化后高次谐波时频分析图

Figure 2. Wavelet time-frequency of the HHG spectra for the cases of (a) initial and (b) optimized two-color laser fields

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图 3 (a) 优化后给定阶次高次谐波强度随时间变化关系; (b)对比优化前后单个阿秒脉冲的产生

Figure 3. (a) Dipole time profiles of harmonics from the 70th to the 170th harmonic order; (b) attosecond pulse generation for the cases of the initial and optimized two-color laser fields

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图 4 (a) 优化前和优化后的三色组合激光场; (b)优化前和优化后的三色组合激光场驱动He原子产生的高次谐波谱

Figure 4. (a) Initial laser field and the optimized three-color laser field; (b) corresponding HHG power spectra

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图 5 (a) 优化前高次谐波时频分析图; (b)优化后高次谐波时频分析图

Figure 5. Wavelet time-frequency of the HHG spectra for the cases of (a) initial and (b) optimized three-color laser fields

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图 6 (a) 优化后给定阶次高次谐波强度随时间变化关系; (b)优化前后单个阿秒脉冲的产生

Figure 6. (a) Dipole time profiles of harmonics from the 110th to the 200th harmonic order; (b) attosecond pulse generation for the cases of the initial and optimized three-color laser fields

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图 7 优化的宏观双色组合激光场空间传播效应　(a)演化前激光场; (b)演化后激光场; (c)轴上演化前和演化后激光场对比; (d)驱动单原子激光场与宏观演化后轴上激光场对比

Figure 7. Macroscopic propagation effects of the optimized two-color laser fields: (a) Entrance; (b) exit; (c) comparison of entrance and exit on axis; (d) comparison of the fields for single-atom case and mac-field on axis

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图 8 (a) 远场高次谐波空间分布; (b)单原子与远场高次谐波对比; (c)远场阿秒脉冲空间分布

Figure 8. (a) Spatial distribution of far-field HHG; (b) comparison of single atom and far-field HHG; (c) spatial distribution of far-field attosecond pulse.

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图 9 (a) 轴上高次谐波时频分析; (b)轴外0.37 mm处高次谐波时频分析; (c)轴上与轴外0.37 mm处获得的单个最短阿秒脉冲

Figure 9. (a) Wavelet time-frequency of the HHG spectra on axis; (b) wavelet time-frequency of the HHG spectra at 0.37 mm off axis; (c) on-axis and off-axis attosecond pulse generation

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图 10 轴上不同气体靶位置产生的单个阿秒脉冲对比

Figure 10. Comparison of single attosecond pulse for the different target position

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表 1 He原子模型势参数(原子单位制)^[65]

Table 1. Model potential parameters for He (in a.u.)^[65]

$ l $	$ \alpha $	$r_{\rm{c}}$	S	$ A_1 $	$ A_2 $	$ B_1 $	$ B_2 $
$ 0 $	$ 0.28125 $	$ 2.0 $	$ -7.9093912 $	$ -10.899664 $	0	$ 1.7 $	$ 3.8 $
$ 1 $	$ 0.28125 $	$ 2.0 $	$ 1.50094970 $	$ 0.11297684 $	0	$ 1.3 $	$ 3.8 $
$ 2 $	$ 0.28125 $	$ 2.0 $	$ 0.88294766 $	$ -0.032043029 $	0	$ 1.3 $	$ 3.8 $
$ 3 $	$ 0.28125 $	$ 2.0 $	$ 0.41193110 $	$ -0.129391180 $	0	$ 1.3 $	$ 3.8 $
$ \geqslant 3 $	$ 0.28125 $	$ 2.0 $	$0$	$0$	0	$ 1.3 $	$ 0 $

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[1]	Telnov D A, Chu S I 2009 Phys. Rev. A 79 041401 Google Scholar
[2]	Garcia Ruiz R F, Vernon A R, Binnersley C L, Sahoo B K, Bissell M, Billowes J, Cocolios T E, Gins W, de Groote R P, Flanagan K T, Koszorus A, Lynch K M, Neyens G, Ricketts C M, Wendt K D A, Wilkins S G, Yang X F 2018 Phys. Rev. X 8 041005
[3]	Wang R, Zhang Q, Li D, Xu S, Cao P, Zhou Y, Cao W, Lu P 2019 Opt. Express 27 6471 Google Scholar
[4]	Ge P, Fang Y, Guo Z, Ma X, Yu X, Han M, Wu C, Gong Q, Liu Y 2021 Phys. Rev. Lett. 126 223001 Google Scholar
[5]	De Silva A H N C, Atri-Schuller D, Dubey S, Acharya B P, Romans K L, Foster K, Russ O, Compton K, Rischbieter C, Douguet N, Bartschat K, Fischer D 2021 Phys. Rev. Lett. 126 023201 Google Scholar
[6]	Liu M M, Shao Y, Han M, Ge P, Deng Y, Wu C, Gong Q, Liu Y 2018 Phys. Rev. Lett. 120 043201 Google Scholar
[7]	Li W K, Lei Y, Li X, Yang T, Du M, Jiang Y, Li J L, Luo S Z, Liu A H, He L H, Ma P, Zhang D D, Ding D J 2021 Chin. Phys. Lett. 38 053202 Google Scholar
[8]	Kelvich S A, Becker W, Goreslavski S P 2017 Phys. Rev. A 96 023427 Google Scholar
[9]	Brennecke S, Lein M 2018 Phys. Rev. A 98 063414 Google Scholar
[10]	Brennecke S, Lein M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 094005 Google Scholar
[11]	Shi M, Lai X, Yu S, Wang Y, Quan W, Liu X 2022 Phys. Rev. A 105 013118 Google Scholar
[12]	Yang Q, Leng J, Wang Y H, Sun Y N, Du H B, Zhang D D, Song L L, He L H, Liu F C 2022 Chin. Phys. Lett. 39 023301 Google Scholar
[13]	Verhoef A J, Mitrofanov A V, Serebryannikov E E, Kartashov D V, Zheltikov A M, Baltuška A 2010 Phys. Rev. Lett. 104 163904 Google Scholar
[14]	Chen Y, Zhou Y, Tan J, Li M, Cao W, Lu P 2021 Phys. Rev. A 104 043107 Google Scholar
[15]	Ni H, Brennecke S, Gao X, He P L, Donsa S, Březinová I, He F, Wu J, Lein M, Tong X M, Burgdörfer J 2020 Phys. Rev. Lett. 125 073202 Google Scholar
[16]	Tan J, Zhou Y, He M, Ke Q, Liang J, Li Y, Li M, Lu P 2019 Phys. Rev. A 99 033402 Google Scholar
[17]	Luo S, Li M, Xie W, Liu K, Feng Y, Du B, Zhou Y, Lu P 2019 Phys. Rev. A 99 053422 Google Scholar
[18]	Zhao Y, Zhou Y, Liang J, Zeng Z, Ke Q, Liu Y, Li M, Lu P 2019 Opt. Express 27 21689 Google Scholar
[19]	Douguet N, Bartschat K 2018 Phys. Rev. A 97 013402 Google Scholar
[20]	Yoshikawa N, Tamaya T 2017 Science 356 736 Google Scholar
[21]	Ghimire S, DiChiara A D, Sistrunk E, Agostini P, DiMauro L F, Reis D A 2011 Nat. Phys. 7 138 Google Scholar
[22]	Uchida K, Mattoni G, Yonezawa S, Nakamura F, Maeno Y, Tanaka K 2020 Phys. Rev. Lett. 128 127401 Google Scholar
[23]	Yu C, Jiang S, Lu R 2019 Adv. Phys. X 4 1562982
[24]	Zhang J, Hua L Q, Chen Zh, Zhu M F, Gong Ch, Liu X J 2020 Chin. Phys. Lett. 37 124203 Google Scholar
[25]	Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163 Google Scholar
[26]	McPherson A, Gibson G, Jara H, Johann U, Luk T S, McIntyre I A, Boyer K, Rhodes C K 1987 J. Opt. Soc. Am. B 4 595 Google Scholar
[27]	Ferray M, L’Huillier A, Li X F, Lompre L A, Mainfray G, Manus C 1988 J. Phys. B: At. Mol. Opt. Phys. 21 3
[28]	L’Huillier A, Balcou Ph 1993 Phys. Rev. Lett. 70 766 Google Scholar
[29]	Macklin J J, Kmetec J D, Gordon Ⅲ C L 1993 Phys. Rev. Lett. 70 774 Google Scholar
[30]	L’Huillier A, Schafer K J, Kulander K C 1991 J. Phys. B: At. Mol. Opt. Phys. 24 3315 Google Scholar
[31]	Corkum P B 1993 Phys. Rev. Lett. 71 13
[32]	Kulander K C, Schafer K J, Krause J L 1991 Phys. Rev. Lett. 66 2601 Google Scholar
[33]	Lewenstein M, Balcou Ph, Ivanov M Yu, L’Huillier A, Corkum P B 1994 Phys. Rev. A 49 2117 Google Scholar
[34]	L’Huillier A, Lewenstein M, Saliěres P, Balcou Ph, Ivanov M Yu, Larsson J, Wahlström C G 1993 Phys. Rev. A 4 8
[35]	Kulander K C 1988 Phys. Rev. A 38 778 Google Scholar
[36]	Krause J L, Schafer K J, Kulander K C 1992 Phys. Rev. A 45 4998 Google Scholar
[37]	Runge E, Gross E K U 1984 Phys. Rev. Lett. 52 997 Google Scholar
[38]	魏志义, 钟诗阳, 贺新奎, 赵昆, 滕浩, 王帅, 梁玥瑛, 王佶, 喻苏玉, 陈云琳, 朱江峰 2021 中国激光 48 0501001 Google Scholar Wei Z Y, Zhong S Y, He X K, Zhao K, Teng H, Wang S, Liang Y Y, Wang J, Yu S Y, Chen Y L, Zhu J F 2021 Chin. J. Lasers 48 0501001 Google Scholar
[39]	Spielmann C, Burnett N H, Sartania S, Koppitsch R, Schnurer M, Kan C, Lenzner M, Wobrauschek P, Krausz F 1997 Science 278 661 Google Scholar
[40]	Chang Z, Rundquist A, Wang H, Murnane M M, Kapteyn H C 1997 Phys. Rev. Lett. 79 2967 Google Scholar
[41]	Tong X M, Chu S I 2001 Phys. Rev. A 64 013417 Google Scholar
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[43]	Baltuska A, Fuji T, Kobayashi T 2002 Phys. Rev. Lett. 88 133901 Google Scholar
[44]	Gibson E A, Paul A, Wagner N, Tobey R, Backus S, Christov I P, Murnane M M, Kapteyn H C 2004 Phys. Rev. Lett. 92 033001 Google Scholar
[45]	Schiessl K, Ishikawa K L, Persson E, Burgdorfer J 2007 Phys. Rev. Lett. 99 253903 Google Scholar
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