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Chirp waveform control to produce broad harmonic plateau and single attosecond pulse

  • Hang Liu , Cui-Yan Xu , Xiao-Dan Jing , Yan Qiao and Li-Qiang Feng EMAIL logo
Published/Copyright: June 25, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 9

Abstract

Waveform control of three kinds of chirped pulses (i.e. βt, βt 2 and βt 3) to produce harmonic spectra and attosecond pulses has been investigated. It is found that by properly choosing the chirps, the chirp delays and the other laser parameters, not only the instantaneous frequency of some specific half profiles can be decreased, but also its intensity can be increased. As a result, the free electron can receive more energy when it accelerates in these regions, thus leading to the extension of the harmonic cutoff and harmonic plateau. Finally, through the Fourier transformation of the harmonic spectra and by superposing some harmonics, three single attosecond pulses with the durations of 30 as, 33 as and 39 as can be obtained.

Keywords: chirp waveform control; chirped pulses; high-order harmonic generation; single attosecond pulse
PACS Nos: 42.65.Re; 42.65.Ky; 32.80.Fb
Corresponding author: Li-Qiang Feng, Laboratory of Molecular Reaction Dynamics, Liaoning University of Technology, Jinzhou, 121001, China, E-mail:

Funding source: Natural Science Foundation of Liaoning Province

Award Identifier / Grant number: 2019-MS-167

Funding source: Basic Research Project of Liaoning Provincial Education Department

Award Identifier / Grant number: JJL201915405

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work was supported by Natural Science Foundation of Liaoning Province, China (Grant No. 2019-MS-167) and Basic Research Project of Liaoning Provincial Education Department (Grant No. JJL201915405).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature, vol. 466, p. 604, 2010. https://doi.org/10.1038/nature09185.Search in Google Scholar PubMed

[2] P. M. Kraus, B. Mignolet, D. Baykusheva, et al.., “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science, vol. 350, p. 790, 2015. https://doi.org/10.1126/science.aab2160.Search in Google Scholar PubMed

[3] L. He, Q. Zhang, P. Lan, et al.., “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun., vol. 9, p. 1108, 2018. https://doi.org/10.1038/s41467-018-03568-3.Search in Google Scholar PubMed PubMed Central

[4] D. A. Telnov and S. I. Chu, “Effects of multiple electronic shells on strong-field multiphoton ionization and high-order harmonic generation of diatomic molecules with arbitrary orientation: An all-electron time-dependent density-functional approach,” Phys. Rev. A, vol. 80, p. 043412, 2009. https://doi.org/10.1103/physreva.80.043412.Search in Google Scholar

[5] C. Yu, S. Jiang, and R. Lu, “High order harmonic generation in solids: a review on recent numerical methods,” Adv. Phys. X, vol. 4, p. 1562982, 2019. https://doi.org/10.1080/23746149.2018.1562982.Search in Google Scholar

[6] Y.-T. Zhao, S.-y. Ma, S.-C. Jiang, Y.-J. Yang, X. Zhao, and J.-G. Chen, “All-optical reconstruction of k-dependent transition dipole moment by solid harmonic spectra from ultrashort laser pulses,” Opt. Express, vol. 27, p. 34392, 2019. https://doi.org/10.1364/oe.27.034392.Search in Google Scholar PubMed

[7] Y.-T. Zhao, S.-C. Jiang, X. Zhao, J.-G. Chen, and Y.-J. Yang, “Effect of interband polarization on a solid’s high-order-harmonic generation just below the band gap,” Opt. Lett., vol. 45, p. 2874, 2020. https://doi.org/10.1364/ol.389787.Search in Google Scholar PubMed

[8] Y. T. Zhao, X. Q. Xu, S. C. Jiang, X. Zhao, J. G. Chen, and Y. J. Yang, “Cooper minimum of high-order harmonic spectra from an MgO crystal in an ultrashort laser pulse,” Phys. Rev. A, vol. 101, p. 033413, 2020. https://doi.org/10.1103/physreva.101.033413.Search in Google Scholar

[9] J. G. Chen, R. Q. Wang, Z. Zhai, et al., “Frequency-selected enhancement of high-order-harmonic generation by interference of degenerate Rydberg states in a few-cycle laser pulse,” Phys. Rev. A, vol. 86, p. 033417, 2012. https://doi.org/10.1103/physreva.86.033417.Search in Google Scholar

[10] F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys., vol. 81, p. 163, 2009. https://doi.org/10.1103/revmodphys.81.163.Search in Google Scholar

[11] G.-T. Zhang, “Intense isolated ultrashort attosecond pulse generation in a multi-cycle three-colour laser field,” Z. Naturforsch., A: Phys. Sci., vol. 69, p. 673, 2014. https://doi.org/10.5560/zna.2014-0067.Search in Google Scholar

[12] H. Liu and A. Y. Feng, “Selection and enhancement of the single harmonic emission event in the water window region,” Z. Naturforsch., A: Phys. Sci., vol. 73, p. 985, 2018. https://doi.org/10.1515/zna-2018-0253.Search in Google Scholar

[13] K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett., vol. 110, p. 023003, 2013. https://doi.org/10.1103/physrevlett.110.023003.Search in Google Scholar

[14] L.-Q. Feng, Y. Qiao, and L. Li, “Internuclear distance dependent on a single-order harmonic enhancement of hydrogen molecular ion,” Spectrosc. Lett., vol. 54, p. 80, 2021. https://doi.org/10.1080/00387010.2020.1850479.Search in Google Scholar

[15] L. Feng, J. Mccain, and Y. Qiao, “Half-cycle waveform control for producing a broad and intense harmonic spectral continuum and an isolated attosecond pulse,” Laser Phys., vol. 31, p. 055301, 2021. https://doi.org/10.1088/1555-6611/abf241.Search in Google Scholar

[16] P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett., vol. 71, p. 1994, 1993. https://doi.org/10.1103/physrevlett.71.1994.Search in Google Scholar PubMed

[17] S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature, vol. 453, p. 757, 2008. https://doi.org/10.1038/nature07012.Search in Google Scholar PubMed

[18] L. Q. Feng, “Molecular harmonic extension and enhancement from H2+ ions in the presence of spatially inhomogeneous fields,” Phys. Rev. A, vol. 92, p. 053832, 2015. https://doi.org/10.1103/physreve.92.023011.Search in Google Scholar

[19] M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, et al.., “Attosecond physics at the nanoscale,” Rep. Prog. Phys., vol. 80, p. 054401, 2017. https://doi.org/10.1088/1361-6633/aa574e.Search in Google Scholar PubMed

[20] I. Yavuz, M. F. Ciappina, A. Chacón, Z. Altun, M. F. Kling, and M. Lewenstein, “Controlling electron localization in H2+ by intense plasmon-enhanced laser fields,” Phys. Rev. A, vol. 93, p. 033404, 2016. https://doi.org/10.1103/physreva.93.033404.Search in Google Scholar

[21] I.-Y. Park, S. Kim, J. Choi, et al.., “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics, vol. 5, p. 677, 2011. https://doi.org/10.1038/nphoton.2011.258.Search in Google Scholar

[22] Z. Wang, P. F. Lan, J. H. Luo, L. X. He, Q. B. Zhang, and P. X. Lu, “Control of electron dynamics with a multicycle two-color spatially inhomogeneous field for efficient single-attosecond-pulse generation,” Phys. Rev. A, vol. 88, p. 063838, 2013. https://doi.org/10.1103/physreva.88.063838.Search in Google Scholar

[23] G. Zhang and T. Bai, “Intense isolated short attosecond pulse generation from a coherent superposition state in a spatially inhomogeneous field,” Z. Naturforsch., A: Phys. Sci., vol. 73, p. 303, 2018. https://doi.org/10.1515/zna-2017-0403.Search in Google Scholar

[24] G. Zhang, Z. Wang, T. Bai, et al.., “Generation of intense single short attosecond pulse with a multicycle spatially inhomogeneous field,” J. Mod. Opt., vol. 68, p. 382, 2021. https://doi.org/10.1080/09500340.2021.1899322.Search in Google Scholar

[25] L. Q. Feng and T. S. Chu, “Generation of an isolated sub-40-as pulse using two-color laser pulses: Combined chirp effects,” Phys. Rev. A, vol. 84, p. 053853, 2011. https://doi.org/10.1103/physreva.84.053853.Search in Google Scholar

[26] H. Yuan, F. Li, and H. Long, “Control of high-order harmonic generation with chirped inhomogeneous fields,” J. Opt. Soc. Am. B, vol. 34, p. 2390, 2017. https://doi.org/10.1364/josab.34.002390.Search in Google Scholar

[27] Y. Li, L. Feng, and Y. Qiao, “Selective enhancement of single-order and two-order harmonics from He atom via two-color and three-color laser fields,” Chem. Phys., vol. 527, p. 110497, 2019. https://doi.org/10.1016/j.chemphys.2019.110497.Search in Google Scholar

[28] Y. Li, L.-Q. Feng, and Y. Qiao, “Improvement of high-order harmonic generation via controlling multiple acceleration–recombination process,” Z. Naturforsch., A: Phys. Sci., vol. 74, p. 561, 2019. https://doi.org/10.1515/zna-2018-0549.Search in Google Scholar

[29] H. Liu, L. Feng, Y. Qiao, and Y. Li, “Controlling three-step harmonic emission for intense attosecond pulses using water window harmonic spectra,” J. Mod. Opt., vol. 68, p. 267, 2021. https://doi.org/10.1080/09500340.2021.1890848.Search in Google Scholar

[30] Y. Li, R. L. Feng, and Y. Qiao, “Improvement of harmonic spectra from superposition of initial state driven by homogeneous and inhomogeneous combined field,” Can. J. Phys., vol. 98, p. 198, 2020. https://doi.org/10.1139/cjp-2019-0002.Search in Google Scholar

[31] L. Li, M. Zheng, R. L. Feng, and Y. Qiao, “Waveform control in generations of intense water window attosecond pulses via multi-color combined field,” Int. J. Mod. Phys. B, vol. 33, p. 1950130, 2019. https://doi.org/10.1142/s0217979219501303.Search in Google Scholar

[32] C. Xu, L. Feng, Y. Qiao, and Y. Li, “Pulse duration dependence of harmonic yield of H2+ and its isotopic molecule,” Eur. Phys. J. D, vol. 74, p. 139, 2020. https://doi.org/10.1140/epjd/e2020-10121-9.Search in Google Scholar

[33] H. Liu, L. Feng, W. Li, and Y. Li, “Spatial position scaling on harmonic generation from He atom in bowtie-shaped nanostructure,” Opt. Commun., vol. 398, p. 31, 2017. https://doi.org/10.1016/j.optcom.2017.04.031.Search in Google Scholar

[34] Q. Zhang, L. He, P. Lan, and P. Lu, “Shaped multi-cycle two-color laser field for generating an intense isolated XUV pulse toward 100 attoseconds,” Opt. Express, vol. 22, p. 13213, 2014. https://doi.org/10.1364/oe.22.013213.Search in Google Scholar

[35] C. Jin, G. Wang, H. Wei, A.-T. Le, and C. D. Lin, “Waveforms for optimal sub-keV high-order harmonics with synthesized two- or three-colour laser fields,” Nat. Commun., vol. 5, p. 4003, 2014. https://doi.org/10.1038/ncomms5003.Search in Google Scholar PubMed

[36] C. Jin and C. D. Lin, “Optimization of multi-color laser waveform for high-order harmonic generation,” Chin. Phys. B, vol. 25, p. 094213, 2016. https://doi.org/10.1088/1674-1056/25/9/094213.Search in Google Scholar

[37] C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A, vol. 87, p. 043406, 2013. https://doi.org/10.1103/physreva.87.043406.Search in Google Scholar

[38] H. Liu, L. Feng, Y. Qiao, and X. Jing, “Extreme ultraviolet photon effect on ionization and recombination of high-order harmonic generation,” Eur. Phys. J. D, vol. 75, p. 144, 2021. https://doi.org/10.1140/epjd/s10053-021-00153-0.Search in Google Scholar

[39] C. Jin, G. Wang, A.-T. Le, and C. D. Lin, “Route to optimal generation of soft X-ray high harmonics with synthesized two-color laser pulses,” Sci. Rep., vol. 4, p. 7067, 2014. https://doi.org/10.1038/srep07067.Search in Google Scholar PubMed PubMed Central

[40] S. Haessler, T. Balčiunas, G. Fan, et al., “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X, vol. 4, p. 021028, 2014. https://doi.org/10.1103/physrevx.4.021028.Search in Google Scholar

[41] L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett., vol. 102, p. 063003, 2009. https://doi.org/10.1103/physrevlett.102.063003.Search in Google Scholar

[42] A. Wirth, M. T. Hassan, I. Grguraš, et al.., “Synthesized light transients,” Science, vol. 334, p. 195, 2011. https://doi.org/10.1126/science.1210268.Search in Google Scholar PubMed

[43] X. Cao, S. Jiang, C. Yu, Y. Wang, L. Bai, and R. Lu, “Generation of isolated sub-10-attosecond pulses in spatially inhomogeneous two-color fields,” Opt. Express, vol. 22, p. 26153, 2014. https://doi.org/10.1364/oe.22.026153.Search in Google Scholar

[44] C. Yu, S. Jiang, X. Cao, et al.., “Interference effects on harmonic generation from H2+ in nonhomogeneous laser field,” Opt. Express, vol. 24, p. 19736, 2016. https://doi.org/10.1364/oe.24.019736.Search in Google Scholar PubMed

[45] L.-Q. Feng, W.-L. Li, and H. Liu, “Electron-nuclear dynamics in molecular harmonic generation driven by a plasmonic nonhomogeneous field,” Ann. Phys., vol. 529, p. 1700093, 2017. https://doi.org/10.1002/andp.201700093.Search in Google Scholar

[46] P. Wei, J. Miao, Z. Zeng, et al.., “Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control,” Phys. Rev. Lett., vol. 110, p. 233903, 2013. https://doi.org/10.1103/physrevlett.110.233903.Search in Google Scholar PubMed

[47] X. D. Jing, J. McCain, and L. Q. Feng, “Non-homogeneous multi-color laser beams optimization to obtain a stronger intensity single harmonic radiation path,” Z. Naturforsch., A: Phys. Sci., 2021. https://doi.org/10.1515/zna-2020-0337.Search in Google Scholar

[48] L. He, G. Yuan, K. Wang, W. Hua, C. Yu, and C. Jin, “Optimization of temporal gate by two-color chirped lasers for the generation of isolated attosecond pulse in soft X rays,” Photon. Res., vol. 7, p. 1407, 2019. https://doi.org/10.1364/prj.7.001407.Search in Google Scholar

[49] R. F. Lu, P. Y. Zhang, and K. L. Han, “Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields,” Phys. Rev. E, vol. 77, p. 066701, 2008. https://doi.org/10.1103/physreve.77.066701.Search in Google Scholar

[50] J. Hu, K.-L. Han, and G.-Z. He, “Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution,” Phys. Rev. Lett., vol. 95, p. 123001, 2005. https://doi.org/10.1103/physrevlett.95.123001.Search in Google Scholar PubMed

[51] Z. Wang, S. Jiang, G. Yuan, et al.., “Strain effect on the orientation-dependent harmonic spectrum of monolayer aluminum nitride,” Sci. China Phys. Mech. Astron., vol. 63, p. 257311, 2020. https://doi.org/10.1007/s11433-019-1467-2.Search in Google Scholar

[52] S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett., vol. 120, p. 253201, 2018. https://doi.org/10.1103/physrevlett.120.253201.Search in Google Scholar

[53] D. Wu, F.-M. Guo, J.-G. Chen, J. Wang, and Y.-J. Yang, “Ionization of an atom with different initial angular momenta in an intense circular polarized laser field,” J. Phys. B Atom. Mol. Opt. Phys., vol. 53, p. 235601, 2020. https://doi.org/10.1088/1361-6455/abbf40.Search in Google Scholar

[54] Y. Qiao, D. Wu, J. G. Chen, J. Wang, F. M. Guo, and Y. J. Yang, “High-order harmonic generation from H2+ irradiated by a co-rotating two-color circularly polarized laser field,” Phys. Rev. A, vol. 100, p. 063428, 2019. https://doi.org/10.1103/physreva.100.063428.Search in Google Scholar

[55] J. G. Chen, Y. J. Yang, J. Chen, and B. Wang, “Probing dynamic information and spatial structure of Rydberg wave packets by harmonic spectra in a few-cycle laser pulse,” Phys. Rev. A, vol. 91, p. 043403, 2015. https://doi.org/10.1103/physreva.91.043403.Search in Google Scholar

[56] S. S. Zhou, Y. J. Yang, F. M. Guo, J. G. Chen, and J. Wang, “Multielectron effect for high-order harmonic generation from molecule irradiated by bichromatic counter-rotating circularly polarized laser pulses,” IEEE J. Quant. Electron., vol. 56, p. 9000207, 2020. https://doi.org/10.1109/jqe.2020.2984767.Search in Google Scholar

[57] P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in a strong electromagnetic field,” Phys. Rev. A, vol. 51, p. R1750, 1995. https://doi.org/10.1103/physreva.51.r1750.Search in Google Scholar PubMed

[58] H. Liu, Y. Li, H. Liu, A. Y. Feng, L. Feng, and Y. Qiao, “Multiple-acceleration in "W" waveform structure for high-order harmonic improvement,” J. Nonlinear Opt. Phys. Mater., vol. 28, p. 1950037, 2019. https://doi.org/10.1142/s0218863519500371.Search in Google Scholar
Received: 2021-04-25
Accepted: 2021-06-07
Published Online: 2021-06-25
Published in Print: 2021-09-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Chirp waveform control to produce broad harmonic plateau and single attosecond pulse
  4. Dynamical Systems & Nonlinear Phenomena
  5. Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma
  6. Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment
  7. Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion
  8. Hydrodynamics
  9. Curvilinear flow of micropolar fluid with Cattaneo–Christov heat flux model due to oscillation of curved stretchable sheet
  10. Quantum Theory
  11. Accuracy of the typicality approach using Chebyshev polynomials
  12. Solid State Physics & Materials Science
  13. Impact of Sn ions on structural and electrical description of TiO2 nanoparticles
  14. The effect of non-bridging oxygen on the electrical transport of some lead borate glasses containing cobalt
  15. Thermodynamics & Statistical Physics
  16. Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles
https://doi.org/10.1515/zna-2021-0115
Keywords for this article
chirp waveform control; chirped pulses; high-order harmonic generation; single attosecond pulse

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Chirp waveform control to produce broad harmonic plateau and single attosecond pulse
  4. Dynamical Systems & Nonlinear Phenomena
  5. Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma
  6. Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment
  7. Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion
  8. Hydrodynamics
  9. Curvilinear flow of micropolar fluid with Cattaneo–Christov heat flux model due to oscillation of curved stretchable sheet
  10. Quantum Theory
  11. Accuracy of the typicality approach using Chebyshev polynomials
  12. Solid State Physics & Materials Science
  13. Impact of Sn ions on structural and electrical description of TiO2 nanoparticles
  14. The effect of non-bridging oxygen on the electrical transport of some lead borate glasses containing cobalt
  15. Thermodynamics & Statistical Physics
  16. Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles
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