Abstract
We present a theoretical investigation of high-order harmonics and isolated short attosecond pulse generation by a spatially inhomogeneous combined field. The calculation results show that this spatiotemporally synthesized field can not only extend the spectral cutoff but also realize the quantum path control, whereupon an ultrawide supercontinuum with a smooth and regular structure is generated. By filtering a wide range of continuous harmonics around the cutoff region, an isolated 17.6 as pulse with a bandwidth of 279 eV is directly obtained without any phase compensation. Moreover, we also investigate the influence of the CEP, time delay, spatial nonhomogeneity, and laser intensity on the harmonic spectrum.
Funding source: Scientific Research Program Funded by Shaanxi Provincial Education Department
Award Identifier / Grant number: 18JK0050
Funding source: College Student Innovation Training Plan of Baoji University of Arts and Sciences
Award Identifier / Grant number: 2019XJ067
Award Identifier / Grant number: 2019XJ077
Award Identifier / Grant number: 2019XJ083
Funding source: Science and Technology Plan Project of Baoji
Award Identifier / Grant number: 2018JH-04
Funding source: National Undergraduate Training Program for Innovation and Entrepreneurship
Award Identifier / Grant number: S202010721019
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11904192
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department [Grants no. 18JK0050], the National Undergraduate Training Program for Innovation and Entrepreneurship [Grants no. S202010721019], and the College Student Innovation Training Plan of Baoji University of Arts and Sciences [Grants nos. 2019XJ067, 2019XJ077, and 2019XJ083]. Z.H. Yang was supported by the Science and Technology Plan Project of Baoji (Grants no. 2018JH-04). X. Zhao was supported by the National Natural Science Foundation of China (Grants no. 11904192).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] R. Kienberger, E. Goulielmakis, M. Uiberacker, et al.., “Atomic transient recorder,” Nature, vol. 427, no. 6977, p. 817, 2004. https://doi.org/10.1038/nature02277.Search in Google Scholar PubMed
[2] M. Hentschel, R. Kienberger, C. Spielmann, et al.., “Attosecond metrology,” Nature, vol. 414, no. 6863, p. 509, 2001. https://doi.org/10.1038/35107000.Search in Google Scholar PubMed
[3] 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, no. 23, p. 34392, 2019. https://doi.org/10.1364/oe.27.034392.Search in Google Scholar PubMed
[4] 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, no. 3, p. 033413, 2020. https://doi.org/10.1103/physreva.101.033413.Search in Google Scholar
[5] 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 belowthe band gap,” Opt. Lett., vol. 45, no. 10, p. 2874, 2020. https://doi.org/10.1364/ol.389787.Search in Google Scholar PubMed
[6] 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, no. 6, p. 063428, 2019. https://doi.org/10.1103/physreva.100.063428.Search in Google Scholar
[7] Y. Qiao, Y. Q. Huo, S. C. Jiang, Y. J. Yang, and J. G. Chen, “All-optical reconstruction of three-band transition dipole moments by the crystal harmonic spectrum from a two-color laser pulse,” Opt. Express, vol. 30, no. 6, p. 9971, 2022. https://doi.org/10.1364/oe.446432.Search in Google Scholar PubMed
[8] P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett., vol. 71, no. 13, p. 1994, 1993. https://doi.org/10.1103/physrevlett.71.1994.Search in Google Scholar
[9] K. J. Schafer, B. R Yang, L. I. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett., vol. 70, no. 11, p. 1599, 1993. https://doi.org/10.1103/physrevlett.70.1599.Search in Google Scholar PubMed
[10] A. Baltuška, T. Udem, M. Uiberacker, et al.., “Attosecond control of electronic processes by intense light fields,” Nature, vol. 421, no. 6923, p. 611, 2003. https://doi.org/10.1038/nature01414.Search in Google Scholar PubMed
[11] Z. H. Chang, “Electric dipole moment in the split supersymmetry models,” Phys. Rev. A, vol. 71, no. 7, p. 023813, 2005. https://doi.org/10.1103/physrevd.71.076006.Search in Google Scholar
[12] G. Sansone, E. Benedetti, F. Calegari, et al.., “Isolated single-cycle attosecond pulses,” Science, vol. 314, no. 5798, p. 443, 2006. https://doi.org/10.1126/science.1132838.Search in Google Scholar PubMed
[13] T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne mixing of laser fields for temporal gating of high-order harmonic generation,” Phys. Rev. Lett., vol. 97, no. 16, p. 163901, 2006. https://doi.org/10.1103/physrevlett.97.163901.Search in Google Scholar PubMed
[14] Z. N. Zeng, Y. Cheng, X. H. Song, R. X. Li, and Z. Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett., vol. 98, no. 20, p. 203901, 2007. https://doi.org/10.1103/physrevlett.98.203901.Search in Google Scholar PubMed
[15] P. F. Lan, P. X. Lu, W. Cao, Y. H. Li, and X. L. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A, vol. 76, no. 2, p. 011402(R), 2007. https://doi.org/10.1103/physreva.76.021801.Search in Google Scholar
[16] R. F. Lu, H. X. He, Y. H. Guo, and K. L. Han, “Theoretical study of single attosecond pulse generation with a three-colour laser field,” J. Physiol. Biochem., vol. 42, no. 22, p. 225601, 2009. https://doi.org/10.1088/0953-4075/42/22/225601.Search in Google Scholar
[17] L. X. He, Y. Li, Q. B. Zhang, and P. X. Lu, “Ultra-broadband water window supercontinuum generation with high efficiency in a three-color laser field,” Opt Express, vol. 21, no. 3, p. 2683, 2013. https://doi.org/10.1364/oe.21.002683.Search in Google Scholar PubMed
[18] L. Q. Feng and T. S. Chu, “High-order harmonics extension and isolated attosecond pulse generation in three-color field: controlling factors,” Phys. Rev. A, vol. 375, no. 41, p. 3641, 2011. https://doi.org/10.1016/j.physleta.2011.08.039.Search in Google Scholar
[19] P. F. Lan, P. X. Lu, W. Cao, and X. L. Wang, “Efficient generation of an isolated single-cycle attosecond pulse,” Phys. Rev. A, vol. 76, no. 4, p. 043808, 2007. https://doi.org/10.1103/physreva.76.043808.Search in Google Scholar
[20] S. F. Zhao, X. X. Zhou, P. C. Li, and Z. J. Chen, “Isolated short attosecond pulse produced by using an intense few-cycle shaped laser and an ultraviolet attosecond pulse,” Phys. Rev. A, vol. 78, no. 6, p. 063404, 2008. https://doi.org/10.1103/physreva.78.063404.Search in Google Scholar
[21] J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A, vol. 74, no. 2, p. 023404, 2006. https://doi.org/10.1103/physreva.74.023404.Search in Google Scholar
[22] W. Y. Hong, P. X. Lu, W. Cao, P. F. Lan, and X. L. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B: At. Mol. Opt. Phys., vol. 40, no. 12, p. 2321, 2007. https://doi.org/10.1088/0953-4075/40/12/008.Search in Google Scholar
[23] Y. Xiang, Y. P. Niu, and S. Q. Gong, “Control of the high-order harmonics cutoff through the combination of a chirped laser and static electric field,” Phys. Rev. A, vol. 79, no. 5, p. 053419, 2009. https://doi.org/10.1103/physreva.79.053419.Search in Google Scholar
[24] Z. H. Chang, “Controlling attosecond pulse generation with a double optical gating,” Phys. Rev. A, vol. 76, no. 5, p. 051403, 2007. https://doi.org/10.1103/physreva.76.051403.Search in Google Scholar
[25] H. Mashiko, S. Gilbertson, C. Q. Li, et al.., “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett., vol. 100, no. 10, p. 103906, 2008. https://doi.org/10.1103/physrevlett.100.103906.Search in Google Scholar PubMed
[26] T. Gaumnitz, A. Jain, Y. Pertot, et al.., “Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver,” Opt. Express, vol. 25, no. 22, p. 27506, 2017. https://doi.org/10.1364/oe.25.027506.Search in Google Scholar
[27] J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett., vol. 98, no. 1, p. 013901, 2007. https://doi.org/10.1103/physrevlett.98.013901.Search in Google Scholar
[28] E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window X ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett., vol. 101, no. 25, p. 253901, 2008. https://doi.org/10.1103/physrevlett.101.253901.Search in Google Scholar
[29] G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond synchronization of high-order harmonics from midinfrared drivers,” Phys. Rev. Lett., vol. 102, no. 9, p. 093002, 2009. https://doi.org/10.1103/physrevlett.102.093002.Search in Google Scholar PubMed
[30] W. Y. Hong, Q. B. Zhang, Z. Y. Yang, and P. X. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A, vol. 80, no. 5, p. 053407, 2009. https://doi.org/10.1103/physreva.80.053407.Search in Google Scholar
[31] H. C. Du and B. T. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express, vol. 18, no. 25, p. 25958, 2010. https://doi.org/10.1364/oe.18.025958.Search in Google Scholar PubMed
[32] C. Jin, A. T. Le, C. A. Trallero-Herrero, and C. D. Lin, “Generation of isolated attosecond pulses in the far field by spatial filtering with an intense few-cycle mid-infrared laser,” Phys. Rev. A, vol. 84, no. 4, p. 043411, 2011.10.1007/978-3-319-01625-2_5Search in Google Scholar
[33] Y. H. Zheng, Z. N. Zeng, R. X. Li, and Z. Z. Xu, “Isolated-attosecond-pulse generation due to the nuclear dynamics of H2+ in a multicycle midinfrared laser field,” Phys. Rev. A, vol. 85, no. 2, p. 023410, 2012. https://doi.org/10.1103/physreva.85.023410.Search in Google Scholar
[34] Y. Chou, P. C. Li, T. S. Ho, and S. I. Chu, “Optimal control of high-order harmonics for the generation of an isolated ultrashort attosecond pulse with two-color midinfrared laser fields,” Phys. Rev. A, vol. 91, no. 6, p. 063408, 2015. https://doi.org/10.1103/physreva.91.063408.Search in Google Scholar
[35] M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, et al.., “Attosecond physics at the nanoscale,” Rep. Prog. Phys., vol. 80, no. 5, p. 054401, 2017.10.1088/1361-6633/aa574eSearch in Google Scholar PubMed
[36] J. Schoetz, Z. Wang, E. Pisanty, M. Lewenstein, M. F. Kling, and M. Ciappina, “Perspective on petahertz electronics and attosecond nanoscopy,” ACS Photonics, vol. 6, no. 5, p. 3057, 2019. https://doi.org/10.1021/acsphotonics.9b01188.Search in Google Scholar
[37] 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, no. 7196, p. 757, 2008. https://doi.org/10.1038/nature07012.Search in Google Scholar PubMed
[38] I. Y. Park, S. Kim, J. Choi, et al.., “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics, vol. 5, no. 11, p. 677, 2011. https://doi.org/10.1038/nphoton.2011.258.Search in Google Scholar
[39] M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A, vol. 85, no. 3, p. 033828, 2012. https://doi.org/10.1103/physreva.85.033828.Search in Google Scholar
[40] T. Shaaran, M. F. Ciappina, R. Guichard, et al.., “High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles,” Phys. Rev. A, vol. 87, no. 4, p. 041402(R), 2013. https://doi.org/10.1103/physreva.87.041402.Search in Google Scholar
[41] J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett., vol. 110, no. 5, p. 053001, 2013.10.1103/PhysRevLett.110.053001Search in Google Scholar
[42] I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Publisher’s note: generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A, vol. 85, no. 2, p. 013416, 2012. https://doi.org/10.1103/physreva.85.029905.Search in Google Scholar
[43] 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, no. 6, p. 063838, 2013. https://doi.org/10.1103/physreva.88.063838.Search in Google Scholar
[44] L. Q. Feng, H. Liu, Y. Li, and W. L. Li, “Generation of high-intensity KeV single-attosecond pulse using multi-cycle spatial inhomogeneous mid-infrared field,” J. Opt. Soc. Am. B, vol. 35, no. 5, p. A84, 2018. https://doi.org/10.1364/josab.35.000a84.Search in Google Scholar
[45] Y. N. Zheng, C. P. Zhang, H. F. Cui, X. H. Xu, C. L. Xia, and X. Y. Miao, “Isolated-attosecond-pulse generation by suppressing multiple rescatterings with plasmon-enhanced laser fields,” Spectrosc. Lett., vol. 50, no. 3, p. 176, 2017. https://doi.org/10.1080/00387010.2017.1305418.Search in Google Scholar
[46] G. T. Zhang and T. T. Bai, “Intense isolated short attosecond pulse generation from a coherent superposition state in a spatially inhomogeneous field,” Z. Naturforschu. A, vol. 73, no. 4, p. 303, 2018. https://doi.org/10.1515/zna-2017-0403.Search in Google Scholar
[47] G. T. Zhang, Z. Q. Wang, T. T. Bai, et al.., “Generation of intense single short attosecond pulse with a multicycle spatially inhomogeneous field,” J. Mod. Opt., vol. 68, no. 7, p. 382, 2021. https://doi.org/10.1080/09500340.2021.1899322.Search in Google Scholar
[48] M. D. Feit, J. A. FleckJr, and A. Steiger, “Solution of the schrödinger equation by a spectral method,” J. Comput. Phys., vol. 47, no. 3, p. 412, 1982. https://doi.org/10.1016/0021-9991(82)90091-2.Search in Google Scholar
[49] K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A, vol. 45, no. 5, p. 3347, 1992. https://doi.org/10.1103/physreva.45.3347.Search in Google Scholar PubMed
[50] 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, no. 3, p. R1750, 1995. https://doi.org/10.1103/physreva.51.r1750.Search in Google Scholar PubMed
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