Intensity of Resonant Harmonic Generated in the Multiphoton Ionization Regime


The relative intensities of the resonant and nonresonant high-order harmonics, generated by singly charged gallium and indium ions in the field of a laser pulse with a duration of 20 fs and intensity ranging from 5 × 1013 to 2 × 1014 W/cm2, are calculated. The harmonic intensity is found via the matrix element of multiphoton transition within the perturbation theory including the resonant contribution. The latter increases the harmonic intensity at the transition from the ground state to the autoionizing state. We consider laser wavelength when this transition corresponds to 7 and 15 photons.

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  1. 1

    L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys.-JETP. 20 (5), 1307–1314 (1965).

    MathSciNet  Google Scholar 

  2. 2

    R. A. Ganeev, L. B. Elouga Bom, J.-C. Kieffer, and T. Ozaki, “Systematic investigation of resonance-induced single-harmonic enhancement in the extreme-ultraviolet range,” Phys. Rev. A. 75, 063806 (2007).

    ADS  Article  Google Scholar 

  3. 3

    R. A. Ganeev, “High-order harmonic generation in laser surface ablation: current trends,” Phys.-Usp. 56 (8) 772 (2013).

    ADS  Article  Google Scholar 

  4. 4

    L. Plaja and L. Roso, “High-order harmonic generation in a two-level atom effect of the multiphoton resonances tuned by the light shift,” J. Mod. Opt. 40, 793 (1993).

    ADS  Article  Google Scholar 

  5. 5

    C. F. Faria, R. Kopold, W. Becker, and J.-M. Rost, “Resonant enhancements of high-order harmonic generation,” Phys. Rev. A. 65, 023404 (2002).

    ADS  Article  Google Scholar 

  6. 6

    R. Taieb, V. Veniard, J. Wassaf, and A. Maquet, “Roles of resonances and recollisions in strong-field atomic phenomena. II. High-order harmonic generation,” Phys. Rev. A. 68, 033403 (2003).

    ADS  Article  Google Scholar 

  7. 7

    M. B. Gaarde and K. Schafer, “Enhancement of many high-order harmonics via a single multiphoton resonance,” Phys. Rev. A. 64, 013820 (2001).

    ADS  Article  Google Scholar 

  8. 8

    M. Plummer and C. J. Noble, “Resonant enhancement of harmonic generation in argon at 248 nm,” J. Phys. B: At. Mol. Opt. Phys. 35, L51 (2002).

    ADS  Article  Google Scholar 

  9. 9

    K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003).

    ADS  Article  Google Scholar 

  10. 10

    P. A. Oleinikov, V. T. Platonenko, and G. Ferrante, “Erratum: “Resonant generation of high harmonics,” JETP Lett. 60 (4), 246 (1994).

    ADS  Google Scholar 

  11. 11

    D. Milošević, “High-energy stimulated emission from plasma ablation pumped by resonant high-order harmonic generation,” J. Phys. B: At. Mol. Opt. Phys. 40, 3367 (2007).

    ADS  Article  Google Scholar 

  12. 12

    M. V. Frolov, N. L. Manakov, T. S. Sarantseva, M. Yu. Emelin, M. Yu. Ryabikin, and A. F. Starace, “Analytic description of the high-energy plateau in harmonic generation by atoms: Can the harmonic power increase with increasing laser wavelengths?” Phys. Rev. Lett. 102 (24), 243901 (2009).

    ADS  Article  Google Scholar 

  13. 13

    V. Strelkov, “Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production,” Phys. Rev. Lett. 104, 123901 (2010).

    ADS  Article  Google Scholar 

  14. 14

    V.-M. Gkortsas, S. Bhardwaj, C.-J. Lai, K.-H. Hong, E. L. Falcão-Filho, and F. X. Kärtner, “Interplay of mulitphoton and tunneling ionization in short-wavelength-driven high-order harmonic generation,” Phys. Rev. A. 84, 013427 (2011).

    ADS  Article  Google Scholar 

  15. 15

    E. Fiordilino, F. Morales, G. Castiglia, P. P. Corso, R. Daniele, and V. V. Strelkov, “High-order harmonic generation via bound–bound transitions in an elliptically polarized laser field,” J. Opt. Sos. Am. B. 34 (1), 2673–2681 (2017).

    ADS  Article  Google Scholar 

  16. 16

    E. A. Migal, S. Y. Stremoukhov, and F. V. Potemkin, “Ionization-free resonantly enhanced low-order harmonic generation in a dense gas mixture by a mid-IR laser field,” Phys. Rev. A. 101 (2), 021401 (2020).

    ADS  Article  Google Scholar 

  17. 17

    J. M. Ngoko Djiokap and A.F. Starace, “Origin of the multiphoton-regime harmonic-generation plateau structure,” Phys. Rev. A. 102, 013103 (2020).

    ADS  Article  Google Scholar 

  18. 18

    M. Tudorovskaya and M. Lein, “High-order harmonic generation in the presence of a resonance,” Phys. Rev. A. 84, 013430 (2011).

    ADS  Article  Google Scholar 

  19. 19

    V. V. Strelkov, M. A. Khokhlova, and N. Yu Shubin, “High-order harmonic generation and Fano resonances,” Phys. Rev. A. 89, 053833 (2014).

    ADS  Article  Google Scholar 

  20. 20

    T. Sato and K. L. Ishikawa, “Time-dependent complete-active-space self-consistent-field method for multielectron dynamics in intense laser fields,” Phys. Rev. A. 88, 023402 (2013).

    ADS  Article  Google Scholar 

  21. 21

    Y. Orimo, T. Sato, and K. L. Ishikawa, “Application of the time-dependent surface flux method to the time-dependent multiconfiguration self-consistent-field method,” Phys. Rev. A. 100, 013419 (2019).

    ADS  Article  Google Scholar 

  22. 22

    V. V. Kim, G. S. Boltaev, M. Iqbal, N. A. Abbasi, H. Al-Harmi, I. S. Wahyutama, T. Sato, K. L. Ishikawa, R. A. Ganeev, and A. S. Alnaser, “Resonance enhancement of harmonics in the vicinity of 32 nm spectral range during propagation of femtosecond pulses through the molybdenum plasma,” J. Phys. B: At. Mol. Opt. Phys. 53, 195401 (2020).

    ADS  Article  Google Scholar 

  23. 23

    A. I. Magunov and V. V. Strelkov, “S-matrix approach to the problem of high-harmonic generation in the field of intense laser wave,” Phys. Wave Phenom. 25 (1), 24–29 (2017).

    ADS  Article  Google Scholar 

  24. 24

    U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).

    ADS  Article  MATH  Google Scholar 

  25. 25

    S. L. Chin and P. A. Golovinski, “High harmonic generation in the multiphoton regime: correlation with polarizability,” J. Phys. B: At. Mol. Opt. Phys. 28, 55–63 (1995).

    ADS  Article  Google Scholar 

  26. 26

    Atomic Spectra Database, atomic-spectra-database

  27. 27

    B. Peart, I. C. Lyon, and K. Dolder, “Measurements of absolute photoionisation cross sections of Ga+ and Zn+ ions,” J. Phys. B: At. Mol. Phys. 20, 5403–5410 (1987).

    ADS  Article  Google Scholar 

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This study was supported by the Russian Science Foundation (project no. 16-12-10279).

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Correspondence to A. I. Magunov.

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Translated by Yu. Sin’kov

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Magunov, A.I., Strelkov, V.V. Intensity of Resonant Harmonic Generated in the Multiphoton Ionization Regime. Phys. Wave Phen. 28, 369–374 (2020).

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