Skip to main content
SpringerLink
Log in

Phase-dependent effects in strong-field ionization induced by a two-component ultrashort laser pulse

  • Regular Article - Optical Phenomena and Photonics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We investigate above-threshold detachment induced by an ultrashort laser pulse with one or two carrier frequencies. Particular attention is devoted to the phase-dependent effects in the low- and medium-energy parts of the spectrum. In particular, we show that the photoelectron spectra can be controlled using the phases of the field components and the ellipticity as parameters. Also, using the saddle-point method, we show that the interference between various ionization pathways can also be controlled using these parameters. Depending on the value of the phases and the ellipticity, one or more saddle-point solutions can be significant in the examined part of the photoelectron spectra. If the contribution of only one saddle-point solution is dominant, the photoelectron yield is a smooth function of the photoelectron energy. On the other hand, when two or more contributions have to be taken into consideration, it is important whether the corresponding ionization times are within the same optical cycle or not. If they are, the interference pattern of these contributions is characterized by deep minima. On contrary, if the ionization times of the contributions which have to be taken into consideration are in different optical cycles, their interference would produce a rapidly oscillating spectrum. We propose a scheme for analyzing the asymmetry of the photoelectron spectra emitted in the directions characteristic for a particular driving field. We show that, by using a two-component driving pulse, it is possible to achieve a fine control on which contributions are significant and which can be neglected. This control is more advanced than the control by the linearly polarized field for which the electron dynamics is rather simple.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. The manuscript has associated data in a data repository.

References

  1. W. Becker, F. Grasbon, R. Kopold, D.B. Milošević, G.G. Paulus, H. Walther, Above-threshold ionization: from classical features to quantum effects. Adv. At. Mol. Opt. Phys. 48, 35 (2002)

    ADS  CAS  Google Scholar 

  2. D.B. Milošević, F. Ehlotzky, Scattering and reaction processes in powerful laser fields. Adv. At. Mol. Opt. Phys. 49, 373 (2003)

    ADS  Google Scholar 

  3. M.C. Kohler, T. Pfeifer, K.Z. Hatsagortsyan, C.H. Keitel, Frontiers of atomic high-harmonic generation. Adv. At. Mol. Opt. Phys. 61, 159 (2012)

    ADS  CAS  Google Scholar 

  4. P. Agostini, L.F. DiMauro, Atomic and molecular ionization dynamics in strong laser fields: from optical to X-rays. Adv. At. Mol. Opt. Phys. 61, 117 (2012)

    ADS  CAS  Google Scholar 

  5. S.V. Popruzhenko, Keldysh theory of strong field ionization: history, applications, difficulties and perspectives. J. Phys. B 47, 204001 (2014)

    ADS  Google Scholar 

  6. F. Calegari, G. Sansone, S. Stagira, C. Vozzi, M. Nisoli, Advances in attosecond science. J. Phys. B 49, 062001 (2016)

    ADS  Google Scholar 

  7. W. Becker, S.P. Goreslavski, D.B. Milošević, G.G. Paulus, The plateau in above-threshold ionization: the keystone of rescattering physics. J. Phys. B 51, 162002 (2018)

    ADS  Google Scholar 

  8. K. Amini, J. Biegert, F. Calegari, A. Chacón, M.F. Ciappina, A. Dauphin, D.K. Efimov, Figueira de Morisson, C. Faria, K. Giergiel, P. Gniewek et al., Symphony on strong field approximation. Rep. Prog. Phys. 82, 116001 (2019)

    ADS  CAS  PubMed  Google Scholar 

  9. F. Lindner, M.G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D.B. Milošević, D. Bauer, W. Becker, G.G. Paulus, Attosecond double-slit experiment. Phys. Rev. Lett. 95, 040401 (2005)

    ADS  CAS  PubMed  Google Scholar 

  10. D.B. Milošević, G.G. Paulus, D. Bauer, W. Becker, Above-threshold ionization by few-cycle pulses. J. Phys. B 39, R203 (2006)

    ADS  Google Scholar 

  11. D.G. Arbó, E. Persson, J. Burgdörfer, Time double-slit interferences in strong-field tunneling ionization. Phys. Rev. A 74, 063407 (2006)

    ADS  Google Scholar 

  12. R. Gopal, K. Simeonidis, R. Moshammer, Th. Ergler, M. Dürr, M. Kurka, K.-U. Kühnel, S. Tschuch, C.-D. Schröter, D. Bauer et al., Three-dimensional momentum imaging of electron wave packet interference in few-cycle laser pulses. Phys. Rev. Lett. 103, 053001 (2009)

    ADS  CAS  PubMed  Google Scholar 

  13. M. Kübel, M. Arbeiter, C. Burger, N.G. Kling, T. Pischke, R. Moshammer, T. Fennel, M.F. Kling, B. Bergues, Phase- and intensity-resolved measurements of above threshold ionization by few-cycle pulses. J. Phys. B 51, 134007 (2018)

  14. M. Kübel, P. Wustelt, Y. Zhang, S. Skruszewicz, D. Hoff, D. Würzler, H. Kang, D. Zille, D. Adolph, G.G. Paulus et al., High-order phase-dependent asymmetry in the above-threshold ionization plateau. Phys. Rev. Lett. 126, 113201 (2021)

    ADS  PubMed  Google Scholar 

  15. G.G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, S. De Silvestri, Absolute-phase phenomena in photoionization with few-cycle laser pulses. Nature 414, 182 (2001)

    ADS  CAS  PubMed  Google Scholar 

  16. D.B. Milošević, G.G. Paulus, W. Becker, Phase-dependent effects of a few-cycle laser pulse. Phys. Rev. Lett 89, 153001 (2002)

    ADS  PubMed  Google Scholar 

  17. D.B. Milošević, G.G. Paulus, W. Becker, High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase. Opt. Exp. 11, 1418 (2003)

    Google Scholar 

  18. F. Grasbon, G.G. Paulus, H. Walther, P. Villoresi, G. Sansone, S. Stagira, M. Nisoli, S. De Silvestri, Above-threshold ionization at the few-cycle limit. Phys. Rev. Lett 91, 173003 (2003)

    ADS  CAS  PubMed  Google Scholar 

  19. M. Hentschel, R. Kienberger, C. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, Attosecond metrology. Nature 414, 509 (2001)

    ADS  CAS  PubMed  Google Scholar 

  20. J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, A. L’Huillier, K.J. Schafer, Coherent electron scattering captured by an attosecond quantum stroboscope. Phys. Rev. Lett. 100, 073003 (2008)

    ADS  CAS  PubMed  Google Scholar 

  21. D.M. Villeneuve, P. Hockett, M.J.J. Vrakking, H. Niikura, Coherent imaging of an attosecond electron wave packet. Science 356, 1150 (2017)

    CAS  PubMed  Google Scholar 

  22. M. Kübel, Z. Dube, A.Y. Naumov, M. Spanner, G.G. Paulus, M.F. Kling, D.M. Villeneuve, P.B. Corkum, A. Staudte, Streak camera for strong-field ionization. Phys. Rev. Lett. 119, 183201 (2017)

    ADS  PubMed  Google Scholar 

  23. M. Spanner, O. Smirnova, P.B. Corkum, M.Y. Ivanov, Reading diffraction images in strong field ionization of diatomic molecules. J. Phys. B 37, L243 (2004)

    ADS  CAS  Google Scholar 

  24. A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D.B. Milošević, F. Kelkensberg, W.K. Siu, M.J.J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, M.F. Kling, Above-threshold ionization of diatomic molecules by few-cycle laser pulses. Phys. Rev. A 84, 043426 (2011)

    ADS  Google Scholar 

  25. Y. Huismans, A. Gijsbertsen, A.S. Smolkowska, J.H. Jungmann, A. Rouzée, P.S.W.M. Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko et al., Scaling laws for photoelectron holography in the midinfrared wavelength regime. Phys. Rev. Lett. 109, 013002 (2012)

    ADS  CAS  PubMed  Google Scholar 

  26. S. Borbély, A. Tóth, K. Tokési, L. Nagy, Spatial and temporal interference during the ionization of H by few-cycle XUV laser pulses. Phys. Rev. A 87, 013405 (2013)

    ADS  Google Scholar 

  27. N.I. Shvetsov-Shilovski, M. Lein, L.B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D.G. Arbó, K. Tokési, Semiclassical two-step model for strong-field ionization. Phys. Rev. A 94, 013415 (2016)

    ADS  Google Scholar 

  28. S. Borbély, A. Tóth, D.G. Arbó, K. Tokési, L. Nagy, Photoelectron holography of atomic targets. Phys. Rev. A 99, 013413 (2019)

    ADS  Google Scholar 

  29. S.D. López, D.G. Arbó, Holographic interference in atomic photoionization from a semiclassical standpoint. Phys. Rev. A 100, 023419 (2019)

    ADS  Google Scholar 

  30. M. Murakami, G.-P. Zhang, Observation of attosecond electron dynamics in the photoelectron momentum distribution of atoms using few-cycle laser pulses. Phys. Rev. A 101, 053439 (2020)

    ADS  CAS  Google Scholar 

  31. Li. Guo, S. Chen, S. Hu, R. Lu, S. Han, J. Zhang, J. Chen, Investigation of the middle-energy region of the above-threshold ionization spectrum in a few-cycle laser field. J. Phys. B 55, 225401 (2022)

    ADS  CAS  Google Scholar 

  32. M.-H. Yuan, A.D. Bandrauk, X.-B. Bian, Exploring recollision of ultrafast electrons from photoelectron momentum distributions using single-cycle near-infrared laser pulses. Phys. Rev. A 103, 013108 (2021)

    ADS  CAS  Google Scholar 

  33. A. Taoutioui, K. Tokési, Identifying the complexity of the holographic structures in strong field ionization. Sci. Rep. 12, 2877 (2022)

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  34. A.C. Brown, G.S.J. Armstrong, J. Benda, D.D.A. Clarke, K.R. Hamilton, Z. Mašín, J.D. Gorfinkiel, H.W. van der Hart, RMT: R-matrix with time-dependence. Solving the semi-relativistic, time-dependent Schrödinger equation for general, multielectron atoms and molecules in intense, ultrashort, arbitrarily polarized laser pulses. Comput. Phys. Commun. 250, 107062 (2020)

    CAS  Google Scholar 

  35. B. Fetić, W. Becker, D.B. Milošević, Extracting photoelectron spectra from the time-dependent wave function: comparison of the projection onto continuum states and window-operator methods. Phys. Rev. A 102, 023101 (2020)

    ADS  Google Scholar 

  36. D. Habibović, D.B. Milošević, Above-threshold detachment by strong ultrashort two-component laser pulses. Phys. Rev. A 107, 053110 (2023)

    ADS  Google Scholar 

  37. A. Kramo, E. Hasović, D.B. Milošević, W. Becker, Above-threshold detachment by a two-color bicircular laser field. Laser Phys. Lett. 4, 279 (2007)

    ADS  CAS  Google Scholar 

  38. A. Gazibegović-Busuladžić, D. Habibović, M. Busuladžić, D.B. Milošević, Molecular strong-field approximation for photodetachment of electrons from homonuclear diatomic molecular anions. J. Opt. Soc. Am. B 37, 813 (2020)

    ADS  Google Scholar 

  39. J.M. Ngoko Djiokap, S.X. Hu, L.B. Madsen, N.L. Manakov, A.V. Meremianin, A.F. Starace, Electron vortices in photoionization by circularly polarized attosecond pulses. Phys. Rev. Lett. 115, 113004 (2015)

    ADS  CAS  PubMed  Google Scholar 

  40. J.M. Ngoko Djiokap, A.V. Meremianin, N.L. Manakov, S.X. Hu, L.B. Madsen, A.F. Starace, Kinematical vortices in double photoionization of helium by attosecond pulses. Phys. Rev. A 96, 013405 (2017)

    ADS  Google Scholar 

  41. K.-J. Yuan, S. Chelkowski, A.D. Bandrauk, Photoelectron momentum distributions of molecules in bichromatic circularly polarized attosecond UV laser fields. Phys. Rev. A 93, 053425 (2016)

    ADS  Google Scholar 

  42. K.-J. Yuan, H. Lu, A.D. Bandrauk, Photoionization of triatomic molecular ions \({{{\rm H}}}_{3}^{2+}\) by intense bichromatic circularly polarized attosecond UV laser pulses. J. Phys. B 50, 124004 (2017)

    ADS  Google Scholar 

  43. D. Pengel, S. Kerbstadt, D. Johannmeyer, L. Englert, T. Bayer, M. Wollenhaupt, Electron vortices in femtosecond multiphoton ionization. Phys. Rev. Lett. 118, 053003 (2017)

    ADS  CAS  PubMed  Google Scholar 

  44. G.S.J. Armstrong, D.D.A. Clarke, J. Benda, J. Wragg, A.C. Brown, H.W. van der Hart, Modeling tomographic measurements of photoelectron vortices in counter-rotating circularly polarized laser pulses. Phys. Rev. A 100, 063416 (2019)

    ADS  CAS  Google Scholar 

  45. L. Geng, F. Cajiao Vélez, J.Z. Kamiński, L.-Y. Peng, K. Krajewska, Vortex structures in photodetachment by few-cycle circularly polarized pulses. Phys. Rev. A 102, 043117 (2020)

    ADS  CAS  Google Scholar 

  46. M.M. Majczak, F. Cajiao Vélez, J.Z. Kamiński, K. Krajewska, Carrier-envelope-phase and helicity control of electron vortices and spirals in photodetachment. Opt. Exp. 30, 43330 (2022)

    CAS  Google Scholar 

  47. N. Bleistein, R.A. Handelsman, Asymptotic Expansions of Integrals (Dover Publications, New York, 1975)

    Google Scholar 

  48. A.A. Radzig, B.M. Smirnov, Reference Data on Atoms, Molecules, and Ions (Springer, Berlin, 1985)

    Google Scholar 

  49. G.F. Gribakin, M.Y. Kuchiev, Multiphoton detachment of electrons from negative ions. Phys. Rev. A 55, 3760 (1997)

    ADS  CAS  Google Scholar 

  50. X.X. Zhou, Z. Chen, T. Morishita, A.-T. Le, C.D. Lin, Retrieval of electron-atom scattering cross sections from laser-induced electron rescattering of atomic negative ions in intense laser fields. Phys. Rev. A 77, 053410 (2008)

    ADS  Google Scholar 

  51. M.F. Kling, J. Rauschenberger, A.J. Verhoef, E. Hasović, T. Uphues, D.B. Milošević, H.G. Muller, M.J.J. Vrakking, Imaging of carrier-envelope phas e effects in above-threshold ionization with intense few-cycle laser fields. New J. Phys. 10, 025024 (2008)

  52. D. Habibović, W. Becker, D.B. Milošević, Symmetries and selection rules of the spectra of photoelectrons and high-order harmonics generated by field-driven atoms and molecules. Symmetry 13, 1566 (2021)

    ADS  Google Scholar 

  53. A. Jašarević, E. Hasović, R. Kopold, W. Becker, D.B. Milošević, Application of the saddle-point method to strong-laser-field ionization. J. Phys. A 53, 125201 (2020)

    ADS  MathSciNet  Google Scholar 

  54. D.B. Milošević, G.G. Paulus, W. Becker, Ionization by few-cycle pulses: tracing the electron orbits. Phys. Rev. A 71, 061404(R) (2005)

    ADS  Google Scholar 

  55. D.G. Arbó, K.L. Ishikawa, K. Schiessl, E. Persson, J. Burgdörfer, Intracycle and intercycle interferences in above-threshold ionization: the time grating. Phys. Rev. A 81, 021403(R) (2010)

    ADS  Google Scholar 

  56. A. de Bohan, P. Antoine, D.B. Milošević, G.L. Kamta, B. Piraux, Phase sensitivity of harmonic emission with ultrashort laser pulses. Laser Phys. 9, 175 (1999)

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge support by the Ministry for Science, Higher Education and Youth, Canton Sarajevo, Bosnia and Herzegovina. We thank A. S. Jašarević for useful discussions and comments.

Author information

Authors and Affiliations

  1. University of Sarajevo, Faculty of science, Zmaja od Bosne 35, 71000, Sarajevo, Bosnia and Herzegovina

    D. Habibović & D. B. Milošević

  2. Academy of Sciences and Arts of Bosnia and Herzegovina, Bistrik 7, 71000, Sarajevo, Bosnia and Herzegovina

    D. B. Milošević

Authors
  1. D. Habibović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. B. Milošević
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to the paper.

Corresponding author

Correspondence to D. Habibović.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Habibović, D., Milošević, D.B. Phase-dependent effects in strong-field ionization induced by a two-component ultrashort laser pulse. Eur. Phys. J. D 78, 8 (2024). https://doi.org/10.1140/epjd/s10053-024-00806-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-024-00806-w

Search

Navigation