Modified saddle-point method applied to direct ionization of noble gas atoms

Jašarević, Abdulah S.; Hasović, E.; Milošević, D. B.

doi:10.1088/1751-8121/ace811

J. Phys. A: Math. Theor.

2023

DOI: 10.1088/1751-8121/ace811

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Modified saddle-point method applied to direct ionization of noble gas atoms

Abdulah S. Jašarević

E. Hasović

D. B. Milošević

Abstract: When exposed to strong laser ﬁelds, atoms or molecules can absorb more photons from the laser ﬁeld than is necessary for ionization. This process is called above-threshold ionization (ATI). In analyzing this process, the strong-ﬁeld approximation (SFA) turns out to be a very useful theoretical tool. In the SFA the diﬀerential ionization rate, which is an observable quantity, can be expressed as an integral over the ionization time and can be calculated by numerical integration (NI) or using the saddle-point me… Show more

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2024

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Cited by 2 publications

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Asymptotic methods applied to integrals occurring in strong-laser-field processes

Milošević,

Jašarević,

Habibović

et al. 2024

J. Phys. A: Math. Theor.

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The quantum-mechanical transition amplitudes for atomic and molecular processes in strong laser fields are expressed in the form of multidimensional integrals of highly oscillatory functions. Such integrals are ideally suited for the evaluation by asymptotic methods for integrals. Furthermore, using these methods it is possible to identify, in the sense of Feynman's path-integral formalism, the partial contributions of quantum orbits, which are related to particular solutions of the saddle-point equations. This affords insight into the physics of the problem, which would not have been possible by only solving these integrals numerically. We apply the saddle-point method to various quantum processes, which are important in strong-field physics and attoscience. The special case of coalescing or near-coalescing saddle points requires application of the uniform approximation. We also present two modifications of the saddle-point method, for the cases where a singular point of the subintegral function exactly overlaps with a saddle point or is located in its close vicinity. Particular emphasis is on the classification of the saddle-point solutions. This problem is solved for the one-dimensional integral over the ionization time, relevant for above-threshold ionization (ATI), while for two-dimensional integrals a classification by the multi-index $(\alpha,\beta,m)$ is introduced, which is particularly useful for the medium- and high-energy spectrum of high-order harmonic generation (HHG) and backward-scattered electrons (for high-order ATI). For the low-energy structures a classification using the multi-index $(\nu,\rho,\mu)$ is introduced for the forward-scattering quantum orbits. In addition to laser-induced processes such as ATI, HHG and high-order ATI, we consider laser-assisted scattering as an example of laser-assisted processes for which real solutions of the saddle-point equation exist. Particular attention is devoted to the quantum orbits that describe and visualize these processes. We also consider finite laser pulses, the semiclassical approximation, the role of the Coulomb field and the case of laser fields intense enough to lead into the relativistic regime.

show abstract

Asymptotic methods applied to integrals occurring in strong-laser-field processes

Milošević,

Jašarević,

Habibović

et al. 2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

Jašarević,

Hasović,

Milošević

2024

Phys. Rev. A

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Modified saddle-point method applied to direct ionization of noble gas atoms

Cited by 2 publications

References 37 publications

Asymptotic methods applied to integrals occurring in strong-laser-field processes

Asymptotic methods applied to integrals occurring in strong-laser-field processes

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

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