Classical backpropagation for probing the backward rescattering time of a tunnel-ionized electron in an intense laser field

Yang Hwan Kim, Igor A. Ivanov, and Kyung Taec Kim

Phys. Rev. A 104, 013116 – Published 26 July 2021

Abstract

We present a method to estimate the backward rescattering time of a tunnel-ionized electron in an intense laser pulse. The idea of the classical backpropagation method is applied to determine the backward rescattering time and its dependence on various parameters such as the ionization potential of the parent ion, its spatial profile and the peak intensity and wavelength of the driving laser field. The accurate estimation of the rescattering time would provide critical information in analyzing ultrafast rescattering dynamics in applications such as high-order harmonic generation, above-threshold ionization, and laser-induced electron diffraction experiments. We find that the backward rescattering time is significantly affected by the peak intensity of the laser pulse. The rescattering time changes by a few hundred attoseconds when the peak intensity varies from $1 \times 10^{14}$ to $5 \times 10^{14} W / c m^{2}$ .

Received 26 March 2021
Accepted 13 July 2021

DOI:https://doi.org/10.1103/PhysRevA.104.013116

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields Multiphoton or tunneling ionization & excitation Ultrafast phenomena

Atomic, Molecular & Optical

Authors & Affiliations

Yang Hwan Kim^1,2, Igor A. Ivanov¹, and Kyung Taec Kim ^1,2,*

¹Center for Relativistic Laser Science, Institute for Basic Science, Gwangju 61005, Korea
²Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, Korea

^*kyungtaec@gist.ac.kr

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Vol. 104, Iss. 1 — July 2021

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Images

Figure 1
Concept of the classical backpropagation for probing backward rescattering time. (a) Electron probability distribution (blue line) calculated by solving the TDSE and spatial derivative of phase (red line) in Ar. The blue area is the region where the classical backpropagation method is applied. (b) Evolution of an electron wave function colored in the logarithmic scale with an electric field (blue solid line) and electron trajectories (white solid and dashed lines) obtained using the classical backpropagation. The wave function shown in (a) is the part of the wave function shown in (b) at the end of the propagation time. (c) Backward rescattering times $t_{r}$ obtained for different final momenta using the classical backpropagation for the right direction (red line with diamonds, $x > 0$ ) and the left direction (blue line with circles, $x < 0$ ). Note that the range of the $y$ axis for the left and the right directions are different. A cos-squared envelope for the laser pulse as $E (t) \propto {cos}^{2} (π t / 4 T_{1}) cos (2 π t / T_{1} + ϕ_{CEP})$ . Here, the center wavelength is 800 nm, $T_{1}$ is 2.6 fs, and $ϕ_{CEP}$ is $0.5 π$ . The peak intensity is $2.0 \times 10^{14} W / {cm}^{2}$ .
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Figure 2
BRTs of an electron gaining high energy in Ar going out to the right ( $x > 0$ ) for 14 different CEPs. Solid lines are BRTs obtained by the classical backpropagation and circles are BRTs obtained by the simple man model. Gaussian enveloped, 3 fs full width at half maximum electric field with peak intensity of $1 \times 10^{14} W / {cm}^{2}$ , and center wavelength of 800 nm was used to obtain the results.
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Figure 3
Potential profile and intensity dependence of BRTs obtained by the classical backpropagation. (a) Potential profile dependence of BRT of the electron at the cutoff. Electric field with the peak intensity of $2.5 \times 10^{14} W / {cm}^{2}$ , the center wavelength of 730 nm, and the CEP of $0.5 π$ was used to obtain the result. (b) Intensity dependence of BRTs of the electron for nine different intensities. The BRTs obtained for Ar (dashed lines) and Xe (solid lines) are compared. (c) Difference between the BRTs of the electron in the high energy plateau for Ar and Xe potential, where $Δ t_{r} = t_{r}^{Xe} - t_{r}^{Ar}$ . For all intensities from $1.0 \times 10^{14}$ to $5.0 \times 10^{14} W / {cm}^{2}$ , the BRTs of the electron in the high energy plateau for Ar is earlier in time than that for Xe. Inset: magnified plot $p_{| |} - p_{cutoff}$ between 0.38 and 0.52 atomic units.
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Figure 4
Peak intensity dependence of BRTs in the soft-core Yukawa potential. (a) BRTs as a function of momentum near the cutoff momentum for each peak intensity. Solid lines are BRTs obtained for $b = 0$ , and dashed lines corresponds to BRTs obtained for $b = 2$ . (b) BRTs obtained for different $b$ values at 0.4 atomc units in momentum relative to the classical cutoff momentum denoted by dotted-dashed line shown in (a). Inset: a magnified plot near $I_{0} = 2.5 \times 10^{14} W / {cm}^{2}$ . (c) BRTs shown in (b) relative to the BRTs in soft-core potential without the exponential factor, which is equivalent to $b = 0$ .
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Figure 5
Center wavelength dependence of BRTs in Ar soft-core potential. Ponderomotive energy of the electron is fixed to 12 eV so that peak intensity of the laser field is adjusted accordingly. The legend denotes center wavelength of the laser pulse used for each result.
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