Photoelectron holography from multiple-return backscattering electron orbits

ShaoGang Yu, XuanYang Lai, YanLan Wang, SongPo Xu, LinQiang Hua, Wei Quan, and XiaoJun Liu

Phys. Rev. A 101, 023414 – Published 27 February 2020

Abstract

We theoretically investigate the photoelectron momentum distributions of a diatomic molecule in a linearly polarized two-color laser field by solving the time-dependent Schrödinger equation. An upward curvature interference pattern is found in the two-dimensional photoelectron momentum spectra. Resorting to a simple semiclassical analysis and the strong-field approximation theory, we show that the interference pattern corresponds to a holographic pattern from the second-return backscattering electron orbits and, furthermore, the underlying physics of the distinct observation of such interference pattern is revealed. The holographic patterns from the backscattering electron orbits with the different return times may encode the information of the target structure at different times after ionization.

Received 16 December 2019
Accepted 4 February 2020

DOI:https://doi.org/10.1103/PhysRevA.101.023414

Physics Subject Headings (PhySH)

Multiphoton or tunneling ionization & excitation

Strong-field approximation

Atomic, Molecular & Optical

Authors & Affiliations

ShaoGang Yu ¹, XuanYang Lai^1,*, YanLan Wang¹, SongPo Xu^1,2, LinQiang Hua¹, Wei Quan¹, and XiaoJun Liu^1,†

¹State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
²University of Chinese Academy of Sciences, Beijing 100049, China

^*xylai@wipm.ac.cn
^†xjliu@wipm.ac.cn

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Issue

Vol. 101, Iss. 2 — February 2020

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Images

Figure 1
TDSE simulated two-dimensional photoelectron momentum distributions of $N_{2}$ in the ( $p_{z}, p_{x}$ ) plane. In the upper panels, the spectra calculated with the two-color laser pulses at the relative phase $Δ φ = 0$ for the parallel (a) and perpendicular (b) alignments, respectively. In the lower panels, the spectra simulated in the few-cycle two-color laser pulse with optical cycle numbers $N_{c} = 4$ (c) and $N_{c} = 2$ (d), respectively. The white solid curves in (a) and (b) denote the different types of interference structures. The laser peak intensity is $4.0 \times 10^{14} W / {cm}^{2}$ and the fundamental laser wavelength is 760 nm. For more details, see the text.
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Figure 2
Temporal variation of the electric field $E (t)$ (black solid curve) of the few-cycle two-color laser field with optical cycles $N_{c} = 4$ for (a) and $N_{c} = 2$ for (b), respectively. The pink filled areas indicate the ADK ionization rate. The red dash-dotted curve in each panel (belonging to the right axis) represents a trajectory of electron calculated with the simple man's model. (c) The SFA calculated photoelectron momentum distribution including overall electron orbits. The spectrum with $| p_{z} | < 0.1$ is not shown due to a divergence for large-angle scattering with low momentum. (d)–(f) SFA simulations of the holographic patterns from the FSEO, first-return BSEO and second-return BSEO, respectively. (g) Blowup of Fig. 1 for better visualization. The upward curvature interference stripes are marked by the white solid curves.
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Figure 3
(a) Temporal variation of electric field within two optical cycles of the fundamental laser field for the long pulse duration. The pink filled areas indicate the ADK ionization rate. $t_{i}^{sig}$ represents the ionization time of the rescattering orbits, and $t_{r}^{{sig}_{1}}$ , $t_{r}^{{sig}_{2}}$ , and $t_{r}^{{sig}_{3}}$ are the return times for BSPH, MBSPH, and FSPH, respectively. The corresponding ionization times of the direct orbits are $t^{{ref}_{1}}$ , $t^{{ref}_{2}}$ , and $t^{{ref}_{3}}$ . All of these times are obtained by solving the saddle-point equations. Panel (b) shows the schematic diagrams of the paths of the different types of electron orbits for MBSPH, BSPH, and FSPH, respectively. The black ball denotes the position of the parent ion.
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Figure 4
(a) Electric field of the two-color laser pulse for $Δ φ = 0$ (black solid curve), $Δ φ = 0.2 π$ (red dash-dotted curve), and $Δ φ = 0.4 π$ (blue dotted curve), respectively. (b),(c) The TDSE calculated photoelectron momentum distribution for the relative phase at $Δ φ = 0.2 π$ and $Δ φ = 0.4 π$ , respectively.
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Figure 5
Ionization time $t_{i}$ (a) and rescattering time $t_{r}$ (b) of the rescattering orbits for the BSPH (red solid curve) and MBSPH (blue dashed curve) with respect to the scattered momentum $| k + A (t_{r}) |$ . The corresponding final momentum, $| p_{z} | \in [0.3, 1.2]$ a.u., is along the laser polarization.
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