Linearly polarized RABBIT beyond the dipole approximation

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Linearly polarized RABBIT beyond the dipole approximation

Yijie Liao, Yongkun Chen, Jan Marcus Dahlström, Liang-Wen Pi, Peixiang Lu, and Yueming Zhou

Phys. Rev. A 110, 023109 – Published 21 August 2024

Abstract

We theoretically investigate nondipole effects in the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) of helium using linearly polarized extreme ultraviolet and infrared fields. By scanning the time delay between the two fields, we observe modulations in sidebands (SBs) both for angular-integrated photoelectron yield and forward-backward asymmetry in photoelectron distribution along the light-propagation direction. The SB modulations of the forward-backward asymmetry reveal Wigner and continuum-continuum time delays of the electron wave packets ionized via nondipole paths, different from the conventional RABBIT where only the dipole paths are involved. Furthermore, the time delays extracted from the forward-backward asymmetry show an abrupt jump as a function of polar emission angle of photoelectrons, due to the competition among continuum partial waves in nondipole laser-assisted photoionization.

Received 3 June 2024
Accepted 29 July 2024

DOI:https://doi.org/10.1103/PhysRevA.110.023109

Physics Subject Headings (PhySH)

Multiphoton or tunneling ionization & excitation Photoemission Single- and few-photon ionization & excitation

Atomic, Molecular & Optical

Authors & Affiliations

Yijie Liao ¹, Yongkun Chen¹, Jan Marcus Dahlström ^2,*, Liang-Wen Pi ^3,†, Peixiang Lu^1,4, and Yueming Zhou ^1,5,‡

¹School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
²Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
³Center for Attosecond Science and Technology, Xi'an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences, Xi'an 710119, China
⁴Optics Valley Laboratory, Hubei 430074, China
⁵Hubei Optical Fundamental Research Center, Wuhan 430074, China

^*Contact author: [email protected]
^†Contact author: [email protected]
^‡Contact author: [email protected]

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Issue

Vol. 110, Iss. 2 — August 2024

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Images

Figure 1
The schematic of essential ionization channels in the nondipole RABBIT scheme for (a) dipole-dipole paths $P_{DD}$ , (b) dipole-quadrupole paths $P_{DQ}$ , and (c) quadrupole-dipole paths $P_{QD}$ . The purple and red arrows indicate the transitions by exchanging the XUV and IR photons, respectively. The upward (downward) arrows denote the absorption (emission) of a photon. The solid (dashed) arrows denote the relatively more (less) probable transition according to the propensity rule in laser-assisted photoionization when comparing each step of absorption and emission from the same state. The partial waves of each ionization channel are illustrated as the real spherical harmonics represented on polar plots. The inset depicts the coordinate system in our discussions, where $\hat{ε}, \hat{k}$ , and $\hat{p} = (θ, φ)$ , respectively, denote the directions for the polarization of the electric field, the light-propagation, and the emission of photoelectrons.
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Figure 2
(a) The angular-integrated photoelectron energy spectra obtained by solving the TDSE, as a function of time delay between the XUV and IR fields. The intensities of the XUV and IR fields are $1 \times 10^{13}$ and $1 \times 10^{10} W / {cm}^{2}$ , respectively. (b) The same as (a), but for the forward-backward asymmetry of the photoelectron spectra at polar emission angle $θ = 71^{\circ}$ of photoelectrons. (c) The normalized $2 ω τ$ oscillations of photoelectron yields for SB 20 and SB 28 of the angular-integrated photoelectron spectra. (d) The same as (c), but for the forward-backward asymmetry of the photoelectron spectra at polar emission angle $θ = 71^{\circ}$ . The solid and dashed lines correspond to SB 20 and SB 28, respectively.
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Figure 3
The photoionization time delays extracted from the angular-integrated photoelectron spectra as a function of the photoelectron energy. The orange triangles and blue circles correspond to the results obtained by solving the TDSE beyond and within the DA, respectively. The red squares and green rhombuses refer to the PT results excluding and including the nondipole paths $P_{DQ}, P_{QD}$ , and $P_{EDMD}$ in addition to the dipole path $P_{DD}$ , respectively.
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Figure 4
(a) The photoionization time delays as a function of polar emission angle of photoelectrons for all SBs, which are extracted from the forward-backward asymmetry of the angular-resolved photoelectron spectra calculated by solving the TDSE including nondipole effects. (b) The same as (a), but calculated by PT. The stars, rhombuses, triangles, circles, and squares correspond to SBs 20, 22, 24, 26, and 28, respectively. (c) The photoionization time delay extracted from the asymmetry photoelectron spectra at polar emission angle $θ = 40^{\circ}$ as a function of the photoelectron energy. (d) The same as (c), but for polar emission angle $θ = 71^{\circ}$ . The rhombuses correspond to the TDSE results. The circles (dots) refer to the PT results including all the paths $P_{DD}, P_{DQ}, P_{QD}$ , and $P_{EDMD}$ (only the paths $P_{DD}, P_{DQ}$ , and $P_{QD}$ ). The triangles and squares refer to the PT results only including the paths $P_{DD}$ and $P_{DQ}$ , and only including the paths $P_{DD}$ and $P_{QD}$ , respectively.
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Figure 5
(a) The Wigner phases as a function of the photoelectron energy. The circles and squares correspond to the angular momentum quantum numbers $λ = 1$ and 2 of the intermediate state, respectively. (b) The CC phases as a function of the photoelectron energy. The upper (lower) plane corresponds to absorption (emission) of the IR photon in the continuum. The dashed (solid) lines correspond to the analytical results for electric-dipole (electric-quadrupole) CC transitions. The circles, triangles, and squares, respectively, correspond to the paths $P_{DD}, P_{DQ}$ , and $P_{QD}$ in Fig. 1, with their specific partial waves indicated by the legend. The solid (hollow) symbols refer to the lower (higher) final angular momentum in each path.
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Figure 6
The ratios of the modules of the reduced ionization amplitudes $M_{P, N}^{(\pm)}$ with a larger final angular momentum $L_{>}$ to those with a smaller final angular momentum $L_{<}$ for all paths in Fig. 1, as a function of the photoelectron energy. The dashed (solid) lines correspond to the absorption (emission) of the IR photon in the continuum. The circles, triangles, and squares refer to the paths $P_{DD}, P_{DQ}$ , and $P_{QD}$ , respectively.
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