Matter and Radiation at Extremes, Volume. 8, Issue 6, 064004(2023)

Density-dependent carrier-envelope phase shift in attosecond pulse generation from relativistically oscillating mirrors

Rishat Zagidullin1... Stefan Tietze2,3, Matt Zepf2,3, Jingwei Wang4 and Sergey Rykovanov1 |Show fewer author(s)
Author Affiliations
  • 1Center for AI Technologies, Skolkovo Institute of Science and Technology, Moscow, Russia
  • 2Helmholtz-Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
  • 3Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät, Max-Wien-Platz 1, 07743 Jena, Germany
  • 4State Key Laboratory of High Field Laser Physics and Chinese Academy of Sciences Center for Excellence in Ultra-Intense Laser Science, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
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    Figures & Tables(8)
    Left: fixed-time snapshot of 2D PIC experiment before the pulse hits the target. Right: spatio-temporal electron density distribution zoomed on the plasma surface. The white line is the analytical solution and the red line the numerical solution (1D PICWIG) for a single particle. The parameters are n = 80nc, a0 = 5, and a sin2-enveloped laser pulse with a duration of four optical cycles and linear polarization. The inset on the right shows the evolution of the target density in the relativistic case (n = 80nc, a0 = 20).
    (a) Field strength and (b) intensity of incident, reflected, and combined fields in the nonrelativistic case for two different densities (10nc and 40nc), with a0 = 0.9. (c) Results of PIC simulations with a laser intensity a0 = 4 and a sharp step in density of 40nc. (d) Ultrarelativistic case with a0 = 20 and 80nc. The incident and reflected pulse intensities measured at the critical density surface are plotted as solid and dashed green lines, respectively. The combined laser pulse intensity is shown as a solid black line.
    Dependence of the phase shift of the reflected radiation with respect to the incoming radiation (Δφ = φr − φ0) on the plasma density for different values of a0. Curves are given by Eq. (5). For a ≥ 1, the relativistically corrected plasma density from Eq. (7) is utilized. Smaller and more lightly shaded markers correspond to the cases where the relativistic pulse breaks the too-thin plasma mirror.
    Dependence of the phase shift of the reflected radiation with respect to the incoming radiation (Δφ = φr − φ0) on the value of n0/Lλ for different values of a0. Results for a0 = 0.1 are shown in green and those for a0 = 1 in black. Curves are given by Eq. (6). For a0 = 1, the relativistically corrected plasma density from Eq. (7) was used. Circles and crosses are the results of 1D PIC simulations.
    Dependence of the phase shift of the reflected radiation with respect to the incoming radiation (Δφ = φr − φ0) on the value of n0/Lλ for different values of a0. Results for a0 = 10 are shown by the red curve and triangles, those for a0 = 20 by the brown curve and squares, and those for a0 = 40 by the blue curve and diamonds. The curves are given by Eq. (6), using the relativistically corrected plasma density from Eq. (7), and the markers with the corresponding colors are the results of 1D PIC simulations.
    (a) Attosecond XUV pulses generated by a three-cycle incident pulse with a0 = 20 normally incident on a step-like target with ne = 80nc. For the ROM, the reflected XUV pulses have been filtered from the 10th to the 30th harmonic. A single XUV pulse is generated only in the case of the sine incident pulse. (b) Generation of attosecond pulse in transmission. Similar to the case of reflection, a sine-shaped incident pulse generates a single XUV pulse in transmission. A cosine-shaped incident pulse generates two distinct transmitted pulses. No filter has been applied to the transmitted pulses.
    (a) Dependence of the intensity of the reflected ROM attosecond pulses on time measured in cycles and CEP phase φ0 of the incoming laser pulse (color-coded image). Colored curves outline the intensity of the attosecond pulses (harmonics with numbers >10) for four different values of φ0. The laser pulse has a0 = 20, a duration of three cycles, and ne = 400nc. (b) The same, but in the case when a linear preplasma with length λL/10 is added to the target.
    Intensity of reflected pulses and pulses in transmission in 2D, showing that the result is independent of the simulation code and the dimensionality. (a) corresponds to the reflected pulse and CSE pulse of the incident “sine” pulse, and (b) corresponds to the reflected pulse and CSE pulse of the incident “cosine” pulse. Incident pulses had an amplitude of a0 = 20, and the target density in all cases was ne = 80nc.
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    Rishat Zagidullin, Stefan Tietze, Matt Zepf, Jingwei Wang, Sergey Rykovanov. Density-dependent carrier-envelope phase shift in attosecond pulse generation from relativistically oscillating mirrors[J]. Matter and Radiation at Extremes, 2023, 8(6): 064004

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    Paper Information

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    Received: Apr. 25, 2023

    Accepted: Aug. 21, 2023

    Published Online: Mar. 21, 2024

    The Author Email:

    DOI:10.1063/5.0155957

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