Nonlinear branched flow of intense laser light in randomly uneven media

K. Jiang; T. W. Huang; C. N. Wu; M. Y. Yu; H. Zhang; S. Z. Wu; H. B. Zhuo; A. Pukhov; C. T. Zhou; S. C. Ruan

doi:10.1063/5.0133707

Volume 8 Issue 2

Mar. 2023

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K. Jiang, T. W. Huang, C. N. Wu, M. Y. Yu, H. Zhang, S. Z. Wu, H. B. Zhuo, A. Pukhov, C. T. Zhou, S. C. Ruan. Nonlinear branched flow of intense laser light in randomly uneven media[J]. Matter and Radiation at Extremes, 2023, 8(2): 024402. doi: 10.1063/5.0133707

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K. Jiang, T. W. Huang, C. N. Wu, M. Y. Yu, H. Zhang, S. Z. Wu, H. B. Zhuo, A. Pukhov, C. T. Zhou, S. C. Ruan. Nonlinear branched flow of intense laser light in randomly uneven media[J]. Matter and Radiation at Extremes, 2023, 8(2): 024402. doi: 10.1063/5.0133707

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Nonlinear branched flow of intense laser light in randomly uneven media

doi: 10.1063/5.0133707

K. Jiang^{1, 2
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T. W. Huang^{2
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C. N. Wu^2
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M. Y. Yu^2
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H. Zhang^2
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S. Z. Wu²,
H. B. Zhuo^2
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A. Pukhov^3
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C. T. Zhou^{1, 2
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S. C. Ruan^{1, 2}

1.
College of Applied Sciences, Shenzhen University, Shenzhen 518060, People’s Republic of China
2.
Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, People’s Republic of China
3.
Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany

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Corresponding author: a)Authors to whom correspondence should be addressed: taiwu.huang@sztu.edu.cn and zcangtao@sztu.edu.cn
Received Date: 2022-11-05
Accepted Date: 2023-01-22

Available Online: 2023-03-01

Publish Date: 2023-03-01

Abstract

Abstract

Branched flow is an interesting phenomenon that can occur in diverse systems. It is usually linear in the sense that the flow does not alter the properties of the medium. Branched flow of light on thin films has recently been discovered. It is therefore of interest to know whether nonlinear light branching can also occur. Here, using particle-in-cell simulations, we find that in the case of an intense laser propagating through a randomly uneven medium, cascading local photoionization by the incident laser, together with the response of freed electrons in the strong laser fields, triggers space–time-dependent optical unevenness. The resulting branching pattern depends dramatically on the laser intensity. That is, the branching here is distinct from the existing linear ones. The observed branching properties agree well with theoretical analyses based on the Helmholtz equation. Nonlinear branched propagation of intense lasers potentially opens up a new area for laser–matter interaction and may be relevant to other branching phenomena of a nonlinear nature.

Conflict of Interest
The authors have no conflicts to disclose.
K. Jiang: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (lead); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). T. W. Huang: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (supporting); Writing – review & editing (equal). C. N. Wu: Formal analysis (supporting); Visualization (supporting). M. Y. Yu: Investigation (supporting); Writing – original draft (supporting); Writing – review & editing (equal). H. Zhang: Data curation (supporting); Formal analysis (supporting); Resources (equal); Software (equal); Validation (supporting). S. Z. Wu: Data curation (supporting); Resources (supporting); Software (supporting); Validation (supporting). H. B. Zhuo: Formal analysis (supporting); Investigation (supporting); Validation (supporting). A. Pukhov: Formal analysis (supporting); Investigation (supporting); Resources (supporting); Supervision (supporting); Validation (supporting). C. T. Zhou: Data curation (supporting); Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (supporting). S. C. Ruan: Resources (supporting); Supervision (supporting).
K.J. and T.W.H. developed the theoretical work. K.J. conducted the simulations. K.J., T.W.H., and C.N.W. analyzed the data and produced the figures. H.Z., S.Z.W., H.B.Z., and A.P. helped review and interpret the data. K.J., T.W.H., and M.Y.Y. wrote the article. T.W.H., C.T.Z., and S.C.R. supervised the work. All authors have reviewed, discussed, and agreed to the complete article.
Author Contributions
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Our PIC simulations are conducted using the epoch code.²⁹ For the simulations of the Gaussian laser pulse, “simple_laser” and “simple_outflow” longitudinal boundaries and open lateral boundaries are used. Periodic lateral boundaries are used for the reference simulations of plane waves. Unless otherwise stated, “field_ionization” is turned on, which accounts for different modes of photoionization, including multiphoton ionization, tunneling ionization, and barrier-suppression ionization. In 2D (3D) simulations, the simulation box is −5 µm < x < 215 µm, −55 µm < y (and z in 3D) < 55 µm, with 2200 × 1100 (1100 × 550 × 550) grid cells and 30 (2) macroparticles per cell for each species. Note that more macroelectrons will be produced by photoionization. For the interacting medium, we choose a weakly pre-ionized SiO₂ plasma (Si²⁺ and O⁺) with uneven density distribution, which is located in 0 µm < x < 215 µm, −55 µm < y (and z in 3D) < 55 µm. The average densities of Si²⁺, O⁺, and electrons are 0.02n_c, 0.04n_c, and 0.08n_c, respectively, where n_c ∼ 1.1 × 10²¹ cm−3/λ02 is the critical density. The uneven density distribution is generated by assigning random points at a minimum separation of 2 µm within the plasma area with values taken from a set satisfying a Gaussian random distribution between zero and three times the average densities. The full plasma density map with C² continuity is obtained by applying biharmonic spline interpolation based on these random points. The overall average densities and a coefficient of density variation of 30% are used as constraint conditions. The obtained density unevenness is of an isotropic correlation length l_c = 4.8 µm, defined as the shortest distance in which the value of the corresponding autocorrelation function (ACF) drops to 10% of the zero-shift value.²⁸ The ACF is calculated as ACF(i,j)=∑m=0M−1∑n=0N−1ne(m,n)ne(m+i,n+j), where n_e is the initial electron density, M and N are the numbers of grid cells occupied by the electrons in the longitudinal and lateral directions, respectively, and 0 ≤ i < 2M − 1 and 0 ≤ j < 2 N − 1. The input laser pulse is simulated as a Gaussian beam with circular polarization incident normally from the left boundary. Its central wavelength λ₀ = 1.06 µm, peak intensity I₀ = 10¹⁴–10²⁰ W/cm², and FWHM spot size r₀ = 16.65 µm. The laser pulse duration is 1.5 ps, with a flat-top time profile for simplicity. The reference simulations of plane waves use identical parameters.

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