Interaction of Ultraintense Radially-Polarized Laser Pulses with Plasma Mirrors

We present experimental results of vacuum laser acceleration (VLA) of electrons using radially polarized laser pulses interacting with a plasma mirror. Tightly focused, radially polarized laser pulses have been proposed for electron acceleration because of their strong longitudinal electric field, making them ideal for VLA. However, experimental results have been limited until now because injecting electrons into the laser field has remained a considerable challenge. Here, we demonstrate experimentally that using a plasma mirror as an injector solves this problem and permits us to inject electrons at the ideal phase of the laser, resulting in the acceleration of electrons along the laser propagation direction while reducing the electron beam divergence compared to the linear polarization case. We obtain electron bunches with few-MeV energies and a 200-pC charge, thus demonstrating, for the first time, electron acceleration to relativistic energies using a radially polarized laser. High-harmonic generation from the plasma surface is also measured, and it provides additional insight into the injection of electrons into the laser field upon its reflection on the plasma mirror. Detailed comparisons between experimental results and full 3D simulations unravel the complex physics of electron injection and acceleration in this new regime: We find that electrons are injected into the radially polarized pulse in the form of two spatially separated bunches emitted from the p-polarized regions of the focus. Finally, we leverage on the insight brought by this study to propose and validate a more optimal experimental configuration that can lead to extremely peaked electron angular distributions and higher energy beams.

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Popular Summary

Femtosecond lasers are nowadays intense enough to push electrons to relativistic speeds. This has led researchers to attempt using the immense electric fields of these lasers to directly accelerate electrons in vacuum over very short distances, a process known as vacuum laser acceleration. Recent work with plasma mirrors has helped optimize injection of electrons into the laser field, but a fundamental issue remains unresolved: The electric field of a laser beam is perpendicular to its propagation direction, which means that electrons are accelerated transversely, leading to electron beams with large angular spreads. In this work, we overcome this problem by spatially shaping the laser to generate radially polarized laser pulses, which possess a strong longitudinal electric field.

We experimentally observe that this field can directly accelerate electrons in vacuum in the laser propagation direction, resulting in a 50% reduction of the angular spread compared to linear polarization. The combination of these experimental results with cutting-edge 3D simulations of the interaction between a radially polarized laser and a plasma mirror reveals in detail the complex physics leading to electron injection in this scenario.

Building on these findings, we show that these results can be further improved by optimizing the laser parameters and angle of incidence, making vacuum laser acceleration with radial polarization a promising path for generating high-quality ultrashort relativistic electron beams.

Figure 1

(a) Sketch of the experiment. An ultraintense laser pulse (red) is reflected on the target (gray). Relativistic electrons (light blue) and high-harmonics (dark blue) are generated from the interaction and are measured simultaneously. A phase mask made of eight octants, depicted in the top-left corner, can be inserted to convert the laser polarization from linear to radial. By rotating the phase mask, the polarization can then be continuously varied from radial to azimuthal. (b) The left panel shows a focal spot for linear polarization, i.e., without the phase mask, while the right panel shows a focal spot for radial polarization. In these focal spots, a value of 1 on the color bar corresponds to $1.1\times {10}^6\mathrm{J}/{\mathrm{cm}}^2$ for linear polarization and to $9\times {10}^5\mathrm{J}/{\mathrm{cm}}^2$ for radial polarization. (c)–(f) Typical experimental angular electron distributions. The specular direction corresponds to ${\theta }_x={\theta }_y=0$, while the insets depict the polarization of the laser. (c) Linear polarization: The electron beam is located between the specular and normal directions. (d) Azimuthal polarization: Electrons are located on both sides of the specular direction. (e,f) Radial polarization: Panel (e) shows a typical angular distribution, while panel (f) is a result from one of the best shots. Both distributions display an electron beam in the specular direction. The dashed black circles show the angular extent of the reflected laser beam. In these images, a value of 1 on the color bar corresponds to $100\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (c), $35\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (d), $22\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (e), and $31\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (f). See also Supplemental Material [35] for a sample of consecutive shots obtained with linear, radial, and azimuthal polarizations.

Figure 2

(a) Angularly resolved energy spectra of the electrons emitted near the incidence plane (${\theta }_y=0$) for linear polarization (top panel), radial polarization (middle panel), and azimuthal polarization (bottom panel). The dashed line marks the specular direction. In these images, a value of 1 on the color bar corresponds to $22\mathrm{fC}/\mathrm{MeV}/{\mathrm{mrad}}^2$ for the top panel, $28\mathrm{fC}/\mathrm{MeV}/{\mathrm{mrad}}^2$ for the middle panel, and $12\mathrm{fC}/\mathrm{MeV}/{\mathrm{mrad}}^2$ for the bottom panel. (b) Electron energy spectra obtained at the position of the square markers in Figs. 1 for linear polarization (blue curve), radial polarization (red curve), and azimuthal polarization (green curve).

Figure 3

(a)–(c) Experimental, angularly resolved, harmonic spectra in the case of (a) linear polarization, (b) azimuthal polarization, and (c) radial polarization. (d)–(f) Schematic view of the laser field footprint on the plasma surface for (d) linear, (e) azimuthal, or (f) radial polarization. Electrons and harmonics are only emitted when the laser is close to p-polarized (i.e., when the electric field is almost parallel to the incidence plane), which results in two spatially separated sources in the case of radial and azimuthal polarization.

Figure 4

Results from 3D PIC simulations. Angularly resolved harmonic spectra for (a) linear, (b) azimuthal, or (c),(d) radial polarization are shown. The angular dependence is shown with respect to the ${\theta }_y$ angle in panels (a)–(c), which corresponds to the experimental case, and with respect to the ${\theta }_x$ angle in panel (d) so that the interference pattern produced with a radially polarized beam becomes apparent. The spectra are obtained by calculating the spatial 3D Fourier transform of the $B_y$ field for the linear and radial polarization cases and of the $E_x/c/\sin {\theta }_i$ field, where ${\theta }_i$ is the incidence angle, for the azimuthal polarization case. We use the convention $F(\overrightarrow{k})={\int }_{{\mathbb{R}}^3}f(\overrightarrow{r})e^{-i\overrightarrow{k}.\overrightarrow{r}}{d}^3\overrightarrow{r}$ to compute the Fourier transform.

Figure 5

Results from 3D PIC simulations. Initial position of the electrons that are ejected $4\mu \mathrm{m}$ away from the plasma in the case of (a) linear, (b) azimuthal, or (c) radial polarization. In these images, a value of 1 on the color bar corresponds to $53\mathrm{pC}/\mu {\mathrm{m}}^2$ for panel (a), $62.\mathrm{pC}/\mu {\mathrm{m}}^2$ for panel (b), and $104\mathrm{pC}/\mu {\mathrm{m}}^2$ for panel (c).

Figure 6

Results from a 3D PIC simulation. We show the laser magnetic field in the incidence plane with radial polarization, either (a) $10\mu \mathrm{m}$ before or (b) $60\mu \mathrm{m}$ after reflection.

Figure 7

Results from 3D PIC simulations. Angular distributions of the electrons with an energy greater than 1 MeV obtained at the end of the simulations with (a) radial polarization and $a_{0,r}=3.3$, (b) linear polarization and $a_0=3.6$, (c) radial polarization and $a_{0,r}=1.6$, and (d) azimuthal polarization and $a_{0,r}=1.6$. In these images, a value of 1 on the color bar corresponds to $2.68\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (a), $3.72\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (b), $1.68\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (c), and $0.45\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (d).

Figure 8

Results from 3D PIC simulations. Electron energy distributions are computed in a 30-mrad cone at the angle defined by the black circles shown in Fig. 7.

Figure 9

Schematic illustration of electron emission from the plasma in the incident plane for linear (a) and radial (b) polarization. The black arrows represent the incident electric field. The green arrows in the reflected field indicate the direction of the transverse electric field seen by the electrons immediately after they are injected. The electrons are always emitted at a phase of the laser field such that they tend to deviate towards the normal direction (this implies, in particular, that the time at which electrons are ejected is shifted by half a laser period between spot A and spot B). For radial polarization, the electrons originating from spot B are more likely to interact with the $E_z$ field than those coming from spot A.

Figure 10

3D-PIC simulations. (a)–(d) Angular distribution of electrons with $z>0$ initially, with (a,b) $a_{0,r}=1.6$ or (c,d) $a_{0,r}=3.3$. The distributions are shown either approximately 80 fs after reflection or approximately 270 fs after reflection, which corresponds to the end of the simulation. In these images, a value of 1 on the color bar corresponds to $1.34\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (a), $1.66\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (b), $8.86\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (c), and $1.85\mathrm{fC}/{\mathrm{mrad}}^2$ for panel (d). (e)–(h) Similar angular distributions reproduced in test-particle simulations. The laser intensity is slightly reduced in the test-particle simulations to take into account the energy absorption by the plasma mirror.

Figure 11

Results from the PIC simulation at normal incidence. (a) Angular distribution of the electrons with an energy greater than 1 MeV around the specular direction. (b) Energy spectrum of the electrons such that $\theta <10\mathrm{mrad}$ (dark blue curve), $85\mathrm{mrad}<\theta <95\mathrm{mrad}$ (green curve), $175\mathrm{mrad}<\theta <185\mathrm{mrad}$ (red curve), and $195\mathrm{mrad}<\theta <205\mathrm{mrad}$ (light blue curve), where $\theta$ is the angle with respect to the specular direction. In this plot, a value of 1 on the $y$ axis corresponds to $0.46\mathrm{pC}/\mathrm{MeV}$ for the dark blue curve, $0.34\mathrm{pC}/\mathrm{MeV}$ for the green curve, and $0.74\mathrm{pC}/\mathrm{MeV}$ for the red and light blue curves.