Interaction of Ultraintense Laser Vortices with Plasma Mirrors

Laser beams carrying orbital angular momentum (OAM) have found major applications in a variety of scientific fields, and their potential for ultrahigh-intensity laser-matter interactions has since recently been considered theoretically. We present an experiment where such beams interact with plasma mirrors up to laser intensities such that the motion of electrons in the laser field is relativistic. By measuring the spatial intensity and phase profiles of the high-order harmonics generated in the reflected beam, we obtain evidence for the helical wavefronts of the high-intensity laser at focus, and study the conservation of OAM in highly nonlinear optical processes at extreme laser intensities. The physical effects determining the field mode content of the twisted harmonic beams are elucidated.

Figure 1

Left panels: laser focal spots measured without (a),(e) and with (b),(f) the spiral phase plate in the path of a $\varphi -25\mathrm{mm}$ (up) and $\varphi -45\mathrm{mm}$ (down) diameter laser beam. The bar scale indicates a length of $10\mu \mathrm{m}$. Central panels: raw images of the spectrally resolved high-order harmonic 1D angular profiles at ${\theta }_x=0\mathrm{mrad}$, produced by the UHI vortices in the CWE (panel c, $L\approx \lambda /70$ and $I\approx 5.10^{17}\mathrm{W}/{\mathrm{cm}}^2$), and ROM (panel g, $L\approx \lambda /15$ and $I\approx 10^{19}\mathrm{W}/{\mathrm{cm}}^2$) regimes. These values of $L$ were determined using the SDI interferometric technique described in [26]. Right panels: reconstructed 2D angular intensity profile of the 12th CWE (d) and ROM (h) harmonic beams.

Figure 2

(a) Experimental spectrally resolved interference pattern of the high-order harmonics, generated by the three focal spots presented in the inset (the bar scale corresponds to $20\mu \mathrm{m}$). (b) Reconstructed 2D interference pattern of the 9th harmonic. The 2D phase profile retrieved from this interferogram is presented in (c), showing a variation of $9\times 2\pi$ of the phase over one azimuthal turn. The unwrapped azimuthal phases measured for the 9th, 11th, and 13th harmonics are presented as dots in (d) and compared with the theoretical expectation when OAM is conserved (full lines). All aspects of this measurement compare well with our numerical simulations detailed in [21].

Figure 3

Amplitude (a),(c) and phase (b),(d) profiles at focus of an ideal ${\mathrm{LG}}_{p=0,l=1}$ laser mode, and of the associated 5th harmonic beam calculated in a nonperturbative regime, using the CWE generation model [21]. (e) Absolute values $|c_p|$ of the coefficients of the multiple ${\mathrm{LG}}_{p,nl}$ modes contributing to the harmonic beam of panel (c),(d). (f) Lineouts of the resulting laser (red) and harmonic (blue) beam angular profiles.

Figure 4

Left panels: simulated angular intensity profiles of the 12th harmonic, with (light blue) and without (blue) convolution with the detector resolution (8 mrad angular width). Right panels: comparison of the measured (black) and calculated (light blue) ring and hole diameters characterizing the harmonic vortex beams. The error bars correspond to the standard deviation, deduced from a statistical study on multiple laser shots. The upper and lower lines correspond to the CWE and ROM regime, respectively. The red lines show the prediction in the perturbative regime.