Home Electromagnetic Reflection of the vortex beam of the relativistic flying mirror

# Reflection of the vortex beam of the relativistic flying mirror

The reflection process was studied using the three-dimensional (3D) particle-in-the-cell (PIC) code EPOCH35. The famous Laguerre-Gaussian (LG01) mode is used as a typical vortex beam, and it can be expressed as36.37

$$uleft(L{G}_{01}right)=sqrt{frac{2}{pi }}frac{rsqrt{2}}{{w}^{2} left(xright)}mathrm{exp}left[-frac{{r}^{2}}{{w}^{2}left(xright)}right]mathrm{exp}left(ivarphiright)mathrm{exp}left[frac{i{k}_{0}{r}^{2}x}{2left({x}^{2}+{x}_{r}^{2}right)}right]mathit{exp}left[-2i{mathrm{tan}}^{-1}left(frac{x}{{x}_{r}}right)right]{mathrm{sin}}^{2}left(frac{pi t}{2tau}right)$$

when it spreads in X direction. Here, (r=sqrt{{y}^{2}+{z}^{2}}); (varphi =mathrm{arctan}(z/y)); ({k}_{0}=2pi /{lambda}_{0}) is the wave number; and the wavelength of the incident beam is ({lambda }_{0}=0.8 mathrm{mu m}). In addition, (wleft(xright)={w}_{0}sqrt{{(x}^{2}+{x}_{r}^{2})/{x}_{r} ^{2}}),(mathrm{where } {w}_{0}=6.25{lambda }_{0}) is the beam waist radius and ({x}_{r}) is the Rayleigh length. The longitudinal profile was composed of ({mathrm{sin}}^{2}(pi t/2tau )) and (tau = 26.7mathrm{ fs}). The dimensionless amplitude ({a}_{0}=e{E}_{0}/{m}_{e}c{omega }_{0}=1)where (e), ({me}), ({omega }_{0}), ({E}_{0})and (vs) are respectively the charge of the electron, the mass of the electron, the laser frequency, the maximum amplitude of the laser field and the speed of light in vacuum. In our PIC simulation, a linearly polarized LG01 incident beam obliquely on the flying mirror with ({theta }_{in}=pi /6) (compared to the X axis), as shown in Fig. 1. Initially, the LG laser was injected from (x=-5{lambda}_{0})and the flying mirror was standing and occupying the domain in (13.75{lambda}_{0})X (15{lambda}_{0}), (-18.75{lambda}_{0})there (18.75{lambda}_{0}), (-10{lambda}_{0})z (10{lambda}_{0}). The electron density of the mirror was 20 ({NC}) to ensure that the laser pulse has been completely reflected17.38here,({NC}) is the critical density. The flying mirror was moving in the –Xsteering at a speed of(v=0.5mathrm{c}). Here we note that the speed of the flying mirror was set to 0.5c instead of a more relativistic speed to save computational resources, i.e. to achieve fast separation of the laser from the target and avoid the influence of digital heating. The simulation box was a (25{lambda}_{0})× (50{lambda}_{0}) × (25{lambda}_{0}) cuboid corresponding to a window of 400 × 800 × 400 cells in the X× there × zdirection, and each cell had 10 macroparticles.

The simulation configurations of the incident and reflected electric fields are shown respectively in Figures 2a,b. Compared to the field before reflection, the distribution of the reflected field changed significantly, including the profile and the direction of propagation. In Fig. 2b, the arrow indicates the direction of the LM of the reflected beam, defined according to the direction of the LM, which must be perpendicular to that of the electromagnetic field. The wavelength of the reflected beam was lower than that of the incident beam and the angle of reflection was lower than the angle of incidence due to the relativistic effect. As shown in Figure 2c, the laser was tightly focused and the longitudinal component of the electromagnetic field could not be ignored; So the k -the profile of the spatial spectrum of the reflected field has undergone a spectral broadening. According to the coordinates of the center of gravity of the laser, the wavelength and the emission angle of the reflected beam were ({lambda }_{1}=0.283 mathrm{mu m}) and ({theta}_{re}=0.174) rad, respectively.