Vortex laser beam generation from laser interaction with azimuthal plasma phase slab at relativistic intensities

It is shown theoretically and by simulation that a Gaussian laser beam of relativistic intensity interacting with a uniform-thickness plasma slab of azimuthally varying density can acquire orbital angular momentum (OAM). During the interaction, the laser ponderomotive force and the charge-separation force impose a torque on the plasma particles. The affected laser light and plasma ions gain oppositely directed axial OAM, but the plasma electrons remain almost OAM free. High OAM conversion efficiency is achieved due to the strong azimuthal electromagnetic energy flow during the laser phase modulation. The present scheme should provide useful reference for applications requiring relativistic-intense vortex light.

Figure 1

(a) Transverse electron density profile of the plasma phase plate. (b) Helical phase profile of the $l=1$ vortex mode. The color code corresponds to the phase velocity. (c) Normalized instantaneous electric field component $E_y$ of the generated vortex laser at $68T_0$ in the $x,z$ plane. The dash-dotted line marks the plasma left boundary. (d) $E_y$ in the transverse plane at $x=34.1\mu \mathrm{m}$, marked by the dashed line in (c).

Figure 2

Azimuthal momentum density distribution in the ($\varphi ,x$) plane at $r=2\mu \mathrm{m}$ and $t=44T_0$ for (a) electrons and (b) protons, for simplicity denoted by $P{\varphi }_e$ and $P{\varphi }_p$, respectively. The dot-dashed lines outline the plasma boundaries. The black curve in (b) shows the normalized laser field intensity $a/a_0$ at $x=16.7\mu \mathrm{m}$ (marked by a dashed line), or the laser-pulse center at $t=44T_0$. (c) Evolution of the total azimuthal momentum of the electrons (upper curve) and protons (lower curve) in a $0.8\mu \mathrm{m}$ thick slice centered at $r=2\mu \mathrm{m}$. Points A and B correspond to (a) and (b). (d) and (e) Instantaneous $y$ component proton momentum density in the $y,z$ plane at $x=1.1\mu \mathrm{m}$ and $t=22T_0$ and at $x=25.5\mu \mathrm{m}$ and $t=57T_0$, respectively. The color scale in (b), (d), and (e) is the same as that in (a). (f) Evolution of the total normalized axial angular momentum of electrons (upper curve), protons (lower curve with oscillations), and all particles (lower curve without the oscillations). Points D and E correspond to (d) and (e).

Figure 3

(a) The dashed curves are for the laser field intensity (orange) and phase velocity (blue) along the circular loop $(r,x)=(2,0)\mu \mathrm{m}$ at $20T_0$. The solid curves are for the laser field intensity (orange) and phase velocity (blue) along the circular loop $(r,x)=(2,26)\mu \mathrm{m}$ at $57T_0$. (b) The mode coefficient amplitude versus the minimum plasma density $n_2$, with the maximum density $n_1$ fixed at $0.1n_c$. $C_{01,L}$ and $C_{02,L}$ correspond to ${\text{LG}}_{01}$ and ${\text{LG}}_{02}$ modes in cases with plasma slab length given by $L$, same for $C_{01,L^{\prime }}$ and $C_{02,L^{\prime }}$ while with plasma slab length given by $L^{\prime }$.

Figure 4

Evolution of the laser equiphase surfaces during their modulation for (a) the azimuthal plasma phase slab scheme proposed in this paper, (b) the light fan or spiral shaped plasma schemes. The color bar corresponds to the normalized periodic longitudinal displacement of the phase surfaces.