Controlling multiple filaments by relativistic optical vortex beams in plasmas

Filamentation dynamics of relativistic optical vortex beams (OVBs) propagating in underdense plasma is investigated. It is shown that OVBs with finite orbital angular momentum (OAM) exhibit much more robust propagation behavior than the standard Gaussian beam. In fact, the growth rate of the azimuthal modulational instability decreases rapidly with increase of the OVB topological charge. Thus, relativistic OVBs can maintain their profiles for significantly longer distances in an underdense plasma before filamentation occurs. It is also found that an OVB would then break up into regular filament patterns due to conservation of the OAM, in contrast to a Gaussian laser beam, which in general experiences random filamentation.

Figure 1

(a) The growth rate of AMI with different values of topological charge $m=1,2,3$, where $r_0=10$ $\mu \mathrm{m}$, $n_e=0.2n_c$, and $P=20P_{\mathrm{cr}}$ are assumed. (b) The maximum number of filaments as a function of $m$ for $P=20P_{\mathrm{cr}}$, $40P_{\mathrm{cr}}$, and $60P_{\mathrm{cr}}$.

Figure 2

The initial intensity distribution and the corresponding phase of different optical vortex beams: (a, d) $m=0$; (b, e) $m=1$; and (c, f) $m=2$ with noise level $max\left(\delta \right)=0.05$, where $P=20P_{cr}$, $r_0=10$ $\mu$, and $n_e=0.2n_c$ are taken in the simulations. The unit of the intensity is $\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

The intensity patterns at some special positions for the optical vortex beams: (a, d, g) $m=0$, (b, e, h) $m=1$, and (c, f, i) $m=2$. The noise level is set as $max\left(\delta \right)=0.05$ and the initial parameters with $P=20P_{\mathrm{cr}}$, $r_0=10$ $\mu \mathrm{m}$, and $n_e=0.2n_c$ are taken. The unit of the intensity is $\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

The evolutions of the maximum intensity with the propagation distance $z$ for $m=0,1,2$, where the noise level is set as $max\left(\delta \right)=0.05$, and $P=20P_{\mathrm{cr}}$, $r_0=10$ $\mu \mathrm{m}$, and $n_e=0.2n_c$ are taken. The dashed lines indicate the distance that the filamentation instability occurs.

Figure 5

Filamentation patterns of different optical vortex beams at the same propagation distance with different noise levels of $max\left(\delta \right)=0.08$ and 0.1 (a, d) for $m=0$, (b, e) for $m=1$, and (c, f) for $m=2$. The initial parameters are the same as in Fig. 3. The unit of the intensity is $\mathrm{W}/{\mathrm{cm}}^2$.

Figure 6

Filamentation patterns of different optical vortex beams with different input powers and topological charge $m$ (a–c) for $P=20P_{\mathrm{cr}}$, $m=1$, 2, and 3; (d–f) for $P=40P_{\mathrm{cr}}$, $m=1$, 2, and 3; and (g–i) for $P=60P_{\mathrm{cr}}$, $m=1$, 2, and 3. The initial parameters are set as $max\left(\delta \right)=0.05$, $r_0=10$ $\mu \mathrm{m}$, and $n_e=0.2n_c$. The unit of the intensity is $\mathrm{W}/{\mathrm{cm}}^2$.