Extended laser filamentation in air generated by femtosecond annular Gaussian beams

Extending the longitudinal range of plasma channels produced by femtosecond annular (ring) Gaussian beams in atmosphere is numerically investigated. We find that the length of a stable plasma channel induced by the annular Gaussian beam, comparing with a Gaussian beam under the same initial condition, has a significant improvement, which can be well understood from two aspects. The dynamic complementation caused by the optical system composing of an axicon and a diverging lens can extend the plasma channel greatly, and the special initial transverse distribution of ring-Gaussian pulse leads to pulse splitting and redistribution of the pulse energy before the formation of optical filament. The ultrashort ring-Gaussian beam perhaps offers a new and an efficient route towards the generation of extended optical filament.

Figure 1

(a) The focusing scheme of an axicon only (red dashed lines) and an axicon preceded by a diverging lens (blue solid lines) for an annular Gaussian beam. Here, $r$ denotes the radius of the ringlike beam. (b) The corresponding axial focusing distance as a function of the transverse radial coordinate.

Figure 2

(a) The spatial plasma density (in units of ${\text{cm}}^{-3}$) distribution on a logarithmic scale with the propagation distance $z$ for ring-Gaussian beam. The input energy is $E_{\mathrm{in}}=5\text{mJ}$, the spatial chirp $C=10{\text{mm}}^{-1}$, and the focal distance of concave $f=-8\text{m}$. (b) The energy fluence (in units of ${\text{J/cm}}^2$) distribution of the laser beam as a function of $z$ and variation of the beam radius at $e^{-2}$ of the fluence distribution is indicated by a pair of yellow lines. (c) The fluence on the axis as a function of $z$.

Figure 3

(a) The peak laser intensity. (b) The peak electron density. (c) The energy loss as a function of the propagation distance $z$ for the Gaussian beam ($r_0=0$, dashed line) and ring-Gaussian beam ($r_0=3\text{mm}$, solid line) with no concave lens ($f=\infty$) (black) and $f=-8\text{m}$ (red) under the condition of $C=10{\text{mm}}^{-1}$.

Figure 4

The temporal distribution of the on-axis intensity(in units of $\text{W}/{\text{cm}}^2$) as a function of the propagation distance $z$ for the ring-Gaussian beam (a) and the Gaussian beam (b), the parameters $C$ and $f$ are the same as in Fig. 2.

Figure 5

The temporal distribution of the on-axis intensity (a) and (b), and the spatiotemporal intensity distribution (c) and (d) at the different propagation distance $z$ before the formation of optical filament for the ring-Gaussian beam (a) and (c), and the Gaussian beam (b) and (d). The parameters are the same as in Fig. 4.

Figure 6

The temporal distribution of the on-axis intensity at the different propagation distance $z$ after the formation of the optical filament for the ring-Gaussian beam (a) and the Gaussian beam (b). The parameters are the same as used in Fig. 4.