Figure 1

Snapshots of the intensity distribution $|\widehat{E}(z,r,\tau ){|}^2$ [$E(z,r,\tau )=\widehat{E}(z,r,\tau )\exp (i\tau )+\mathrm{c}.\mathrm{c}.$] along the capillary having length $10z_R$ and diameter $185\lambda$ at gas pressure $p=7.5$ ($\beta \simeq 53$) and the corresponding plasma density as well (at the second level, together with the pulse intensity projection density contour lines correspond to 0.25, 0.5, 0.75, 1 deg of gas ionization). Initial laser pulse parameters: ${\tau }_p=50.26$, $E_0=0.2$. In the inset: transverse intensity distribution normalized to its maximum value along $z$ (the unchanging lines are initial distribution and distribution of the fundamental mode ${\stackrel{⟶}{EH}}_{11}$), narrow and wide profiles, respectively.Reuse & Permissions

Figure 2

1D self-compression within the framework of the reduced wave equation (3) at $\beta =1$, $\alpha =5$. Initial pulse parameters: ${\tau }_p^{\mathrm{in}}=9T_0$, ${\mathcal{E}}_{\mathrm{in}}=0.075$. The shortest pulse duration is about ${\tau }_p^{\mathrm{out}}\simeq 1.2T_0$ and the corresponding peak intensity was amplified 2.5-fold as a result of compression (${\mathcal{E}}_{\mathrm{out}}=\sqrt{2.5}{\mathcal{E}}_{\mathrm{in}}$). Solid line, intensity distribution; dotted line, plasma density distribution. The intensity is normalized to the input maximum value.Reuse & Permissions

Figure 3

Snapshots of the intensity distribution $|\widehat{E}(z,r,\tau ){|}^2$ [$E(z,r,\tau )=\widehat{E}(z,r,\tau )\exp (i\tau )+\mathrm{c}.\mathrm{c}.$] of the 60-fs laser pulse with an input amplitude of $E_0=0.55$ and corresponding plasma density (as in Fig. 1 but with additional line corresponding to 2 times He ionization) along the propagation distance in a helium-filled capillary with a diameter of (a) $d=300\mu \mathrm{m}$ at a pressure of $p=2\mathrm{Torr}$ and (b) $d=1200\mu \mathrm{m}$ at $p=0.125\mathrm{Torr}$. The intensity is normalized to its maximum value.Reuse & Permissions

Figure 4

Time profiles of the laser pulse: black solid curve, input pulse; dotted curve, compressed pulse at a length of $L=2.635z_R$; continuous curve, transform-limited pulse.Reuse & Permissions