Fig. 1. Scanning electron microscope (SEM) images of micro-cylinder targets: (a) wire spatial distribution, (b) the orientation of the wires with respect to the Silicon substrate. Laser is incident parallel to the wires (white arrow); (c–e) 3D PIC simulations of laser propagating between the micro-wires. (f) The electron phase-space distribution for the micro-cylinder (MC) target and flat target. The laser amplitude, pulse duration and spot size are $a_{0}=21$ ($\times \,10^{21}~\text{W}/\text{cm}^{2}$), $\unicode[STIX]{x1D70F}_{0}=40$ fs and $w_{0}=4\unicode[STIX]{x1D706}_{0}$, respectively.

Fig. 2. (a) The electron energy distribution for the MC target (red solid) and the flat foil (black solid); (b) experimental results from two experimental shots, with Si array target (shot #1 and #2) and a flat target (flat solid).

Fig. 3. 2D simulations on laser interacting with (a) a short and dense cylinder array target and (b) a long and sparse one. The electron energy distribution for both targets are shown in (c). The electron spectrum for a flat target is added for comparison. The cylinders and substrates [the gray area in (a) and (b)] are made of carbon. The laser amplitude, pulse duration and spot size are $a_{0}=21\times 10^{21}~\text{W}/\text{cm}^{2}$, $\unicode[STIX]{x1D70F}_{0}=40$ fs and $w_{\text{y}}=3\unicode[STIX]{x1D706}_{0}$, respectively.

Fig. 4. Scheme of laser–micro-tube interaction. (a) Design of a relativistic fs laser impinging on a periodic micro-tube target. (b) Iso-surface plots for the laser intensity distribution before and after it enters the tube. The section of the tube shown above is $32~\unicode[STIX]{x03BC}\text{m}$ long; the length of the simulated tube is $120~\unicode[STIX]{x03BC}\text{m}$. (c) Light intensity distribution on the $x$–$y$ plane for the input pulse and in-tube pulse.

Fig. 5. Laser field distribution at $t=$ (a) $14T_{0}$, (b) $22T_{0}$ and (c) $30T_{0}$. The averaged laser intensity distribution in the $y$–$z$ plane is shown for (d) the input laser and (e) in-tube laser.

Fig. 6. (a) The intensity profile on the $y$-axis for inner radius of $2\unicode[STIX]{x1D706}_{0}$ (cyan solid), $3\unicode[STIX]{x1D706}_{0}$ (red solid) and $4\unicode[STIX]{x1D706}_{0}$ (blue solid). The initial pulse profile is denoted in black dashed. (b) The peak in-tube intensity as a function of simulation time for input laser amplitude of $a_{0}=20$, 50, 100, 200, 300, respectively. (c) The intensification factor versus the input laser intensity. (d) The averaged electrons density distribution on the $y$-axis for $a_{0}=1$, 20 and 200.

Fig. 7. The averaged (a) electrostatic field (E-field) and (b) magnetic field (B-field) of the tube. The color bar shows the field strength normalized by the incident laser field amplitude $E_{0}$ and $B_{0}$, while the arrows denote the orientation. We are looking to the opposite of the laser propagation direction. The orientation of the B-field in (b) is clock-wise.

Fig. 8. The laser hitting between the wires in Case A and right on a wire in Case B. The right column shows the energy spectra for both cases. All other simulation parameters are the same as in Figure 1.

Fig. 9. Laser interacting with smaller tubes with inner diameter of $3\unicode[STIX]{x1D706}_{0}$. Case A, B and C show the three different landing spots of the laser beam. The corresponding electron spectra are listed in the lower row. The laser pulse is of peak intensity $10^{21}~\text{W}/\text{cm}^{2}$, duration 40 fs and spot size $8\unicode[STIX]{x1D706}_{0}$.