Fig. 1. The top row shows PIC simulation results for a single slit with w = 2.6 µm and d = 70 nm at t = 24T₀ (79.92 fs): (a) and (b) electron density and E_y field distributions in the (x, y) plane for a₀ = 0.5 and a₀ = 5, respectively; (c) electron density for an intense laser field (a₀ = 5) along the y axis averaged over x = 2–2.07 µm where the single slit was initially located on the x axis. The bottom row (d)–(f) shows the corresponding results at t = 44T₀ (146.52 fs). The dashed black lines indicate the initial positions of the single-slit edges.

Fig. 2. (a) Maximum E_y (a) at the rear side of the target and (b) transmission rate for a₀ = 0.5 and a₀ = 5 plotted as functions of thickness for w = 2.6 µm. (c) and (d) Corresponding quantities plotted as functions of width for d = 20 nm and d = 70 nm. The dashed black lines in all the plots indicate the corresponding results of a classical optical diffraction simulation obtained from the measurements using the Kirchhoff diffraction formula.

Fig. 3. The top row shows simulation results comparing the interactions of a relativistically intense laser with different targets of the same width w = 2.6 µm at t = 59T₀: (a) a single slit of thickness d = 20 nm; (b) periodic slits of thickness d = 20 nm and adjacent spacing ds = 16 µm; (c) a waveguide. The bottom row (d)–(f) shows the corresponding results at t = 139T₀.

Fig. 4. Time evolution of electric field amplitude for targets with different numbers N of slits with w = 2.6 µm, d = 20 nm, and ds = 16 µm. In all other cases of periodic slits, the number of slits varies for different values of ds, because we have fixed the propagation distance with a total length of L = 160 µm.

Fig. 5. The top row shows the effects of thickness on (a) the maximum focusing E_y and (b) its corresponding focal positions, defined as the distances on the x axis away from the initial position of the slits, x = 20 µm. The bottom row shows the effects of (c) adjacent distance and (d) normalized laser amplitude on the maximum focusing E_y. The maximum focusing fields of the periodic slits in (a) and (c) are compared with the corresponding results for a single slit and a waveguide of the same width. The focal positions of the periodic slits in (b) are compared with those for a single slit and the result of optical diffraction focusing. To ensure the validity of the results of the interaction between the ultraintense laser and the slits, the electron density in (d) is set to n_e = 100n_c, whereas n_e = 50n_c is always set in all the other simulations.

Fig. 6. (a) Guiding efficiency of periodic slits, with constant thickness d = 20 nm, plotted as a function of adjacent spacing ds for various widths w = 2.6 µm and w = 8 µm, compared with the results for waveguides with the same width. (b) Time envelope of electric field amplitude for targets of 8 µm width: periodic slits with three different adjacent spacings ds = 16, and 30, and 40 µm, and a channel. (c) Corresponding results for width w = 2.6 µm. (d), (e), and (f) Variations of field energy, particle energy, and electron energy, respectively, with time for the same targets as in (b).

Fig. 7. (a) Maximum E_y and (b) transmission rate for n_e = 50n_c and n_e = 100n_c, plotted as functions of thickness d with w = 2.6 µm.

Fig. 8. (a) Maximum E_y for τ₀ = 66.6 fs and τ₀ = 33.3 fs plotted as a function of thickness d = 20–120 nm with w = 2.6 µm. (b) Corresponding transmission rate under the same conditions as in (a). (c) Maximum E_y for τ₀ = 66.6 fs, plotted as a function of thickness d = 20–200 nm with w = 2.6 µm.

Fig. 9. Distributions of E_y and n_e obtained from 3D simulation at the moment of reaching the maximum value for (a) a single slit and (b) periodic slits with the same width and thickness. The laser propagates from right to left, aligned with the positive direction of the x axis.