Fig. 1. (a) Experimental setup: BS, beam splitter; BPF, bandpass filter; TPS, Thomson parabola spectrometer. (b) 2ω_L and 1ω_L farfield patterns for 300-nm polymer foils. (c) Spectrum of scattered light from screen for a 100-nm polymer foil irradiated by LP laser. (d) Yields of 2ω_L and 1ω_L within θ < 15° and maximum proton energy ɛ_p as functions of defocus distance Δ for 300-nm polymer foils.

Fig. 2. (a) 2ω_L farfield patterns for 500-nm gold and 100-nm polymer foils at different defocus distances Δ. (b) Divergence angle θ_2ω as a function of Δ. The black solid line represents the simulation results for 300-nm polymer foils, and the circles are from Eq. (1) under the assumption of infinite radius of curvature. (c) Maximum proton energy as a function of θ_2ω.

Fig. 3. Simulation results for a 300-nm polymer foil irradiated by a LP laser. (a) 2ω_L farfield pattern at x = 49 cm calculated from the nearfield using the diffraction integral. The circles represent the azimuthally integrated profile, while the red solid line represents the fit with function sin² θ exp(−4 ln 2 sin² θ/D²). (b) Snapshot of electrons with kinetic energy greater than 0.5 MeV in x − r space at 35 fs. The gray area enclosed by the dashed line shows the initial foil. (c) On-target laser intensity distributions and corresponding 2ω_L farfield patterns at different defocus distances.

Fig. 4. (a) Divergence angle θ_2ω as a function of laser spot size D_L for different a₀. (b) A_R = θ_2ωD_L decreases with larger a₀. The solid line is a fit with A01+ηa0κ, where η ≈ 4.44 and κ ≈ −0.76 are fitting parameters. (c) Contours of a₀ and D_L as functions of θ_2ω and laser power P. The circles represent the simulation results. The star represents an experimental result assuming an ideal Gaussian laser spot. The square represents the same result with power corrected according to the focal image at low intensity. (d) Focal spot measured with a microscopic imaging system at low intensity. L1 and L2 represent line profiles along the minor and major diameters of the ellipse, respectively. (e) Farfield patterns from 300-nm copper foils when the OAP was rotated horizontally in the experiments. The red ellipses in the right corners illustrate the shape of the deformed focal spots. The corresponding cutoff proton energies are given at the bottom.

Fig. 5. (a) Farfield patterns at different incidence angles θ_i in simulations and experiments. (b) Divergence angle θ_2ω (circles) and yield W_2ω (squares) as functions of a₀. (c) Farfield patterns of foils with preplasma of different scale length l_s. The numbers at the bottom show the ratio of the corresponding W_2ω to that for l_s = 0 nm.

Fig. 6. Geometry used in CTR calculations. v is the particle velocity, k is the wave (observation) vector, and x axis is normal to the foil’s rear surface.