Fig. 1. Photoelectron momentum distributions of hydrogen atoms simulated by (a)–(c) the semiclassical rescattering model (SRM, α is set to zero; red dots on the interference minima are just for guiding the eyes) and (d)–(f) TDSE. Because there are not many optical cycles in the pulse, the TDSE results are asymmetric with respect to the p_x = 0 axis. The top two panels correspond to wavelengths of (a), (d) λ=1900nm, (b), (e) λ=2000nm, and (c), (f) λ=2100nm, respectively. (g) Typical trajectories that form the spiderlike structure in the SRM: the parent ion is at the origin of the axis. The pink curve is the reference trajectory, and the red curve is the signal trajectory. A scattering angle of 5° is assumed for the signal trajectory. (h) Cut-plot curves taken at p_x = 0.4 a.u. for the SRM (blue) and TDSE (red), and the cut positions are marked by the colored vertical lines in (b) and (e). Intensity of the laser pulse is I = 4×1013W/cm2, and the pulse duration is two optical cycles.

Fig. 2. Spiderlike structures numerically obtained by the SRM. The patterns correspond to phase values of (a) α=0, (b) π/20, (c) π/10, (d) 3π/20, (e) π/5, (f) π/4, and (g) 3π/10, respectively. (h) Cut-plot curves are taken at p_x = 0.4 a.u. from the spiderlike patterns in (a) (blue solid curve), (b) (red solid curve), (c) (green solid curve), (d) (black solid curve), (e) (blue dotted curve), (f) (red dotted curve), and (g) (green dotted curve), respectively. The cut positions are marked by the colored vertical lines in (a)–(g). The laser parameters are the same as in Fig. 1.

Fig. 3. (a) Blue area presents the tunneling time range of signal electron wavepackets and reference electron wavepackets involved in the spiderlike structures. The red curve presents the rescattering time range of signal electron wavepackets. (b) Variations of the time difference between rescattering of the signal electron and ionization of the reference electron with p_x. The red circles, blue circles, and black pluses represent the time difference extracted by fitting the cut-plot curves of the spiderlike structure using Eq. (9), the time differences obtained by the SRM, and the time differences calculated by the saddle-point equations, respectively.

Fig. 4. (a) Cut-plot curves are taken at p_x = 0.4 a.u. from the spiderlike patterns corresponding to α=0 (blue curve), π/10 (red curve), π/5 (green curve), and 3π/10 (black curve), respectively. The first, second, and third interference minimum positions are marked by black dotted circles. (b) Variations of the interference minimum positions (values of transverse momenta or p_y) of the cut-plot curves taken at p_x = 0.4 a.u. with α. The first, second, and third interference minimum positions calculated using Eq. (9) are marked by blue circles. For comparison, the corresponding positions calculated by the SRM are shown by red pluses, red crosses, and red star symbols.

Fig. 5. (a) Values of phase α extracted from the cut-plot curves simulated by TDSE, plotted as a function of p_y. (b) Cut-plot curves taken at p_x = 0.4 a.u. The red dashed curve represents the curve obtained from TDSE. The blue solid curve represents the modified results of Fig. 1(a) after considering a phase value given in Fig. 5(a) in SRM.