Fig. 1. (a) Time-dependent ionization probability of 3s, 3p₀, and 3p₁ valence electrons of Ar atom in intense ultrashort laser fields with the laser peak intensity I = 8.0 × 10¹³ W/cm². The laser wavelength is 800 nm, and the pulse length is 20 optical cycles with sin² pulse shape. (b) Same as (a) for the laser peak intensity I = 3.0×10¹⁴ W/cm².

Fig. 2. Time-dependent ionization probability of the different molecular orbitals electrons of N₂ and CO in 800 nm, sin² laser pulse with 20 optical cycles in pulse duration. (a) N₂ molecule, for the peak intensity of laser field I = 8×10¹³ W/cm². (b) CO molecule, for the laser peak intensity I = 5.0×10¹³ W/cm².

Fig. 3. The orientation-dependent MPI probabilities for N₂ molecule and Ar atom at the peak intensity (a) I = 1×10¹⁴ W/cm² and (b) I = 5×10¹⁴ W/cm².

Fig. 4. The p-state photoelectron-momentum-distribution cross section of (a) Ne and (b) Ar driven by the 800-nm, linearly polarized, 20-cycle laser pulse along the z axis with a peak intensity of I = 1.0×10¹⁴ W/cm².

Fig. 5. (a) Resonance-enhanced structures of the HHG from He as a function of the laser intensity and the photon energy in the single atom response. (b) Same as (a) but for I = 7.0×10¹³ W/cm², I = 8.0×10¹³ W/cm², and I = 9.0×10¹³ W/cm², respectively. The black dashed lines in (a) and (b) indicate the transition energy of the 1s²-1s2p^1P (21.22 eV), and the black solid lines indicate ionization potential I_p.

Fig. 6. (a) Phase-matching of resonance-enhanced structures from Ar atom simulated by the TDDFT/OEP-SIC in a 730-nm laser field. The shift of the phase-matched RESs relative to the bound state energies is indicated in the inset. The laser peak intensity in the center of gas jet is I = 3.0×10¹³ W/cm², the confocal parameter of the laser beam is 35 mm, the length of gas jet is 2.0 mm, the pressure is 40 Torr, and the target is set at the laser focus –2 mm. (b) Same as (a) for the 60 Torr pressure.

Fig. 7. (a) and (c) Evolution of harmonic intensities in space for the 7th order harmonic (7H) and the 15th order harmonic (15H) of H₂ molecules obtained from the mac TDDFT in an 800-nm laser field. The laser peak intensity in the center of gas jet is I = 8.0×10¹³ W/cm², the pulse length is 20 optical cycles with cos² pulse shape. (b) and (d) The corresponding phase difference of the HHG.

Fig. 8. A scheme of dual-gas QPM

Fig. 9. Enhancement of the HHG in dual-gas QPM. For the reference, the corresponding one-gas result (blue dotted lines) is presented.

Fig. 10. (a) High-order harmonic spectra of He atoms driven by two color combined laser field with the proper time delay t_d. (b) Attosecond pulse generation by superposing hundreds of the harmonics shown in (a).

Table 1. High-precision bound state energies of H2+ at internuclear separation 2 a.u.

Table 2. Model potential parameters for He (in a.u.).

Table 3. Comparison of the calculated He atomic energies with the experimental values (in a.u.). For each angular momentum l, two rows of energies E_n,l are listed: the upper row refers to the calculated model-potential energies, and the lower row refers the experimental values.^[NIST]