Fig. 1. Distributions of laser intensity and phase in the near and far fields for three LG beams with different modes. (a) - (c) Near-field (z = 0 mm) intensity, the unit is I₀ = 10¹⁴ W/cm²; (d) - (f) Phase; (g) - (i) Far-field (z = ∞) intensity; (j) - (l) Phase, the intensity has been normalized, the phase is defined within [−π, π]

Fig. 1. [in Chinese]

Fig. 2. Spatial distributions of intensity and phase of the 15th harmonic generated by the three different modes of LG beams in the near and far fields

Fig. 3. Spatial distributions of intensity and phase of the 23th harmonic generated by the three different modes of LG beams in the near and far fields

Fig. 4. Spatial distributions of intensity and phase of the 31th harmonic generated by the three different modes of LG beams in the near and far fields

Fig. 5. Spatial distributions of coherence length of the 15th and 23th harmonics generated by the different modes of LG beams. The first two rows and the last two rows are shown the coherence lengths for short and long trajectories, respectively. Yellow color means the coherence length of harmonic is equal to or larger than 1 mm

Fig. 6. (a)-(c) Map of coherence length of the 31st harmonic under the LG_1,0, LG_1,1 and LG_1,2 beams; (d)-(f) Spatial intensity distribution of three different modes of LG beams.The unit of intensity is I₀ = 10¹⁴ W/cm²

Fig. 7. Spatial evolution of harmonic field inside the gas medium for the 15th (first column), 23th (second column) and 31th (third column) order generated by the different modes of LG beams. In the first, second and third rows, the results are given for the LG_1,0, LG_1,1 and LG_1,2 beams, respectively. The intensity of harmonic field has been normalized