Fig. 1. The approximation of beam propagation into hohlraum. (a) An actual beam (quad) passes through the LEH and reaches the hohlraum wall, the ideal focal spot position locates near the LEH and the incident beam is defocusing in hohlraum. (b) The relationship of beam projection in hohlraum with propagation approximation.

Fig. 2. Beam clearance is required for incident beams. The dashed circle represents the maximal boundary of focal spot at the LEH.

Fig. 3. Two nearest-neighbor beams (quads) pass through the LEH and reach the hohlraum wall. Beam overlapping volume is emphasized with dark color, which represents the integral of two quads propagating in hohlraum.

Fig. 4. Circular spot, elliptical spot and special shaped spot, are designed to reduce the degree of beam overlap on hohlraum section. The dashed line is the maximal area limited from LEH as shown in Figure 2.

Fig. 5. Beam overlap characteristics of the proposed three shaped spots. (a) Circular spot; (b) elliptical spot; (c) special shaped spot.

Fig. 6. Peak intensity of single quad and beam overlapping volume as a function of the dimensionless numbers for (a) elliptical spot and (b) special shaped spot.

Fig. 7. The times of overlapping volume varied with the times of peak intensity of single quad to circular spot for the two proposed shaped spots.

Fig. 8. (a) The contour map of the designed CPP, which produces a special laser spot in the far field with super-Gaussian of order $sg=6$. (b) Speckled far-field intensity patterns produced by the full aperture illumination (no additional phase aberrations applied) of the CPP.

Fig. 9. Energy in shaped contour is plotted as a function of the phase-aberration strength $\unicode[STIX]{x1D6FE}$, the circular spot with equal area is also shown as a comparison.

Fig. 10. (a) Speckled far-field intensity patterns produced by phase aberrations, the profile of focal spot is a Gaussian distribution and the size is $30D_{DL}$. (b) Speckled far-field intensity patterns produced by the full aperture illumination of the CPP and phase aberrations.