Fig. 1. Schematic diagram of GS algorithm

Fig. 2. Geometry diagram of the problem of beam shaping

Fig. 3. The results of the composite design method proposed by Feng et al^[28]. Freeform surfaces designed by different methods and their corresponding irradiance distributions, where the composite method (OTMOC) achieves both surface smoothness and image clarity simultaneously. (Adapted with permission from[28]. © 2015 Optical Society of America)

Fig. 4. The results of the composite design method proposed by Schmidt et al^[26]. Surface sags of the refractive part (geometric optics solution) (a), the pure diffractive part (c), and the freeform hologram (e) as a refractive-diffractive superposition to redistribute the initial Gaussian eigenmode emitted from a single mode fiber into a Yin Yang pattern in the far field; Simulated intensity distributions of the geometric (b) and composite (f) methods, and the difference (d); The realized farfield intensity distribution (g). (Adapted with permission from[26]. © 2020 Optical Society of America)

Fig. 5. The results of the composite design method proposed by Doskolovich et al^[30]. (a), (c), (e), (g) Geometric optics phase distribution (a) and the phase distributions obtained using the GS algorithms without (c) and with (e) phase smoothing. Phase distribution calculated using the GS algorithm with the quadratic initial phase (g); (b), (d), (f), (h) Normalized irradiance distributions generated in the target plane for phase distributions of Figs. (a), (c), (e) and (g), respectively. (Reprinted with permission from[30]. © 2021 Optical Society of America)