Fig. 1. Theoretical values of the derivative terms of each order, schematic diagram of the structure and distribution of unit structures in the database. (a) Theoretical values of the derivative terms of each order; (b) specific design diagram of unit structure; (c) distribution of unit structure and translation processing in the database

Fig. 2. Ring band matching flow chart, distribution chart and hierarchical optimization. (a) Flow chart for ring band matching and ring-band-dataset partitioning; (b) distribution of the structure and schematic diagram of the values taken for each dimension of the particle; (c) hierarchical fitness function design

Fig. 3. Flow chart for each optimization step. (a) Flow chart of the amplitude conversion method; (b) overall flow chart of HPSO

Fig. 4. Overall design flow of super-resolution wavelength-controlled zoom metalens

Fig. 5. GD and GDD matching situation and ring band structures amplitude distribution. （a） GD and GDD matching error； （b） amplitude distribution of each ring band structure

Fig. 6. Curves of focal length, FWHM and focused spot intensity normalization with wavelength of metalenses composed of three times randomly selected ring band structures obtained with VASM. (a)-(c) Curves of focal length;(d)-(f) curves of FWHM; (g)-(i) curves of focused spot intensity normalization

Fig. 7. Curves of hierarchica fitness, FWHM, focal length and focused spot intensity normalization with iterative optimization of metalenses obtained with VASM. (a) Curves of hierarchical fitness; (b) curves of FWHM and diffraction limit profile; (c) curve of focal length; (d) curve of focused spot intensity normalization

Fig. 8. Focal length, FWHM, intensity profile and focused spot intensity distribution of the optimized metalens obtained with VASM at 37 wavelengths and relevant amplitude distribution. (a) Curves of focal length; (b) curves of FWHM; (c) intensity normalization curves of metalens; (d) comparison of focused spot intensity distribution for two metalenses; (e) sidelobe ratio distribution; (f) curve of focused efficiency; (g)-(i) amplitude distribution of super-resolution zoom metalens at 3 wavelengths

Fig. 9. Unit structure corresponds to the position of the ring