Fig. 1. (a) Achromatic metalens designed by topological optimization. Working wavelength of this lens ranges from 450 nm to 650 nm. The figure on the right is the partial enlarged view. (b) Light field on six wavelength along the propagation axis, the white dotted lines are the designed focus plane. (c) Normalized intensity profile in focus plane. (d) Focus efficiency, which is defined as the power within a spot of diameter equal to 3 times the Full Width Half Maximum of the focus spot divided by the total incident power

Fig. 2. Achromatic metalens. (a) Relation between W-H with fixed NA = 0.15 and Δω = 6.28×10¹⁴ s⁻¹ (wavelength range of 500-600 nm); (b) Relation between W-NA with fixed H = 0.6 μm and Δω = 6.28×10¹⁴ s⁻¹; (c) Relation between W-Δω with fixed H = 0.6 μm and NA = 0.15. The dark-red lines are the predicted relation based on Eq. (9) - (11)

Fig. 3. Schematic of a single achromatic MDL. (a) 2D top view; (b) Height distribution along radius

Fig. 4. Intensity distribution of the light field in the focal plane. (a) Simulation result; (b) Calculation result

Fig. 5. (a) Full Width at Half Maximum of theory (blue), simulation (red) and calculation (black); (b) Focus efficiency of simulation (red) and calculation (black)

Fig. 6. Achromatic MDL in visible. (a) Relation between R-H with fixed NA = 0.1 and Δω = 6.28×10¹⁴s⁻¹ (500 - 600 nm); (b) Relation between R-NA with fixed H = 3 μm and Δω=6.28×10¹⁴s⁻¹ ; (c) Relation between R-Δω with fixed H = 3 μm and NA = 0.1; In infrared: (d) Relation between R-H with fixed NA = 0.15 and Δω = 1.54×10¹⁴s⁻¹ (1330-1492 nm); (e) Relation between R-NA with fixed H = 1.5 μm and Δω = 1.54×10¹⁴s⁻¹ ; (f) Relation between R-Δω with fixed H = 1.5 μm and NA = 0.15. The red lines are the predicted relation based on Eq. (15) - (17)