Fig. 1. Achromatic metalens. (a) The schematic of the broadband achromatic metalens. As the incident wavelength changes, the focal point remains focused at the same spot. (b) The phase profile of the broadband achromatic metalens at the working wavelength.

Fig. 2. Unit element of broadband achromatic metalens. (a) Circularly polarized conversion efficiency (black curves) and phase profile (blue curve) for nano-rods with phase compensation of 770°. Insets illustrate the perspective view of the solid nanostructure. The unit element has 2800 nm periods along the $x$ and $y$ axes and its length and width are 1900 nm and 1200 nm, respectively. (b) Normalized electric energy for phase compensation of 770° at different incident wavelengths. The black line indicates the boundary of Si structures. The thickness of all Si nanopillars is fixed at $15\mathrm{\mu }\mathrm{m}$, standing on an ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate.

Fig. 3. Performance of broadband achromatic metalens. (a) The simulated ZX slices of the achromatic metalens with a designed focal length $f=100\mathrm{\mu }\mathrm{m}$. (b) Operating efficiency. (c) Full width at half-maximum (FWHM). (d) The focal lengths are calculated in the mid-infrared region.

Fig. 4. Broadband chromatic aberration controlled gradient metasurfaces. (a) Schematic for achromatic transmission gradient metasurface. (b) The angle of the transmission beam stays at around 26.53° when the incident wavelength is changed from $8\mathrm{to}12\mathrm{\mu }\mathrm{m}$.

Fig. 5. Simulated ZX slices with the simulated focal length between normal dispersion and the broadband super-chromatic aberration metalens, for the wavelength region ranging from 8 to 12 μm. The focal spot sizes are annotated as dashed white lines. (a) The normal dispersion focal lengths are $f=163$, 145, 128, 116, and 107 μm, respectively. (b) The super-chromatic aberration focal lengths are $f=302$, 215, 160, 137, and 107 μm, respectively.

Fig. 6. Contrast between normal dispersion and broadband super-chromatic aberration gradient metasurfaces at various incident wavelength transmission angles. (a) The normal dispersion angle of transmission changes among 28.2°, 32.2°, 35.8°, 40.8°, and 44.8° when the incident wavelength is changed from 8 to $12\mathrm{\mu }\mathrm{m}$. (b) The super-chromatic transmission angle changes among 25°, 30.4°, 35.8°, 41.6°, and 47.6° when the incident wavelength is changed from 8 to $12\mathrm{\mu }\mathrm{m}$.