With the rapid development of micro-nano photonics technology, research on metalenses has mainly focused on light field manipulation, especially in the field of highly integrated imaging systems and optical communications. To address the issue of chromatic aberration caused by the limited working bandwidth of metalenses, as well as the challenges associated with small numerical aperture and large side lobe ratio in achromatic metalenses, we design an achromatic metalens based on the joint control of transmission phase and geometric phase. We also conduct in-depth research on its light field control performance, aiming to apply it in the fields of microscopic imaging, infrared detection, and optical communication.

We scan nanopillars of different sizes at different wavelengths to obtain the corresponding optical responses [Figs. 2(b) and 2(c)]. We find that, with changes in wavelength and nanopillar size, the cell structure can achieve -π?π phase control. Additionally, we observe that the transmittance of the nanopillars remained above 80%, regardless of size changes. We also notice that the light is confined within the nanopillars [Fig. 2(d)]. Therefore, we believe that the nanopillar dielectric unit meets the design requirements for this band. By calculating the ideal phase required for metalens focusing, as shown in Fig. 1(b), and comparing it with the simulated optical response, we notice the closest value, which helped establish the actual required phase response matrix. Using this matrix, the metalens model is created, as shown in Fig. 1(a), and simulated to obtain the light field intensity distribution map and focusing characteristics. To compare with achromatic metalenses, we also design a non-achromatic metalens with an operating wavelength of 1650 nm. We test the performance of the single-wavelength metalens at different wavelengths.

The discrete values of the light waves in the range of 1450?1650 nm are obtained, along with the field intensity distribution of the positive incident left-handed circularly polarized light, as shown in Fig. 3, and the focusing characteristics, as shown in Fig. 4. We calculate that the metalens had an average focal length of 13.89 μm, an average focusing efficiency of 24%, an average polarization conversion efficiency of 45.5%, an average sidelobe ratio of 0.04, and an average full width at half maximum (FWHM) of 1.04 μm at these wavelengths, approximating the diffraction limit. Additionally, we obtain the x-z plane field strength distribution of a single-wavelength metalens (Fig. 5), which operates at a wavelength of 1650 nm, where the focal point of the lens is at 14 μm. However, at other wavelengths, the focal length of the lens is 18.1 μm. The results show that the single-wavelength metalens exhibits significant chromatic aberration, which makes it difficult to achieve achromatism.

Based on the theory of joint control of the transmission phase and Pancharatnam-Berry (PB) phase, we design a metalens operating in the 1450?1650 nm wavelength band, using SiO₂ as the substrate and Si as the nanopillar material. Within the working bandwidth, the phase response of the cell structure can vary in the range of -π?π, and the transmittance remains stable above 0.8. The average focal length of the metalens is 13.89 μm, and the numerical aperture can reach 0.8165, which indicates good focusing performance. Through simulations, a wide-band achromatic metalens is designed with a large working bandwidth, high numerical aperture, and low sidelobe ratio, which makes it suitable for applications in infrared detection, optical communication, microscopic imaging, and other fields.