Objective The diffraction-limited phenomenon in optical imaging make the evanescent wave carrying high-order modes of the beam attenuate rapidly when it leaves the object surface, which results in low resolution and affects imaging quality. At the same time, the modulation mechanism from traditional optics makes an optical system highly integrated, which is still difficult. Owing to the miniaturization and flexible control of phase, amplitude, and polarization of the beam, metalenses have been widely used in a variety of highly compact and efficient devices. To overcome dispersion effect caused by the incident light with different frequencies passing through dielectric materials and to reduce the impact on the imaging effect of an optical system in the wideband spectrum, a metalens is designed herein, which achieves constant focus in the visible light band from 500nm to 550nm based on the titanium dioxide unit nanopillar. At the same time, to reduce the energy loss caused by the introduction of a polarizer in the traditional optical system, the achromatic metalens is introduced, which has also polarization-insensitive characteristics. The lens improves the imaging resolution of a multi-wavelength microscopy imaging system and has good applicability in the fields of digital cameras and optical instruments.

Methods Based on the phase compensation theory, the transmission phase method and the particle swarm optimization algorithm are used in this paper to design an achromatic metalens, and the first and higher derivative terms of the incident light phase information can make the incident light with different wavelengths arrive at the same time. In the same focal plane, to achieve this goal, the unit structure that meets this condition is selected. Usually, the geometric phase method is used for designing with polarization sensitivity. To satisfy the polarization insensitivity of the metalens on the basis of achromatic aberration and ensure both linearly polarized light and circularly polarized light to be incident, square nanopillars are selected as functional units here. After the structure of the unit has been determined, the selection of the unit with different widths and the design of the arrangement mode are studied in order to achieve the effective control of the deflection of the incident light beam with different wavelengths and achieve the correction effect of chromatic aberration. The width and height of a square nanopillar as well as the distance between the centers of adjacent nanopillars are optimized. The cross-sectional area of the square ranges from 0 to 1 to maximize the filling factor range and ensures that the polarization is not sensitive. The height of the square unit pillar is set as 600nm to improve phase coverage. In actual manufacturing, due to the limited process level, the achievable shortest unit column width is 80nm and the maximum width is the center distance of adjacent nanopillars. The Nyquist sampling criterion is followed to ensure the integrity of the beam information and ensure that the efficiency impact is low. The particle swarm optimization algorithm is used to select a structure, which achieves the achromatic effect to match the ideal phase value at each pixel, and the titanium dioxide nanopillars are scanned using the CST Microwave Studio electromagnetic simulation software to obtain the final superstructure with different unit nanopillar widths corresponding to the phases required for lens arrangement. To excite guided-mode resonances with different dispersion, the period of the unit column should be greater than the bandwidth of all transmitted wavelengths and smaller than the wavelength of incident light in free space to suppress higher-order diffraction. Therefore, the period of the unit column is 400nm.

Results and Discussions Due to the dispersion of optical materials, the obtained images have chromatic aberration. The use of polarizers in traditional optical systems causes energy loss, and the overall device energy utilization rate is low. At present, most of the designed metalenses with an achromatic function in visible light and near-infrared light have polarization sensitivity. Therefore, this paper presents the design of an achromatic polarization-insensitive metalens based on the titanium dioxide unit nanopillar. In addition, the selected basic unit column is scanned using the CST Microwave Studio electromagnetic simulation software to make phases of unit columns with different widths linearly propotortional to the incident light frequency (Fig. 3). At the same time, the particle swarm optimization algorithm is used to find the additional constant phase for adjusting the wavefront, and the optimal phase distribution is obtained, which is used for the metalens to achieve the achromatic effect. Compared with the phase distribution obtained without the particle swarm optimization algorithm, the obvious phase compensation improves the focusing efficiency without chromatic aberration (Fig. 4). By simulating the polarization-insensitive achromatic metalens designed in this paper, the achromatic effect is achieved at the focal length of 450nm for the incident light with 500--550 nm wavelength, and it is compared with that of a dispersive metalens with the same numerical aperture (Fig. 6). The CST Microwave Studio electromagnetic simulation software is used to simulate the intensity of the reflected beam by the metalens. It is observed that the intensity of the reflected beam in the xoy plane exceeds 90% (Fig. 7). To verify the polarization insensitivity of the selected functional unit, the polarization angle is set between 0 and 90° with 9° as the step sweep parameter under the incidence of linear polarized light of a single nanopillar. Under different polarization states, the same diffraction efficiency of the incident light at different angles of incidence remains constant, and the diffraction efficiency increases with the increase of the wavelength. Therefore, the metalens designed in this paper effectively realizes the achromatic and polarization-insensitive characteristics.

Conclusions To summarize, this paper presents the use of titanium dioxide nanomaterials to design a reflective metalens under visible light. The chromatic aberration is successfully eliminated between 500nm and 550nm incident light, and the designed achromatic polarization-insensitive metalens is compared with a dispersive metalens with the same numerical aperture. It is a breakthrough in the limitation of traditional diffractive optics. To achieve achromatic effects, the achromatic polarization-insensitive metalens designed in this paper allows linearly polarized light and circularly polarized light with different chirality to be incident. Based on the design method of transmission phase theory and particle swarm optimization algorithm, this paper provides a reference for the field of metasurface device design, makes a contribution to the high integration of optical systems, and the designed achromatic polarization-insensitive metalens has a wide range of application in microscopic imaging and optical instruments.