With the widespread utilization of light-sensing systems and imaging systems, miniaturized and lightweight optical systems have become increasingly popular in the automotive market, industry, and medical and consumer electronics. The development of small-volume optical lenses has become crucial. Traditional optical lenses usually have large volume, low focusing efficiency, large full-width half-maximum of the spot, and poor performance in lenses with high numerical aperture (NA). The optical metasurface with sub-wavelength structures has powerful control over the light phase. Compared to traditional lenses, metalenses feature smaller volumes, thinner thickness, and better focusing performance. In the metalens design, the inverse design method has less computational complexity than the traditional design method, and meanwhile this method can provide an optimal solution for the device in a larger searchable space and improve the design efficiency. We propose an objective-first algorithm-based inverse design approach to design a low refractive index-based metalens structure. At a working wavelength of 1550 nm, the metalens has a thickness of 3.2 μm in the propagation direction, a focusing efficiency of 72%, and a high NA of 0.82. Compared with the traditional design method, this approach has low computational complexity and high efficiency. The designed devices can be rapidly manufactured by the high-precision micro-nano printing technique. Considering possible errors during the metalens fabrication, the effects of metalens contour offset and 3D rotation operations on the designed 2D metalens are further discussed.

In the objective-first algorithm, we define a simulation design area on a two-dimensional plane, and the device function can be determined by giving the incident and exit conditions on the design area. During the metalens design, we require that the device can convert the incident parallel wavefront into a spherical wavefront during exiting. After determining the phase distribution of the input and output, we iteratively update the design area by the objective-first inverse design method. This method employs the norm of Maxwell's equations as the objective function of the optimization algorithm, and the value of this objective function is called the physical residual. During the optimization iteration, we interpolate the dielectric constant, allowing it to continuously change within the design area. The advantage is that the algorithm has a larger searchable space. Meanwhile, we achieve rapid transformation between continuous and binary structures by adding a penalty function.

The materials that make up the lens are air with a dielectric constant of 1 and a low-refractive index polymer material with a dielectric constant of 1.52. The focal length of the metalens is set to 11.3λ, the width of the device along the propagation direction is 2.1λ, and the length is 32.2λ. The grid in the design area is a square with a side length of 0.065λ, and the corresponding NA is 0.82. By utilizing the scalability of Maxwell's equations, we therefore scale the lens to a wavelength of 1550 nm. In theory, the metalens optimized by this method can be scaled as needed to meet the focusing requirements of different wavebands. At the operating wavelength of 1550 nm, the focal length of the metalens is 17.5 μm, the width is 3.2 μm, and the length is 50 μm. The grid in the design area is a square with a side length of 100 nm, and the focusing efficiency is 72%. The 3 dB bandwidth is calculated as 1447 to 1667 nm, and the half-maximum width is 0.9 μm, slightly lower than the 0.96 μm limit imposed by diffraction. Within the offset range of plus or minus 50 nm of the hyperlens profile, the focusing efficiency is above 60%. It can be concluded that the focusing performance of the lens remains essentially unchanged within the offset range of 50 nm. When the lens profile is shifted by plus or minus 100 nm, the focusing efficiency drops to around 50%, and the focusing performance of the lens starts to decline significantly. A metalens with a negative profile shift exhibits a shorter focal length, while a metalens with a positive profile shift exhibits a longer focal length.

To address the problems associated with traditional lenses, such as their large volume, low NA, and insufficient focusing efficiency, we focus on optimizing the structure of polymer lenses with low refractive index. This is achieved by adopting the objective-first inverse design method and the focusing characteristics of metalenses. The goal is to design a metalens structure featuring high NA and focusing efficiency, with the limitations imposed by optical diffraction performance considered. Additionally, the objective-first inverse design method is employed to relax the restrictions of Maxwell's equation and utilize it as the objective function. By breaking down the objective function into two sub-problems, the optimization process can be carried out efficiently without getting stuck in low-efficiency local solutions. Additionally, structural variables are limited to ensure that the finalized structure obtained via interpolation during the optimization is binary in nature and highly efficient. Meanwhile, we discuss the potential for contour deviation during the micro-nano printing preparation of the metalens due to manufacturing tolerances. We analyze the performance changes of the metalens within a profile deviation range of 100 nm. The results demonstrate the robustness of our optimization approach to manufacturing tolerances, with the metalens showing relatively sound focusing performance even with small deviations from the desired profile. Furthermore, we conduct three-dimensional FDTD simulations by rotating the metalens, which reveals that the metalens exhibits polarization-independent characteristics and achieves a focusing efficiency of 62% under incident conditions of circularly polarized light.