Focal Lengths Calculation of Metalens at Mid-infrared Wavelength

The paper proposes polarization insensitive metalens at mid-infrared wavelength (λ = 4 μm), comprising silicon as the emitter and silicon dioxide as the substrate. A 100 μm radius, 302 μm focal length, and 70.72% focal efficiency are achieved for metalens. The difference between the theoretical and simulated focal length is 0.0013%. Multiple metalenses with different radius are designed with the minimum difference between them. These results, including focal length, numerical aperture, focal efficiency, improve the design efficiency for the metalens based on the same structure. The proposed method provides the idea for metalens selection with the minimum difference between focal lengths and the development of an efficient mid-infrared metalens.