Multi-zone taylor expansion method for broadband achromatic polarization-insensitive metalens design

Broadband achromatic polarization-insensitive metalens with large numerical aperture (NA), large diameter and high efficiency are in demand. Existing methods can dramatically improve one of the above performances at the expense of the others. In this work, the multi-zone Taylor expansion method (MZTEM) is proposed to reduce these trade-offs between different key figures of merit. In this method, a metalens is devided into odd ring and even ring regions, then the odd (even) ring metalens focus peak is shifted forward with tailored functions of even (odd) ring region, and finally the arrangement of the meta-units is optimized to get higher efficiency. Based on the MZTEM, an achromatic polarization-insensitive lithium niobate on insulator (LNOI) metalens is designed working in the visible from wavelength lambda = 430 nm to 750 nm, which exhibits a focusing efficiency of 35%-63% and NA of 0.255. Besides, the full width at half maxima (FWHM) variation is less than 0.14 mu m and the focusing efficiency variation is less than 2% within 0 degrees-10 degrees incidence angle.