High-efficiency, large-scale, high-numerical-aperture achromatic flat lens via focal phasor matching

Flat lenses, including metalenses and diffractive lenses, have attracted considerable attention for enabling miniaturized optical systems. However, achieving large-scale flat lenses with both a large numerical aperture (NA) and high achromatic performance remains a significant challenge. In this work, we propose a structural height optimization method named focal phasor matching to achieve high-performance designs for large apertures. To ensure computational accuracy, an interfacial diffraction integral approach is further employed to account for the complete diffraction process in free space. Numerical results demonstrate that this method achieves significantly higher focusing efficiency than the height sequence obtained through direct optimization. For all considered apertures, the minimum relative intensity at focus is improved to 57% using the proposed method. Experimentally, we successfully design and fabricate an achromatic multi-level diffractive lens (MDL) with a diameter of 0.4 mm and 0.5 NA by two-photon polymerization lithography. The fabricated MDL exhibits excellent achromatic performance, with a focal shift of less than 1%. Due to the single-layer structure and the use of low-refractive-index material, the designed MDL has the potential to be economically and efficiently replicated using nanoimprint lithography.