Focus shift suppression of a wide field-of-view metalens enabled by an optimized quadratic equation

• An innovative approach to suppress quadratic metalens focal shift and improve focusing efficiency by introducing a weak phase gradient is proposed. • Wide-angle imaging mechanisms with quadratic metalenses have inherent limitations such as focus shift and lower focusing efficiency. • Optimized polarization-independent quadratic metalens operating at a wavelength of 4.2μm to achieve minimum focal shift and high focusing efficiency in the mid-wave infrared band. • Its excellent focusing performances are also evaluated by both simulations. Metalenses are novel nanoscale optical elements that have attracted significant interest due to their compact size and high precision. Over the last few years, quadratic metalens has addressed the critical issue of achieving a wide field of view (WFOV) with a single-layer structure. However, the quadratic phase profiles with large phase gradients can cause focal shift and lower focusing efficiency. Therefore, designing a WFOV metalens that can achieve minimum focal shift and high focusing efficiency remains a major challenge. To address the issues, we introduce a weak phase gradient for the quadratic phase profiles by controlling the optimization coefficient to suppress the focus shift and improve the focusing efficiency. As an example, a polarization-independent metalens operating at a wavelength of 4.2 μm is designed based on our proposed optimized quadratic phase profile. Numerical results demonstrate that the optimized quadratic metalens can achieve a minimum focal shift of only 1.95 % within a 120° field-of-view (FOV) and an average focusing efficiency twice that of conventional quadratic metalenses within a 40°FOV. This study recommends an optimized method for the quadratic phase profile to suppress focus shift and improve the focusing efficiency of WFOV metalenses. The design can be extended to other wavebands.