Phase estimation method of metalens based on weighted Minkowski distance

Metalenses can break through the performance limitations of traditional optical systems through specially designed nanostructures, enabling lightweight, high-resolution imaging. There exists a discrepancy between the ideal phase distribution of achromatic metalenses and the actual phase distribution of real meta-atoms, which is difficult to quantify. Methods based on Manhattan or Euclidean distance tend to overlook the impact of large errors at certain frequency points, resulting in poor flexibility. To address the aforementioned issues, an error estimation method based on the weighted Minkowski distance was proposed. By establishing correlation models between the spatial dimension p and radial position, the weight vector w and single-frequency error as well as dispersion, this method enhanced the responsiveness to broadband spectral features and spatial phase gradient variations, thereby more effectively suppressing phase deviations at certain frequency points. Simulation results show that metalenses designed with weighted Minkowski estimation method achieves a higher focusing efficiency of 27.974% and demonstrates superior overall performance compared to designs based on conventional methods.