Momentum Analysis for Metasurfaces

Utilizing discrete phase distribution to fit continuous phase distribution has been a primary routine for designing metasurfaces. In the existing method, the validation of the discrete designs is guaranteed only by using the subwavelength condition of unit cells, which is insufficient-especially for arbitrary phase distribution. Herein, we propose an analytical method to design metasurfaces by estimating the width of the source in a unit cell. Also, by calculating field patterns in both real and momentum space, we provide four guidelines for directing future applications of metasurfaces, such as an arbitrary multifocal lens with the same strength of each focus, a convex-concave double lens, and a lens with a large numerical aperture that can precisely prevent undesired diffraction orders. In addition to metalenses, this methodology can provide a wide platform for designing tailored and multifunctional metasurfaces in the future, especially large-area ones in practical applications.