# Momentum Analysis for Metasurfaces

## TL;DR

This paper introduces an analytical approach for designing metasurfaces by estimating source width within unit cells, enabling precise control over complex phase distributions and improving upon traditional sub-wavelength validation methods.

## Contribution

It presents a novel analytical method based on source width estimation and field pattern calculations, offering four design guidelines for advanced metasurface applications.

## Key findings

- Validated design of multi-foci lenses with equal focus strength
- Development of a convex-concave double lens
- Creation of large numerical aperture lenses with suppressed diffraction

## Abstract

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 sub-wavelength condition of unit cells, which is insufficient, especially for arbitrary phase distribution. Herein, we proposed an analytical method to design metasurfaces via estimating the width of the source in a unit cell. Also, by calculating field patterns in both real- and momentum-space, we provided four guidelines to direct future applications of metasurfaces, such as an arbitrary multi-foci 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. Besides metalens, this methodology can provide a wide platform for designing tailored and multifunctional metasurfaces in future, especially large-area ones in practical applications.