# Generation of Higher-Order Poincaré Beams with Polarization States Varying Along the Propagation Direction Based on Dielectric Metasurfaces

## TL;DR

This paper introduces a metasurface method to generate higher-order Poincaré beams with polarization states that change along the beam's direction.

## Contribution

A novel dielectric metasurface design is proposed to manipulate polarization states of higher-order Poincaré beams along the propagation direction.

## Key findings

- A half-wave plate metasurface is designed using spatial partitioning to control polarization states.
- The metasurface generates first- and second-order vector beams with longitudinally varying polarization.
- Theoretical and simulated results align, confirming the method's feasibility.

## Abstract

Vector beams (VBs) with longitudinally varying polarization states provide a new dimension for light field manipulation, and promote the advancements of related areas such as optical metrology, longitudinal depth detection, and classical and quantum communications. In this study, we propose a half-wave plate dielectric metasurface based on a spatial partitioning method, realizing the longitudinal manipulation of the polarization states of higher-order Poincaré (HOP) beams by changing the elliptical polarization state of the incident light and selecting the appropriate propagation distances. The metasurface is composed of two sub-metasurfaces, and the two sets of a-Si:H meta-atoms are uniformly arranged on concentric rings of different radii with an equal interval. The propagation and Pancharatnam–Berry phases are utilized to construct the axicon and helical phase profiles. As a result, two sub-metasurfaces, respectively, generate the first- and second-order VBs with longitudinally varying polarization states. The polarization states of generated VBs correspond to points on different meridians of nth-order HOP spheres from the south pole to the north pole. The consistency between the theoretical and simulated results demonstrates the feasibility and practicability of the proposed method. This study provides an innovative strategy to extend the modulation of light fields from two-dimensional to three-dimensional space.