Generation and High-Resolution Focusing of Higher-Order Vector Beam via Metasurface

The generation and focusing properties of higher-order vector beam have attracted lots of interests due to its significant applications. In this paper, we derived the formula of transforming linear polarization into higher-order vector beam with high mode purity, and this approach is applicable to generating vector beam with arbitrary polarization pattern. Based on the derived formula, the focusing properties of higher-order vector beam by dielectric metasurface lens are studied, which exhibit an Abbe-limit-breaking feature for small numerical aperture (NA), i.e., NA$< $0.6. When a binary phase (0 $ \& \,\pi$) is further imposed on the aperture of metasurface lens, the focusing spot of fourth-order polarization breaks Abbe limit even by 14.3$\%$ at NA = 0.6. In addition, the effect of fabrication tolerance, say, substrate thickness and central deviation, on the focusing feature of higher-order vector beam is also investigated. Our study may find significant applications in achieving higher-resolution lithography and imaging, say, by just replacing conventional linearly or circularly polarized source with higher-order vector beam.