  The generation and focusing properties of higher-order polarized beams have
attracted lots of interests due to its significant applications. In this
paper,we derived the formula of transforming linear polarization into
higher-order polarization, which is applicable to generating arbitrary order
polarization. Based on the derived formula, the focusing properties of
higher-order polarization by dielectric metasurface lens are studied , which
exhibit an Abbe-limit-breaking feature for small numerical aperture, 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 polarization is also investigated. Our study may find
significant applications in achieving higher-resolution lithography and
imaging, say, by just replacing conventional linear or circular polarization
with higher-order polarization.
