Fig. 1. 2^nd order FPBs (m=2, n=0) with C-point polarization on HyOPS

Fig. 2. Polarization and intensity of beams in (a) low-order correspondence and (b) high-order correspondence. ID: intensity distribution; RCP: right-handed circular polarization; LCP: left-handed circular polarization

Fig. 3. NCC of 2^nd and 4^th order FPBs at different propagation distances and turbulence intensities

Fig. 4. OAM components and mode purity of (a) the 2^nd order FPB and (b) the 4^th order FPB under different turbulence intensities at 3 km

Fig. 5. Comparison on NCC between (a) class 1 and (b) class 2 under different distances and turbulence intensities

Fig. 6. Comparison on MP between class 1 and class 2 under different turbulence intensities at 3 km

Fig. 7. (a) NCC and (b) MP between 2^nd order FPB and 1^st order CVB with 2θ change (2σ=0, r₀ = 0.125 m)

Fig. 8. The first three rows: NCC and MP performance of class 1 and class 2 when changing coordinates along a latitude line with 2θ=0 under (a), (d) weak turbulence (r₀=0.5 m); (b), (e) moderate turbulence (r₀=0.125 m) and (c), (g) strong turbulence (r₀=0.056 m) respectively. The last three rows: the dominated longitude and latitude regions of (g), (h), (i) 2^nd FPBs and (j), (k), (l) 4^th FPBs on HyOPS under weak, moderate and strong turbulence

Fig. 8. [in Chinese]

Fig. 9. Light intensity distributions of 2^nd order FPB in radial direction with 2σ change(without AT)