Fig. 1. Simulation results of propagation of circular swallowtail beam and circular Airy beam in free space. (a) CSB1: w=15 μm, r₀=418 μm; (b) CSB2: w=20 μm, r₀=200 μm; (c) CSB3: w=25 μm, r₀=120 μm; (d) CAB: w=30 μm, r₀=418 μm

Fig. 2. Simulation results of propagation of circular swallowtail beams in atmosphere turbulence. (a) CSB1; (b) CSB2; (c) CSB3; (d) CAB

Fig. 3. SI of CSB varying with propagation distance z under different structure parameters. (a) Cn2=10-9 m^-2/3; (b) Cn2=10-8 m^-2/3; (c) Cn2=10-7 m^-2/3; (d) Cn2=10-6 m^-2/3

Fig. 4. Changes in SI of CSBs with the same focal length under different scale factors w and controlling radius parameters r₀ when Cn2=10-7 m^-2/3. (a) Changes of autofocusing factor K; (b) SI varying with propagation distance z; (c) changes of K and SI at focal position