Light absorption and scattering pose great challenges to applications such as atmospheric optical communication and biological optical manipulation. Exploring special beams with minimal influence has been a research hotspot in light field manipulation. Currently, a mainstream method is to shape the beam by wavefront shaping to restore its light field. However, this method is quite complex and requires pre-calibration of the scattering process and restoration via complex algorithms, which increases the difficulty. Therefore, we directly look for a more robust beam that can reduce the light field distortion in complex environments. Meanwhile, we investigate the propagation characteristics of circular swallowtail beams with autofocusing properties in atmospheric turbulence. By analyzing the distortion and intensity fluctuations of the beam in complex environments, we study circular swallowtail beams' propagation in resisting turbulence scattering. Finally, theoretical support is provided for selecting beams that are stable and have high focal intensity and effective propagation in complex environments.

We utilize the Kolmogorov turbulence theory to model turbulence strength, and employ a modified power spectral density and the multi-phase screen method to simulate turbulence. The turbulence magnitude indicates the level of turbulent disturbance. Initially, we adopt the multi-phase screen method to simulate the propagation of beams in turbulence. Then, we observe the propagation process and perform statistical analysis of instantaneous intensity at the focal point. In experiments, an alcohol lamp and tin foil are leveraged to mimic turbulence conditions. The beam passes above the tin foil during monitoring beam disturbance via a CCD camera. Additionally, we calculate the scintillation index (SI) of the circular swallowtail beam using simulations to observe intensity fluctuations. Finally, we analyze variations in SI and autofocusing factor with parameters of the circular swallowtail beam, providing a quantitative analysis for selecting appropriate parameters.

As turbulence increases, the propagation quality of the swallowtail beam decreases, leading to beam drift and scintillation. By optimizing the beam scale factor and initial transverse position, the autofocusing stability can be improved. Theoretical studies have shown that circular swallowtail beams with strong autofocusing ability perform better in turbulence. This characteristic is attributed to the self-healing ability of swallowtail beams, which allows the beams to quickly restore their intensity distribution to a state close to the original after encountering obstacles. Specifically, based on catastrophe diffraction theory, the self-accelerating propagation properties of swallowtail and Airy beams arise from catastrophe caustics. Catastrophe caustics are regions where light intensity reaches the maximum, and are closely associated with stable“singularities”, also known as caustics. The structural stability of caustics is an inherent feature of catastrophe beams. The results demonstrate that circular swallowtail beams have advantages in resisting turbulence scattering, providing important options for optical communication, optical trapping, and light field manipulation in complex environments.

We analyze the propagation of beams after passing through turbulence, the longitudinal offset at the focal point, and the statistical distribution of the focal intensity position. The results indicate that circular swallowtail beams with strong self-healing abilities exhibit excellent robustness, with relatively small intensity distortion and fluctuations. Furthermore, by studying the SI variation with propagation distance, it is observed that circular swallowtail beams with strong autofocusing abilities are less disturbed, with lighter scintillation and advantages in intensity stability. Finally, by parameter scanning, a series of circular swallowtail beams with the same focal length but different size factors w and control radius parameters r₀ are identified. The autofocusing factor and SI are calculated for these beams. It is observed that the SI initially decreases and then increases with w and r₀, while the autofocusing factor (K) simultaneously increases and then decreases. The research results not only provide a solid basis for regulating the propagation characteristics of circular swallowtail beams in turbulence but also theoretical support for selecting stable, high focal intensity, thus effectively propagating beams in complex environments.