By phase‐modulating ring Airy Gaussian beams, ring Airy‐like beams propagating along predesigned parabolic trajectories are presented which combine the properties of accelerating beams and abruptly autofocusing beams analytically and numerically for the first time. The enhancement of the quadratic term ratio α shortens the autofocus distance and increases the slope of the beams after autofocusing. Interestingly, the main lobe tends to break into pieces as α increases and the possible reasons have been discussed. Furthermore, the distribution factor β and the radius of the primary r₀ can prominently affect the autofocus distance and the intensity at the focal point but do not change the slope of the beams after the autofocusing. In addition, the self‐healing properties are validated to be retainable while RAiG beams via predesigned parabolic trajectories with various α.

中文翻译：

---

沿预先设计的抛物线形轨迹像环形的环形光束

通过对环形艾里斯高斯光束进行相位调制，提出了沿预先设计的抛物线轨迹传播的环形艾里斯光束，这是分析和数字首次结合了加速光束和突然自动聚焦光束的特性。二次项比率α的增加会缩短自动聚焦距离，并增加自动聚焦后光束的斜率。有趣的是，随着α的增加，主瓣趋于破碎成碎片，并且可能的原因已经讨论过。此外，分布因子β和原边r ₀的半径会明显影响自动对焦的距离和焦点的强度，但不会改变自动对焦后光束的倾斜度。此外，RAiG光束通过预先设计的具有各种α的抛物线形轨迹，可验证其自我修复特性是否可保留。