A new type of radially polarized odd-Pearcey Gaussian beam (RPOPGB) whose paraxial propagation in free space is studied analytically and numerically, is introduced. Intriguingly, the energy of RPOPGBs is found to auto-focus several times with the Gaussian beam waist radius increasing to some certain extents. Furthermore, RPOPGBs exhibit a special transversal intensity distribution that has an optical trap in the center. During the propagation, at first the RPOPGBs' two main lobes auto-focus toward the center with side lobes, and then the two main lobes separate after the end of auto-focusing. The Poynting vectors prove that the energy variation of the lobes maintains excellent central symmetry throughout the propagation. In addition, the fractional vortices are observed from the angular momentum and phase. These findings will be of potential use to particle capture.

中文翻译：

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自由空间中径向偏振奇皮尔西高斯光束的近轴传播特性

介绍了一种新型径向极化奇皮尔西高斯光束 (RPOPGB)，其在自由空间中的近轴传播进行了解析和数值研究。有趣的是，随着高斯束腰半径在一定程度上增加，RPOPGBs 的能量会自动聚焦多次。此外，RPOPGB 表现出特殊的横向强度分布，其中心有一个光阱。在传播过程中，RPOPGBs的两个主瓣首先用旁瓣向中心自动聚焦，自动聚焦结束后两个主瓣分离。坡印廷矢量证明，瓣的能量变化在整个传播过程中保持极好的中心对称性。此外，从角动量和相位观察到分数涡。