Manipulating arbitrarily shaped Mathieu bottle beams based on geometric factor design

We demonstrate arbitrarily shaped Mathieu bottle beams (MBBs) based on geometric factor design. By elaborately selecting elliptical trajectory parameters and corresponding orders, the MBBs can be tailored to diverse longitudinal and transversal shapes simultaneously. The proposed method breaks through the limitation that the components of conventional bottle beams can only self-accelerate along paraxial paths with fixed shapes. Moreover, at both ends the MBBs exhibit ideally symmetric as well as abrupt autofocusing properties. The work presented in this paper would be of significance for the generation of optical bottle beams that are anticipated to find applications in optical manipulation and communication.