Autofocusing and self-healing properties of circular Mathieu beam carrying orbital angular momentum

Abrupt autofocusing is defined as a phenomenon that the peak light intensity of an optical beam dramatically increases by several orders of magnitude while remaining low level near the focal point. As one new type of non-paraxial autofocusing light, the circular Mathieu beams (CMBs) exhibit flexible autofocusing features due to their tailorable parameters. In this work, the autofocusing and self-healing dynamics of CMBs carrying OAM have been investigated. The numerical results indicate that the autofocusing properties of CMBs are significantly affected by the topological charges and positions of optical vortices. Moreover, by embedding obstacles of diverse sizes in initial planes, we elaborately demonstrate the self-healing properties of CMBs in different cases. The experimental results are in good accordance with the numerical simulations. The work presented in this paper would be of significance for the generation of non-paraxial abruptly autofocusing beams and paves new way toward various applications such as optical communication, optical metrology and optical tweezer, etc.