Advances on the manipulation of structured beams with multiple degrees of freedom

Structured beams manipulated by single or multiple degrees of freedom (DoFs) present novel physical properties, showing important research significance and practical value. Among them, orbital angular momentum (OAM), as a novel DoF, directly decides the phase and spatial distribution of laser beams. The independent manipulation of OAM or the coupled manipulation with spin angular momentum enables the construction of high-dimensional Hilbert space, which has already found broad applications in domains like ultra-large capacity optical communication, remote sensing detection and quantum communication. On this basis, considering the rapidly evolving application requirements, there is still a significant challenge to integrate the novel degrees of freedom with the traditional degrees of freedom, limiting the extension and expansion of high-dimensional and multi-dimensional structured beams. In this paper, from the perspective of two-degree-of-freedom manipulation methods, a series of structured beams coupled by two intrinsic DoFs is reviewed with emphasis on the vectorial vortex beams. Furthermore, we systematically review the manipulation of complex structured beams with multiple degrees of freedom that overcome the limitations of conventional two-degree-of-freedom. Also, the related work of our team is discussed here.