Topological structure synthesized by three-dimensional spin angular momentum of light

Hopf links are important topological structures found in a range of disciplines. They represent the projection of higher-dimensional objects to three-dimensional (3D) physical space. Optical Hopf fibration texture has been demonstrated by synthesizing the transverse states of polarization and the phase. In this work, we demonstrate synthesizing Hopf links by 3D spin angular momentum (SAM) through tight focusing complex optical fields with a 4Pi confocal optical system. The focal volume under tight focusing provides a platform for manipulating the nonnegligible z-component of the electric field and thus the 3D states of polarization. Hopf links that consist of two and three disjoint and linked circles are shown as examples. Since Hopf links are topological objects that are projected from higher-dimensions, they may find applications in high-dimensional optical data storage and encryption or be exploited as information carriers.