Hopfions are named after Heinz Hopf, who discovered the Hopf fibration in 1931. The preimages of any arbitrary points in S₂ are disjoint and interlinked circles (S₁) in S₃. The S₃ that resides in four-dimensional space can be "seen" by stereographic projection, and the topological features of linkedness of closed loops are preserved.

In a new paper published in eLight, a team of scientists, led by Professor Qiwen Zhan from the University of Shanghai for Science and Technology, have demonstrated dynamic scalar optical hopfions in the shape of a toroidal vortex. The "Scalar Optical Hopfions" paper showed how these toroidal vortices could be expressed as an approximate solution for Maxwell's equations. This research could find applications in artificial materials, nanostructures and optical communication.

The search for hopfions in physical systems started with the seminal work of Korepin and Faddeev. After nearly half a century, hopfions have been unveiled in various branches of science. Hopf structures have been discovered within superfluid helium as particle-like objects with finite dimensions and energy.

Null solutions to Maxwell's equations reveal that electromagnetic field lines, spin or polarization vectors can be tied based on the Hopf fibration to form diverse knots and links and exploited as information carriers.

Vortex lines in fluids appear in Hopf topological structures, and the linkedness and knottedness are conserved in inviscid fluids. Topological defect lines in liquid crystals are tweezed to create Hopf links. The abovementioned hopfions are vector hopfions in which each point in S₂ corresponds to a vector with multiple degrees of freedom.