  A nodal link is a special form of a line degeneracy (a nodal line) between
adjacent bands in the momentum space of a three-dimensional topological
crystal. Unlike nodal chains or knots, a nodal link consists of two or more
mutually-linked rings that do not touch each other. Recent studies on
non-Abelian band topology revealed that the topological charges of the nodal
links can have the properties of quaternions. However, a photonic crystal that
has a nodal link with non-Abelian charges has not been reported. Here, we
propose dielectric photonic crystals in forms of double diamond structures
which realize the nodal links in the momentum space. By examining the evolution
of the eigenstate correlations along the closed loops which enclose the nodal
line(s) of the links, their non-Abelian topological charges are also analyzed.
The proposed design scheme and theoretical approach in this work will allow for
experimental observation of photonic non-Abelian charges in purely dielectric
materials and facilitate the control of the degeneracy in complex photonic
structures.
