Intrinsic in-plane nodal chain and generalized quaternion charge protected nodal link in photonics

Nodal lines are degeneracies formed by crossing bands in three-dimensional momentum space. Interestingly, these degenerate lines can chain together via touching points and manifest as nodal chains. These nodal chains are usually embedded in two orthogonal planes and protected by the corresponding mirror symmetries. Here, we propose and demonstrate an in-plane nodal chain in photonics, where all chained nodal lines coexist in a single mirror plane instead of two orthogonal ones. The chain point is stabilized by the intrinsic symmetry that is specific to electromagnetic waves at the Г point of zero frequency. By adding another mirror plane, we find a nodal ring that is constructed by two higher bands and links with the in-plane nodal chain. The nodal link in momentum space exhibits non-Abelian characteristics on a C₂T - invariant plane, where admissible transitions of the nodal link structure are determined by generalized quaternion charges. Through near-field scanning measurements of bi-anisotropic metamaterials, we experimentally mapped out the in-plane nodal chain and nodal link in such systems.