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.

节点线是由三维动量空间中的带交叉形成的简并性。有趣的是，这些退化的线可以通过接触点链接在一起，并表现为节点链。这些节点链通常嵌入两个正交平面中，并受到相应镜面对称性的保护。在这里，我们提出并证明了光子学中的面内节点链，其中所有链接的节点线共存于一个镜面中，而不是两个正交的镜面中。链点通过固有对称性而稳定，固有对称性在零频率的Г点处对电磁波具有特定性。通过添加另一个镜像平面，我们发现了一个节点环，该节点环由两个较高的带构成，并与平面内节点链链接。动量空间中的节点链接在C上表现出非阿贝尔特征₂ T-不变平面，其中节点链接结构的容许过渡由广义四元数电荷确定。通过对双各向异性超材料的近场扫描测量，我们在这种系统中通过实验绘制出了平面内的节链和节链。