Continuous Lines of Topological Singularities in Metasurface Scattering Matrices: From Nodal to Exceptional

Topological properties of Hamiltonian matrices are well studied. However, photonic systems, often open, interact with their environment, and scattering matrices are used to characterize this interaction. Scattering matrices can exhibit their own unique topological features. We demonstrate that two-dimensional periodic photonic systems with open boundaries exhibit continuous lines of topological singularities (eigenvalue degeneracies) in their scattering matrices that are protected by mirror symmetry. In the three-dimensional frequency-momentum space, we find diabolic points and nodal lines, which transform into exceptional points and lines with material loss. These features in the scattering matrix’s eigenvalue structure appear as vortex lines in the cross-polarization scattering phase, linking the eigen-problem to observable phenomena. We demonstrate these effects numerically and experimentally using a reflective nonlocal metasurface. Our findings extend the understanding of symmetry-protected continuous topological singularities to the realm of scattering matrices, opening new avenues for novel photonic devices and advanced wavefront engineering techniques.