Octopole orbital corner states in terahertz spoof plasmonic crystals with two-dimensional Su-Schrieffer-Heeger lattice

Connecting topological states with $p$-orbital freedom has led to rich, insightful physics phenomena. Yet topological corner states have rarely been associated with modes of higher orbitals than $p$ orbital due to the entanglement proneness of higher orbital bands in photonics. This paper theoretically investigates higher orbital corner states in a two-dimensional (2D) Su-Schrieffer-Heeger (SSH) lattice and experimentally demonstrates octopole orbital corner states in a terahertz spoof plasmonic crystal. The orbital Hamiltonian is derived by introducing a pair of orthogonal orbitals into a 2D SSH lattice tight-binding model. Based on the expanded lattice, the presence of orbital corner states is demonstrated, which can be characterized by the generalized winding number. The counterpart of the tight-binding model in plasmonic crystals is identified, revealing eight octopole corner states. These states, comprising four even and four odd modes, are demonstrated through eigenenergy spectra and field distributions. Interestingly, the octopole corner states emerge without orbital-hopping symmetry, which differs from the $p$-orbital corner states in previous reports. Experimentally, we verify the emergence of octopole orbital corner states in the terahertz frequency range by designing spoof plasmonic crystals with a 2D SSH lattice. Through terahertz time-domain spectroscopy, these corner states are directly observed via spatial mapping of the electric field intensity. We suggest that these results shed light on the unique physics of the interplay between topological phases and higher-order orbitals and broaden the potential application opportunities of plasmonic crystals in particle trapping and biosensing.