We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semianalytical model, determining the appropriate real-space topological invariants. We provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the system is reducible to a chirally symmetric limit and the corner modes are protected by this together with lattice symmetries.

We study the topological properties of a Kagome plasmonic metasurface, modeled with a coupled dipole method that naturally includes retarded long range interactions. We demonstrate that the system supports an obstructed atomic limit phase through the calculation of Wilson loops. Then, we characterize the hierarchy of topological boundary modes hosted by the subwavelength array of plasmonic nanoparticles: both one-dimensional edge modes and zero-dimensional corner modes. We determine the properties of these modes, which robustly confine light at subwavelength scales, calculate the local density of photonic states at edge and corner modes frequencies, and demonstrate the selective excitation of delocalized corner modes in a topological cavity, through nonzero orbital angular momentum beam excitation.

Coupled light‐matter modes supported by plasmonic metasurfaces can be combined with topological principles to yield subwavelength topological valley states of light. This study gives a systematic presentation of the topological valley states available for lattices of metallic nanoparticles (NPs): all possible lattices with hexagonal symmetry are considered as well as valley states emerging on a square lattice. Several unique effects that have yet to be explored in plasmonics are identified, such as robust guiding, filtering, and splitting of modes, as well as dual‐band effects. These are demonstrated by means of scattering computations based on the coupled dipole method that encompass full electromagnetic interactions between NPs.

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

We study a plasmonic metasurface that supports pseudospin dependent edge states confined at a subwavelength scale, considering full electrodynamic interactions including retardation and radiative effects. The spatial symmetry of the lattice of plasmonic nanoparticles gives rise to edge states with properties reminiscent of the quantum spin Hall effect in topological insulators. However, unlike the spin-momentum locking characteristic of topological insulators, these modes are not purely unidirectional and their propagation properties can be understood by analysing the spin angular momentum of the electromagnetic field, which is inhomogenous in the plane of the lattice. The local sign of the spin angular momentum determines the propagation direction of the mode under a near-field excitation source. We also study the optical response under far-field excitation and discuss in detail the effects of radiation and retardation.