Compact Photonic Topological Devices via Wrapped Edge-State Architectures ​​​​​​

Photonic topological insulators have primarily been engineered to exploit their robust boundary states that guide light along the interfaces between topologically distinct regions. However, such designs utilize only a small fraction of the photonic topological insulator, as the topologically protected edge mode propagates only along the topological interface, which a along the lattice perimeter, while the bulk remains unused covering the whole lattice. Here, we propose a new lattice design that maximizes the use of these topological edge states by wrapping the system’s boundary into a snake comb-like geometry with thin rectangular leg. This configuration makes the topological edge state to propagate over a greater lattice area, resulting in the lattice area being used by edge  state. Such design relies on avoiding couplings between the counter-propagating topological modes localized on the opposite boundaries of the legs. During the optimization process, the geometry naturally becomes non-crystalline, requiring real-space characterization of the topology. We employ the spectral localizer framework to quantify the local topology in this regime, where conventional band-based methods fail. This approach opens new directions for compact and efficient nanophotonic devices leveraging topological robustness across the full lattice area.