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Corbino-geometry has well-known applications in physics, as in the design ofgraphene heterostructures for detecting fractional quantum Hall states orsuperconducting waveguides for illustrating circuit quantum electrodynamics.Here, we propose and demonstrate a photonic Kagome lattice in theCorbino-geometry that leads to direct observation of non-contractible loopstates protected by real-space topology. Such states represent the "missing"flat-band eigenmodes, manifested as one-dimensional loops winding around atorus, or lines infinitely extending to the entire flat-band lattice. In finite(truncated) Kagome lattices, however, line states cannot preserve as they areno longer the eigenmodes, in sharp contrast to the case of Lieb lattices. Usinga continuous-wave laser writing technique, we experimentally establish finiteKagome lattices with desired cutting edges, as well as in the Corbino-geometryto eliminate edge effects. We thereby observe, for the first time to ourknowledge, the robust boundary modes exhibiting self-healing properties, andthe localized modes along toroidal direction as a direct manifestation of thenon-contractible loop states.

Realization of robust boundary modes and non-contractible loop states in photonic Kagome lattices