Corbino-geometry has well-known applications in physics, as in the design of graphene heterostructures for detecting fractional quantum Hall states or superconducting waveguides for illustrating circuit quantum electrodynamics. Here, we propose and demonstrate a photonic Kagome lattice in the Corbino-geometry that leads to direct observation of non-contractible loop states protected by real-space topology. Such states represent the missing flat-band eigenmodes, manifested as one-dimensional loops winding around a torus, or lines infinitely extending to the entire flat-band lattice. In finite (truncated) Kagome lattices, however, line states cannot preserve as they are no longer the eigenmodes, in sharp contrast to the case of Lieb lattices. Using a continuous-wave laser writing technique, we experimentally establish finite Kagome lattices with desired cutting edges, as well as in the Corbino-geometry to eliminate edge effects. We thereby observe, for the first time to our knowledge, the robust boundary modes exhibiting self-healing properties, and the localized modes along toroidal direction as a direct manifestation of the non-contractible loop states.
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