Free extension of topological states via double-zero-index media

Topological states, known for their robustness against disorder, offer promising avenues for disorder-resistant devices. However, their intrinsic spatial confinement at interfaces imposes geometric constraints that limit the scalability of topological functionalities. Here, we propose a strategy to overcome this limitation by using double-zero-index media to expand topological interfaces. Although occupying finite space, these media are optically equivalent to infinitesimal points at their working frequencies, effectively altering the geometry of topological interfaces and breaking conventional bulk-edge correspondence. This strategy enables the spatial expansion of uniform topological states beyond their native interface, offering new possibilities for topological photonic devices. Validated by simulations and microwave experiments, our findings offer a universal framework to break the inherent dimensional limitations of topological states, with implications extending to general wave systems.