Single-shot measurement of photonic topological invariant

Topological design enables robustness to be engineered into a system. However, a general challenge remains to experimentally characterize topological properties. In this work, we demonstrate a technique for directly observing a winding-number invariant using a single measurement. By propagating light with a sufficiently broad spectrum along a topological photonic crystal fiber, we calculate the winding number invariant from the output intensity pattern. We quantify the capabilities of this single-shot method, which works even for surprisingly narrow and asymmetric spectral distributions. We demonstrate our approach using topological fiber, but our method is generalizable to other platforms. Our method is experimentally straightforward: we use only a broadband input excitation and a single output to measure the topological invariant.