  Structural disorder can improve the optical properties of metasurfaces,
whether it is emerging from some large-scale fabrication methods, or explicitly
designed and built lithographically. Correlated disorder, induced by a minimum
inter-nanostructure distance or by hyperuniformity properties, is particularly
beneficial in some applications such as light extraction. We introduce
numerical descriptors inspired from topology to provide quantitative measures
of disorder whose universal properties make them suitable for both uncorrelated
and correlated disorder, where statistical descriptors are less accurate. We
prove theoretically and experimentally the accuracy of these topological
descriptors of disorder by using them to design plasmonic metasurfaces of
controlled disorder, that we correlate to the strength of their surface lattice
resonances. These tools can be used for the fast and accurate design of
disordered metasurfaces, or to help tuning large-scale fabrication methods.
