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Structural disorder can improve the optical properties of metasurfaces,whether it is emerging from some large-scale fabrication methods, or explicitlydesigned and built lithographically. Correlated disorder, induced by a minimuminter-nanostructure distance or by hyperuniformity properties, is particularlybeneficial in some applications such as light extraction. We introducenumerical descriptors inspired from topology to provide quantitative measuresof disorder whose universal properties make them suitable for both uncorrelatedand correlated disorder, where statistical descriptors are less accurate. Weprove theoretically and experimentally the accuracy of these topologicaldescriptors of disorder by using them to design plasmonic metasurfaces ofcontrolled disorder, that we correlate to the strength of their surface latticeresonances. These tools can be used for the fast and accurate design ofdisordered metasurfaces, or to help tuning large-scale fabrication methods.

Topological learning for the classification of disorder: an application to the design of metasurfaces